From 59568801248680ab16c465dd95693a83d956e27c Mon Sep 17 00:00:00 2001 From: feng shi Date: Mon, 25 Oct 2021 15:42:20 +0000 Subject: [PATCH 01/13] add price optimization notebook --- .../price_optimization/QUBO-Pricing.ipynb | 12553 ++++++++++++++++ .../qubo_dynamic_pricing.py | 255 + 2 files changed, 12808 insertions(+) create mode 100644 examples/price_optimization/QUBO-Pricing.ipynb create mode 100644 examples/price_optimization/qubo_dynamic_pricing.py diff --git a/examples/price_optimization/QUBO-Pricing.ipynb b/examples/price_optimization/QUBO-Pricing.ipynb new file mode 100644 index 000000000..eaf34d3e2 --- /dev/null +++ b/examples/price_optimization/QUBO-Pricing.ipynb @@ -0,0 +1,12553 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "63297199", + "metadata": {}, + "source": [ + "# Using quantum annealing on Amazon Braket for price optimization\n", + "\n", + "Combinatorial Optimization is one of the most important fields in optimization. Practical applications can be found in virtually every industry. Prominent examples include supply chain optimization in transport and logistics, portfolio management in finance, and the optimization of clinical trials in healthcare, among many others. It is also one of the most active research topics in operation research and computer science. However, many practical combinatorial optimization problems are NP-hard and require massive computation costs to find solution of good quality. \n", + "\n", + "In this blog post, we demonstrate how a quantum annealer on Amazon Braket can be used for price optimization taking into consideration the trade-off between maximizing revenue and minimizing risk. We showcase how to formulate this problem as a quadratic unconstrained binary optimization problem (QUBO) and use D-Wave Systems Inc. Advantage quantum annealer on Amazon Braket to find close-to-optimal solutions. Overall, this blog demonstrates that customers can easily leverage quantum computing through Amazon Braket to solve difficult combinatorial optimization challenges in their daily decision-making process." + ] + }, + { + "cell_type": "markdown", + "id": "3d96a889", + "metadata": {}, + "source": [ + "# Table of content\n", + "### 1. Demand model\n", + " 1. Create demand dataset\n", + " 2. Fit demand model through linear regression\n", + "### 2. Price optimisation with QUBO\n", + " 1. Construct revenue objective\n", + " 2. Add penalty for prediction uncertainty\n", + " 3. Add equality constraints\n", + "### 3. Solve QUBO with Amazon Braket\n", + " 1. Evaluate results\n", + "### 4. Trade-off between revenue expectation and prediction uncertainty\n", + "### 5. Conclusion\n", + "### 6. Literature review\n", + "-----------------" + ] + }, + { + "cell_type": "markdown", + "id": "cbe832a9", + "metadata": {}, + "source": [ + "We start by importing important libraries related to Amazon braket and" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "d5ea8de1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Requirement already satisfied: sklearn in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (0.0)\n", + "Requirement already satisfied: scikit-learn in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from sklearn) (1.0.1)\n", + "Requirement already satisfied: threadpoolctl>=2.0.0 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (3.0.0)\n", + "Requirement already satisfied: scipy>=1.1.0 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.5.2)\n", + "Requirement already satisfied: numpy>=1.14.6 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.19.2)\n", + "Requirement already satisfied: joblib>=0.11 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.1.0)\n" + ] + } + ], + "source": [ + "!pip install sklearn" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "a76144e6", + "metadata": {}, + "outputs": [], + "source": [ + "from braket.aws import AwsDevice\n", + "from braket.ocean_plugin import BraketSampler, BraketDWaveSampler\n", + "\n", + "import matplotlib.pyplot as plt\n", + "# magic word for producing visualizations in notebook\n", + "%matplotlib inline\n", + "import time\n", + "from collections import defaultdict\n", + "from itertools import combinations\n", + "import math\n", + "import networkx as nx\n", + "import dwave_networkx as dnx\n", + "import minorminer\n", + "import dimod\n", + "from dimod.binary_quadratic_model import BinaryQuadraticModel\n", + "from dwave.system.composites import EmbeddingComposite\n", + "import numpy as np\n", + "\n", + "np.random.seed(0)" + ] + }, + { + "cell_type": "markdown", + "id": "b6eb73b1", + "metadata": {}, + "source": [ + "# 1. Demand model" + ] + }, + { + "cell_type": "markdown", + "id": "7e4472cd", + "metadata": {}, + "source": [ + "The usual goal of price optimization is to maximize the revenue in the next certain period, where the revenue can usually be represented by a function of demand and price: \n", + "\n", + "$$R=\\sum_{t=T}^{T+n-1}d_tp_t$$\n", + "\n", + "where $p_t$ and $d_t$ are the price and demand at day $t$.\n", + "\n", + "In order to do price optimization, we need to create a demand model to estimate demand by a function of price: $d_t=f(\\mathbf{p}_t)$, where $\\mathbf{p}$ is a vector of latest prices. In such a way, the revenue objective can be transformed as a function soly depending on price to do optimization $R=\\sum_{t=T}^{T+n-1}f(\\mathbf{p_t})p_t$ " + ] + }, + { + "cell_type": "markdown", + "id": "50714538", + "metadata": {}, + "source": [ + "## 1.1 Create training dataset" + ] + }, + { + "cell_type": "markdown", + "id": "f0d07a51", + "metadata": {}, + "source": [ + "For simplicity, we create a dummy dataset on historical demand and price observations so that a demand estimation model can be trained. \n", + "\n", + "Here we assume the true demand at day $d_t$ follows a linear model of the latest $n$ days' prices $p_i, i\\in [t-n+1, t-n+2, \\ldots, t]$ plus a noise following normal distribution $\\varepsilon\\sim N(0,\\sigma) $.\n", + "\n", + "Thus the demand at day $t$ would be\n", + "$$d_t = \\sum_{i=t-n+1}^{t}a_{i+n-1-t}p_{i} + b + \\varepsilon $$\n", + "where $a_j, j\\in [0, 1, \\ldots, n-1]$ is the elasiticity between the price at day $j+t-n+1$ and demand at day $t$, and\n", + "$b$ is the constant.\n", + "\n", + "We use these assumptions to create our dummy training dataset." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "846bf53a", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "dataset x:\n", + "[[ 8 10 10 ... 8 10 8]\n", + " [10 10 8 ... 10 8 13]\n", + " [10 8 8 ... 8 13 19]\n", + " ...\n", + " [16 5 10 ... 5 8 10]\n", + " [ 5 10 8 ... 8 10 5]\n", + " [10 8 5 ... 10 5 13]]\n", + "dataset y:\n", + "[176.60983362005817, 166.3135122384355, 122.40886555130055, 139.82753849065216, 136.5494478345374, 139.08672451958816, 171.1141344886614, 149.02456906069798, 153.67576697932017, 185.92865845385478, 218.8935596207448, 199.31303748275712, 191.1192719273116, 149.78503274416957, 132.3689836892222, 128.7844958138008, 143.7904523833443, 153.22628621708824, 163.40219274496187, 178.68599188442033, 188.22129139574835, 169.9991590571518, 162.82599073098172, 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139.11153396241502, 160.86763971934738, 150.8376603505646, 144.1658318016542, 156.6925504591095, 174.24179748499725, 154.1849473059578, 197.3900634281876, 196.44181264703545, 202.7832190240412, 205.6429091413778, 208.89812020628023, 193.14033517959047, 203.0088567910412, 169.6034276346709, 162.2283538460438, 164.07746828269188, 180.43213553233696, 207.5734208909289, 206.11331017346728, 196.27212504403425, 192.8472433886354, 198.01213990808535]\n" + ] + } + ], + "source": [ + "a0=[-0.3, -0.5, -1.0, -2.0, -3.0, -3.3, -3.5] # elasticities in linear demand model\n", + "b0=300 # constants in the linear demand model \n", + "sigma=10. # the standard deviation of the noise\n", + "price_levels=[5, 8, 10, 12, 13, 16, 19] # the option of price at each day\n", + "probabilities=[0.3, 0.3, 0.2, 0.05, 0.05, 0.05, 0.05] # the probabilities of taking a price choice at a day\n", + "n_samples=1000 # the number of sample we want to create\n", + "\n", + "def create_data_point(p, a, b, sigma):\n", + " \"\"\"\n", + " estimate the demand\n", + " :param p: np.array, (T,)\n", + " :param a: np.array, (T,)\n", + " :param b: float, the constants\n", + " :return: v\n", + " \"\"\"\n", + " v = np.dot(p,a) + b + np.random.normal(loc=0.0, scale=sigma)\n", + " return v\n", + "\n", + "def create_dataset(a, b, N, price_levels, probabilities, sigma):\n", + " \"\"\"\n", + " create a dataset for training the demand model\n", + " :param a: np.array, (T,)\n", + " :param b: float\n", + " :param N: int number of samples\n", + " :param price_levels: list, price levels\n", + " :param probabilities: list, probabilities distribution of the prices\n", + " :return:\n", + " \"\"\"\n", + " t = len(a)\n", + " prices = np.random.choice(price_levels, N+t-1, p=probabilities)\n", + " data_x = []\n", + " data_y = []\n", + " for i in range(N):\n", + " p = prices[i:i+t]\n", + " v = create_data_point(p, a, b, sigma)\n", + " data_x.append(\n", + " np.expand_dims(p, axis=0)\n", + " )\n", + " data_y.append(v)\n", + "\n", + " data_x = np.concatenate(data_x,axis=0)\n", + " return data_x, data_y\n", + "\n", + "data_x, data_y = create_dataset(a0, b0, n_samples, price_levels, probabilities, sigma)\n", + "print(\"dataset x:\")\n", + "print(data_x)\n", + "print(\"dataset y:\")\n", + "print(data_y)" + ] + }, + { + "cell_type": "markdown", + "id": "7d08dd0c", + "metadata": {}, + "source": [ + "## 1.2. Fit the demand model" + ] + }, + { + "cell_type": "markdown", + "id": "34981246", + "metadata": {}, + "source": [ + "By using the created training dataset, we simply using sklearn to fit a linear demand model. This fitted linear demand model will be used for the following price optimization problem. We round the model coefficents to integer for simplicity to fit with the below QUBO format (quadratic unconstrained binary optimization). " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "552b9579", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "fitted elasticities: [-0.3779074420638822, -0.5723441150118157, -0.8832936349398142, -2.044653528191526, -2.9861902495686956, -3.2337479564086022, -3.6095730899274248]\n", + "fitted constant: 301.2623906306577\n" + ] + } + ], + "source": [ + "from sklearn.linear_model import LinearRegression\n", + "def linear_regression(data_x, data_y):\n", + " reg = LinearRegression().fit(data_x, data_y)\n", + " a = reg.coef_\n", + " b = reg.intercept_\n", + " return a, b\n", + "\n", + "\n", + "a, b = linear_regression(data_x, data_y)\n", + "a = [i for i in a]\n", + "b = b\n", + "\n", + "print(f'fitted elasticities: {a}')\n", + "print(f'fitted constant: {b}')" + ] + }, + { + "cell_type": "markdown", + "id": "22311927", + "metadata": {}, + "source": [ + "# 2. Price optimization with QUBO" + ] + }, + { + "cell_type": "markdown", + "id": "26841444", + "metadata": {}, + "source": [ + "In this blog, we leverage a general-purpose mathematical framework: Quadratic Unconstrained Binary Optimization (QUBO), which has been recently proposed as an effective framework that is able to generalize across a large variety of combinatorial optimization use cases in industries [2, 3]. We take this price optimization as an example and showcase how to formulate it into QUBO framework considering prediction uncertainties as well as equality constraints." + ] + }, + { + "cell_type": "markdown", + "id": "4fa6625c", + "metadata": {}, + "source": [ + "The formal definition of QUBO is expressed as an optimization problem, Minimize:\n", + "$$H=x^TQx$$" + ] + }, + { + "cell_type": "markdown", + "id": "0305adc8", + "metadata": {}, + "source": [ + "Where $x$ is a vector of binary variables representing the decision variables of the combinatorial optimization. $Q$ is a squared matrix of constants inherently encoding the context and constraints of the optimization problems. $Q$ is commonly assumed to be symmetric or upper triangular without loss of generality. The goal is to find the optimal values of the binary decision variables $x$ that minimize the objective $H$.\n", + "\n", + "As shown above, the format of QUBO is strikingly simple, providing a general-purpose framework for a large class of combinatorial optimization problems. Below we show how to transform the objective function together with the constraints into this QUBO format. " + ] + }, + { + "cell_type": "markdown", + "id": "201247df", + "metadata": {}, + "source": [ + "## 2.1 Construct objective function" + ] + }, + { + "cell_type": "markdown", + "id": "e6e63f90", + "metadata": {}, + "source": [ + "Assuming tomorrow is day $T$, then the goal of our price optimization is to find the optimal prices $p_t, t\\in[T, T+1, \\ldots, T+n-1]$ in the next $n$ days in order to maximize the revenue in next $n$ days. Based on the demand model we showed above where the demand at a day is correlated with the latest $n$ days' price, we can construct objective function as below:\n", + "\n", + "$maximize$ $R=\\sum_{t=T}^{T+n-1}d_tp_t$\n", + "\n", + "where $d_t$ is represented by our fitted model above: $d_t = \\sum_{i=t-n+1}^{t}a_{i+n-1-t}p_{i} + b $\n", + "\n", + "Therefore, we need at least the most recent n day's historical prices. Here we random choose a historical range of $n$ days' prices as the most recent price data. " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "ecd62532", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[10, 8, 8, 5, 5, 8, 8]" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p_data = data_x[np.random.randint(0,n_samples)].tolist()\n", + "p_data" + ] + }, + { + "cell_type": "markdown", + "id": "ffb31756", + "metadata": {}, + "source": [ + "Now, let's construct the objective function which is the total revenue $R$ in the next $n$ days.\n", + "\n", + "First, we need to define the price variable $p_t$. Since the price at each day only has a set of fixed $m$ options $c_k, k \\in [0, 1, \\ldots, m-1]$, we can represent the price $p_t$ at day $t$ as: $$p_t=\\sum_{k=0}^{m-1}c_{k}x_{t,k}, \\;subject\\;to \\sum_{k=0}^{m-1}x_{t,k}=1$$ \n", + "\n", + "where $x_{t,k}$ is a binary variable with $1$ meaning the price at day $t$ takes option $c_k$, and $0$ meaning otherwise. Therefore, we can use binary variables $x_{t,k}$ to represent the price variables $p_t$." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "74e05aef", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[10,\n", + " 8,\n", + " 8,\n", + " 5,\n", + " 5,\n", + " 8,\n", + " 8,\n", + " (Binary(X_006)*Num(19.000000)+Binary(X_005)*Num(16.000000)+Binary(X_004)*Num(13.000000)+Binary(X_003)*Num(12.000000)+Binary(X_002)*Num(10.000000)+Binary(X_000)*Num(5.000000)+Binary(X_001)*Num(8.000000)),\n", + " (Binary(X_013)*Num(19.000000)+Binary(X_012)*Num(16.000000)+Binary(X_011)*Num(13.000000)+Binary(X_010)*Num(12.000000)+Binary(X_009)*Num(10.000000)+Binary(X_007)*Num(5.000000)+Binary(X_008)*Num(8.000000)),\n", + " (Binary(X_020)*Num(19.000000)+Binary(X_019)*Num(16.000000)+Binary(X_018)*Num(13.000000)+Binary(X_017)*Num(12.000000)+Binary(X_016)*Num(10.000000)+Binary(X_014)*Num(5.000000)+Binary(X_015)*Num(8.000000)),\n", + " (Binary(X_027)*Num(19.000000)+Binary(X_026)*Num(16.000000)+Binary(X_025)*Num(13.000000)+Binary(X_024)*Num(12.000000)+Binary(X_023)*Num(10.000000)+Binary(X_021)*Num(5.000000)+Binary(X_022)*Num(8.000000)),\n", + " (Binary(X_034)*Num(19.000000)+Binary(X_033)*Num(16.000000)+Binary(X_032)*Num(13.000000)+Binary(X_031)*Num(12.000000)+Binary(X_030)*Num(10.000000)+Binary(X_028)*Num(5.000000)+Binary(X_029)*Num(8.000000)),\n", + " (Binary(X_041)*Num(19.000000)+Binary(X_040)*Num(16.000000)+Binary(X_039)*Num(13.000000)+Binary(X_038)*Num(12.000000)+Binary(X_037)*Num(10.000000)+Binary(X_035)*Num(5.000000)+Binary(X_036)*Num(8.000000)),\n", + " (Binary(X_048)*Num(19.000000)+Binary(X_047)*Num(16.000000)+Binary(X_046)*Num(13.000000)+Binary(X_045)*Num(12.000000)+Binary(X_044)*Num(10.000000)+Binary(X_042)*Num(5.000000)+Binary(X_043)*Num(8.000000))]" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from pyqubo import Binary\n", + "t = len(a) # next number of days to optimize\n", + "n_level = len(price_levels) # number of price options\n", + "\n", + "x = []\n", + "p = []\n", + "# get p\n", + "for i in range(t):\n", + " p_i = 0\n", + " for j in range(n_level):\n", + " x_ij = Binary(f\"X_{i*n_level+j:03d}\")\n", + " x.append(x_ij)\n", + " p_i += x_ij*price_levels[j]\n", + " p.append(p_i)\n", + "# plus historical prices\n", + "all_p = p_data + p\n", + "all_p" + ] + }, + { + "cell_type": "markdown", + "id": "1d79c0d2", + "metadata": {}, + "source": [ + "Next, we can input the price variables into our fitted model to estimate the demand, and then use the demand together with price to represent revenue $R$." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "df83ba8c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Revenue:\n", + "(((Binary(X_048)*Num(19.000000)+Binary(X_047)*Num(16.000000)+Binary(X_046)*Num(13.000000)+Binary(X_045)*Num(12.000000)+Binary(X_044)*Num(10.000000)+Binary(X_042)*Num(5.000000)+Binary(X_043)*Num(8.000000))*Num(-3.609573)+(Binary(X_041)*Num(19.000000)+Binary(X_040)*Num(16.000000)+Binary(X_039)*Num(13.000000)+Binary(X_038)*Num(12.000000)+Binary(X_037)*Num(10.000000)+Binary(X_035)*Num(5.000000)+Binary(X_036)*Num(8.000000))*Num(-3.233748)+(Binary(X_034)*Num(19.000000)+Binary(X_033)*Num(16.000000)+Binary(X_032)*Num(13.000000)+Binary(X_031)*Num(12.000000)+Binary(X_030)*Num(10.000000)+Binary(X_028)*Num(5.000000)+Binary(X_029)*Num(8.000000))*Num(-2.986190)+(Binary(X_027)*Num(19.000000)+Binary(X_026)*Num(16.000000)+Binary(X_025)*Num(13.000000)+Binary(X_024)*Num(12.000000)+Binary(X_023)*Num(10.000000)+Binary(X_021)*Num(5.000000)+Binary(X_022)*Num(8.000000))*Num(-2.044654)+(Binary(X_020)*Num(19.000000)+Binary(X_019)*Num(16.000000)+Binary(X_018)*Num(13.000000)+Binary(X_017)*Num(12.000000)+Binary(X_016)*Num(10.000000)+Binary(X_014)*Num(5.000000)+Binary(X_015)*Num(8.000000))*Num(-0.883294)+(Binary(X_013)*Num(19.000000)+Binary(X_012)*Num(16.000000)+Binary(X_011)*Num(13.000000)+Binary(X_010)*Num(12.000000)+Binary(X_009)*Num(10.000000)+Binary(X_007)*Num(5.000000)+Binary(X_008)*Num(8.000000))*Num(-0.572344)+(Binary(X_006)*Num(19.000000)+Binary(X_005)*Num(16.000000)+Binary(X_004)*Num(13.000000)+Binary(X_003)*Num(12.000000)+Binary(X_002)*Num(10.000000)+Binary(X_000)*Num(5.000000)+Binary(X_001)*Num(8.000000))*Num(-0.377907)+Num(301.262391))*(Binary(X_048)*Num(19.000000)+Binary(X_047)*Num(16.000000)+Binary(X_046)*Num(13.000000)+Binary(X_045)*Num(12.000000)+Binary(X_044)*Num(10.000000)+Binary(X_042)*Num(5.000000)+Binary(X_043)*Num(8.000000))+((Binary(X_041)*Num(19.000000)+Binary(X_040)*Num(16.000000)+Binary(X_039)*Num(13.000000)+Binary(X_038)*Num(12.000000)+Binary(X_037)*Num(10.000000)+Binary(X_035)*Num(5.000000)+Binary(X_036)*Num(8.000000))*Num(-3.609573)+(Binary(X_034)*Num(19.000000)+Binary(X_033)*Num(16.000000)+Binary(X_032)*Num(13.000000)+Binary(X_031)*Num(12.000000)+Binary(X_030)*Num(10.000000)+Binary(X_028)*Num(5.000000)+Binary(X_029)*Num(8.000000))*Num(-3.233748)+(Binary(X_027)*Num(19.000000)+Binary(X_026)*Num(16.000000)+Binary(X_025)*Num(13.000000)+Binary(X_024)*Num(12.000000)+Binary(X_023)*Num(10.000000)+Binary(X_021)*Num(5.000000)+Binary(X_022)*Num(8.000000))*Num(-2.986190)+(Binary(X_020)*Num(19.000000)+Binary(X_019)*Num(16.000000)+Binary(X_018)*Num(13.000000)+Binary(X_017)*Num(12.000000)+Binary(X_016)*Num(10.000000)+Binary(X_014)*Num(5.000000)+Binary(X_015)*Num(8.000000))*Num(-2.044654)+(Binary(X_013)*Num(19.000000)+Binary(X_012)*Num(16.000000)+Binary(X_011)*Num(13.000000)+Binary(X_010)*Num(12.000000)+Binary(X_009)*Num(10.000000)+Binary(X_007)*Num(5.000000)+Binary(X_008)*Num(8.000000))*Num(-0.883294)+(Binary(X_006)*Num(19.000000)+Binary(X_005)*Num(16.000000)+Binary(X_004)*Num(13.000000)+Binary(X_003)*Num(12.000000)+Binary(X_002)*Num(10.000000)+Binary(X_000)*Num(5.000000)+Binary(X_001)*Num(8.000000))*Num(-0.572344)+Num(298.239131))*(Binary(X_041)*Num(19.000000)+Binary(X_040)*Num(16.000000)+Binary(X_039)*Num(13.000000)+Binary(X_038)*Num(12.000000)+Binary(X_037)*Num(10.000000)+Binary(X_035)*Num(5.000000)+Binary(X_036)*Num(8.000000))+((Binary(X_034)*Num(19.000000)+Binary(X_033)*Num(16.000000)+Binary(X_032)*Num(13.000000)+Binary(X_031)*Num(12.000000)+Binary(X_030)*Num(10.000000)+Binary(X_028)*Num(5.000000)+Binary(X_029)*Num(8.000000))*Num(-3.609573)+(Binary(X_027)*Num(19.000000)+Binary(X_026)*Num(16.000000)+Binary(X_025)*Num(13.000000)+Binary(X_024)*Num(12.000000)+Binary(X_023)*Num(10.000000)+Binary(X_021)*Num(5.000000)+Binary(X_022)*Num(8.000000))*Num(-3.233748)+(Binary(X_020)*Num(19.000000)+Binary(X_019)*Num(16.000000)+Binary(X_018)*Num(13.000000)+Binary(X_017)*Num(12.000000)+Binary(X_016)*Num(10.000000)+Binary(X_014)*Num(5.000000)+Binary(X_015)*Num(8.000000))*Num(-2.986190)+(Binary(X_013)*Num(19.000000)+Binary(X_012)*Num(16.000000)+Binary(X_011)*Num(13.000000)+Binary(X_010)*Num(12.000000)+Binary(X_009)*Num(10.000000)+Binary(X_007)*Num(5.000000)+Binary(X_008)*Num(8.000000))*Num(-2.044654)+(Binary(X_006)*Num(19.000000)+Binary(X_005)*Num(16.000000)+Binary(X_004)*Num(13.000000)+Binary(X_003)*Num(12.000000)+Binary(X_002)*Num(10.000000)+Binary(X_000)*Num(5.000000)+Binary(X_001)*Num(8.000000))*Num(-0.883294)+Num(293.660378))*(Binary(X_034)*Num(19.000000)+Binary(X_033)*Num(16.000000)+Binary(X_032)*Num(13.000000)+Binary(X_031)*Num(12.000000)+Binary(X_030)*Num(10.000000)+Binary(X_028)*Num(5.000000)+Binary(X_029)*Num(8.000000))+((Binary(X_027)*Num(19.000000)+Binary(X_026)*Num(16.000000)+Binary(X_025)*Num(13.000000)+Binary(X_024)*Num(12.000000)+Binary(X_023)*Num(10.000000)+Binary(X_021)*Num(5.000000)+Binary(X_022)*Num(8.000000))*Num(-3.609573)+(Binary(X_020)*Num(19.000000)+Binary(X_019)*Num(16.000000)+Binary(X_018)*Num(13.000000)+Binary(X_017)*Num(12.000000)+Binary(X_016)*Num(10.000000)+Binary(X_014)*Num(5.000000)+Binary(X_015)*Num(8.000000))*Num(-3.233748)+(Binary(X_013)*Num(19.000000)+Binary(X_012)*Num(16.000000)+Binary(X_011)*Num(13.000000)+Binary(X_010)*Num(12.000000)+Binary(X_009)*Num(10.000000)+Binary(X_007)*Num(5.000000)+Binary(X_008)*Num(8.000000))*Num(-2.986190)+(Binary(X_006)*Num(19.000000)+Binary(X_005)*Num(16.000000)+Binary(X_004)*Num(13.000000)+Binary(X_003)*Num(12.000000)+Binary(X_002)*Num(10.000000)+Binary(X_000)*Num(5.000000)+Binary(X_001)*Num(8.000000))*Num(-2.044654)+Num(287.727751))*(Binary(X_027)*Num(19.000000)+Binary(X_026)*Num(16.000000)+Binary(X_025)*Num(13.000000)+Binary(X_024)*Num(12.000000)+Binary(X_023)*Num(10.000000)+Binary(X_021)*Num(5.000000)+Binary(X_022)*Num(8.000000))+((Binary(X_020)*Num(19.000000)+Binary(X_019)*Num(16.000000)+Binary(X_018)*Num(13.000000)+Binary(X_017)*Num(12.000000)+Binary(X_016)*Num(10.000000)+Binary(X_014)*Num(5.000000)+Binary(X_015)*Num(8.000000))*Num(-3.609573)+(Binary(X_013)*Num(19.000000)+Binary(X_012)*Num(16.000000)+Binary(X_011)*Num(13.000000)+Binary(X_010)*Num(12.000000)+Binary(X_009)*Num(10.000000)+Binary(X_007)*Num(5.000000)+Binary(X_008)*Num(8.000000))*Num(-3.233748)+(Binary(X_006)*Num(19.000000)+Binary(X_005)*Num(16.000000)+Binary(X_004)*Num(13.000000)+Binary(X_003)*Num(12.000000)+Binary(X_002)*Num(10.000000)+Binary(X_000)*Num(5.000000)+Binary(X_001)*Num(8.000000))*Num(-2.986190)+Num(273.087556))*(Binary(X_020)*Num(19.000000)+Binary(X_019)*Num(16.000000)+Binary(X_018)*Num(13.000000)+Binary(X_017)*Num(12.000000)+Binary(X_016)*Num(10.000000)+Binary(X_014)*Num(5.000000)+Binary(X_015)*Num(8.000000))+((Binary(X_006)*Num(19.000000)+Binary(X_005)*Num(16.000000)+Binary(X_004)*Num(13.000000)+Binary(X_003)*Num(12.000000)+Binary(X_002)*Num(10.000000)+Binary(X_000)*Num(5.000000)+Binary(X_001)*Num(8.000000))*Num(-3.609573)+Num(229.261137))*(Binary(X_006)*Num(19.000000)+Binary(X_005)*Num(16.000000)+Binary(X_004)*Num(13.000000)+Binary(X_003)*Num(12.000000)+Binary(X_002)*Num(10.000000)+Binary(X_000)*Num(5.000000)+Binary(X_001)*Num(8.000000))+((Binary(X_013)*Num(19.000000)+Binary(X_012)*Num(16.000000)+Binary(X_011)*Num(13.000000)+Binary(X_010)*Num(12.000000)+Binary(X_009)*Num(10.000000)+Binary(X_007)*Num(5.000000)+Binary(X_008)*Num(8.000000))*Num(-3.609573)+(Binary(X_006)*Num(19.000000)+Binary(X_005)*Num(16.000000)+Binary(X_004)*Num(13.000000)+Binary(X_003)*Num(12.000000)+Binary(X_002)*Num(10.000000)+Binary(X_000)*Num(5.000000)+Binary(X_001)*Num(8.000000))*Num(-3.233748)+Num(250.714192))*(Binary(X_013)*Num(19.000000)+Binary(X_012)*Num(16.000000)+Binary(X_011)*Num(13.000000)+Binary(X_010)*Num(12.000000)+Binary(X_009)*Num(10.000000)+Binary(X_007)*Num(5.000000)+Binary(X_008)*Num(8.000000)))\n" + ] + } + ], + "source": [ + "def get_demand(coeff, b, prices):\n", + " assert len(coeff) == len(prices)\n", + " d = b\n", + " for i in range(len(coeff)):\n", + " d += coeff[i]*prices[i]\n", + "\n", + " return d\n", + "\n", + "# get d, rev\n", + "def get_demands_rev(a,b,hist_p, p):\n", + " all_p = hist_p + p\n", + " t = len(a)\n", + " d = []\n", + " rev = 0\n", + " for i in range(t):\n", + " d_i = get_demand(\n", + " coeff=a,\n", + " b=b,\n", + " prices=all_p[i+1:i+1+t]\n", + " )\n", + " #print(f'Demand at T+{i}:')\n", + " #print(d_i,'\\n')\n", + " d.append(d_i)\n", + " rev += d_i * p[i]\n", + " return d, rev\n", + "\n", + "d, rev = get_demands_rev(a,b,p_data, p)\n", + "print('Revenue:')\n", + "print(rev)" + ] + }, + { + "cell_type": "markdown", + "id": "c6aa7c69", + "metadata": {}, + "source": [ + "## 2.2 Add penalty for prediction uncertainty" + ] + }, + { + "cell_type": "markdown", + "id": "6f65701b", + "metadata": {}, + "source": [ + "In optimisation, we usually desire to reduce the risk while maximizing the reward, which means we want to reduce the estimated uncertainty/variance of the predicted demands. Therefore, we add a penalty term in the objective function to represent the uncertainty of the predicted demand. The uncertainty of the predicted demand $d_t$ can be represented by its estimated variance.\n", + "\n", + "$$H=Revenue-\\beta\\sum_{t=T}^{T+n-1}var(d_t)$$\n", + "\n", + "Where $\\beta$ is the regularized parameters to control the effect of risk esitmation. The variance of the demand predictions can be estimated as: $$var(d_t)=\\sigma^2(1+\\vec{p}_t'(\\vec{X}'\\vec{X})^{-1}\\vec{p}_t)$$\n", + "\n", + "where $\\vec{p}_t'=[1, p_{t-n+1},p_{t-n+2}, \\ldots,p_{t}]$ is the price vector to estimate demand $d_t$. $\\vec{X}$ are the observations in the training dataset used to fit the demand model, where each row is an observation in the training set.\n", + "\n", + "$$\\vec{X} = \\left[\n", + " \\begin{matrix}\n", + " 1 & p_{0,1} & p_{1,1} & \\dots & p_{n-1,1}\\\\\n", + " 1 & p_{0,2} & p_{1,2} & \\dots & p_{n-1,2}\\\\\n", + " \\vdots& \\vdots& \\vdots&& \\vdots\\\\\n", + " 1 & p_{0,N}& p_{1,N}& \\dots& p_{n-1,N}\n", + " \\end{matrix}\\right].$$" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "e5b620b2", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + 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+ ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "beta=1.\n", + "def get_variance(data_x, p, sigma):\n", + " \"\"\"\n", + " :param data_x (np.array): [n_samples, n_days]\n", + " :param p (list): [n_days]\n", + " :return: variance\n", + " \"\"\"\n", + " n_samples, t = data_x.shape\n", + " ones = np.ones((n_samples, 1), dtype=np.float)\n", + " x_mat = np.concatenate([ones, data_x], axis=1) # [n_samples, n_days+1]\n", + " x_mat = np.linalg.inv(\n", + " np.dot(x_mat.T, x_mat)\n", + " )\n", + " p = np.array([1.]+p)\n", + " variance = (sigma**2) * (1. + p.dot(x_mat).dot(p))\n", + " return variance\n", + "\n", + "def get_overall_variance(data_x, hist_p, p, sigma):\n", + " all_p = hist_p + p\n", + " t = len(p)\n", + " var = 0\n", + " for i in range(t):\n", + " var += get_variance(data_x, all_p[i+1:i+1+t], sigma)\n", + "\n", + " return var\n", + "\n", + "objective = rev - beta * get_overall_variance(data_x, p_data, p, sigma)\n", + "objective" + ] + }, + { + "cell_type": "markdown", + "id": "8d1518cb", + "metadata": {}, + "source": [ + "## 2.3 Add penalty for equality constraints" + ] + }, + { + "cell_type": "markdown", + "id": "5d26aea8", + "metadata": {}, + "source": [ + "As we mentioned above that price can only take one option per day, this means that one and only one of the binary variables in a day must be $1$ and others must be $0$. Formallly, we have equality constraints:\n", + "$$\\sum_{k=0}^{m-1}x_{t,k}=1, \\;t\\in[T, T+1, \\cdots, T+n-1]$$\n", + "\n", + "We can easily incorporate this equality constraint into the objective function by substracting a penalty term $H_p$ with large enough coefficients $L_p$. If the solution satisfies these constraints, the penalty term will be 0, otherwise a large penalty will be imposed.\n", + "\n", + "$$H_p=L_p\\sum_{t=T}^{t=T+n-1}[(\\sum_{k=0}^{m-1}x_{t,k})-1]^{2}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "1ac811e9", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + 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+ ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# add equalty constraints\n", + "Lp=1e13\n", + "for i in range(t):\n", + " penalty = x[i*n_level]\n", + " for j in range(1, n_level):\n", + " penalty += x[i*n_level+j]\n", + " penalty = ((penalty-1)**2)*Lp\n", + " objective -= penalty\n", + "objective" + ] + }, + { + "cell_type": "markdown", + "id": "b961659b", + "metadata": {}, + "source": [ + "# 3. Solve QUBO with Braket" + ] + }, + { + "cell_type": "markdown", + "id": "97fe4b9b", + "metadata": {}, + "source": [ + "Now we have transformed to the total objective function which:\n", + "- maximizes the revenue \n", + "- minimizes the prediction uncertainty \n", + "- incorporates equality constraints, $\\sum_{k=0}^{m-1}x_{t,k}=1, \\;t\\in[T, T+1, \\cdots, T+n-1]$ \n", + "\n", + "$$H=Revenue-\\beta\\sum_{t=T}^{T+n-1}var(d_t) - H_p $$\n", + "where $H_p=L_p\\sum_{t=T}^{t=T+n-1}[(\\sum_{k=0}^{m-1}x_{t,k})-1]^{2} $ is the penalty term for price equality constraints, and $L_p$ is a constant.\n", + "\n", + "We can transform this objective function to binary quadratic model, and solve it using Amazon Braket." + ] + }, + { + "cell_type": "markdown", + "id": "836ade85", + "metadata": {}, + "source": [ + "Amazon Braket provides access to quantum annealers from D-Wave Systems Inc. which are specifically designed to solve QUBO problems. A quantum annealer is a hardware implementation of Quantum Annealing (QA) which is a generic algorithm to solve combinatorial optimization problems by taking advantage of quantum fluctuations to escape local minima in complex energy landscapes by effect of tunnelling through barriers separating local minima [5]. Through a simple Amazon Braket API call, the formatted QUBO problem can be embedded to the hardwired topology of the machine and submitted to machine. In turn, the quantum annealer performs an annealing process and obtains a result. However, because of the sparsity of the underlying chip, one typically faces a certain overhead in embedding the original QUBO problem to the D-Wave hardware, because (typically) one logical binary variable maps onto several physical qubits, in order to effectively distill the connectivity of the original QUBO problem. For more details, we refer to the Amazon Braket tutorial notebook available here (https://github.com/aws/amazon-braket-examples/blob/main/examples/quantum_annealing/Dwave_Anatomy.ipynb)." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "36e0a910", + "metadata": {}, + "outputs": [], + "source": [ + "from braket.aws import AwsDevice\n", + "from braket.ocean_plugin import BraketSampler, BraketDWaveSampler\n", + "\n", + "import matplotlib.pyplot as plt\n", + "# magic word for producing visualizations in notebook\n", + "%matplotlib inline\n", + "import time\n", + "from collections import defaultdict\n", + "from itertools import combinations\n", + "import math\n", + "import networkx as nx\n", + "import dwave_networkx as dnx\n", + "import minorminer\n", + "import dimod\n", + "from dimod.binary_quadratic_model import BinaryQuadraticModel\n", + "from dwave.system.composites import EmbeddingComposite" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": 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Similar to classical simulated annealing, we take several independent shots in order to increase our chances for success in finding a high-quality solution to the QUBO problem. The response contains a number of rows. Each row represents the optimization result of a single shot, including the binary decision variables $[x_T,\\cdots,x_{T+n-1}]$, and corresponding energy which is the negative value of objective function, i.e. $H$. Below we show how to submit a QUBO problem to D-Wave and provide a sample response. Here, the key figure of merit is listed in the column labelled with energy, representing the value for the objective function . We can then easily read off the best bit string found." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "0f7cb64f", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " X_000 X_001 X_002 X_003 X_004 ... 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100000000000898.62 1 ...\n", + "9752 0 1 0 1 1 ... 1 100000000001263.12 1 ...\n", + "9939 0 0 0 1 1 ... 1 100000000001286.22 1 ...\n", + "9938 0 0 0 1 1 ... 1 100000000001320.44 1 ...\n", + "9598 0 0 0 1 0 ... 1 100000000002359.72 1 ...\n", + "9819 0 0 1 0 1 ... 0 100000000003572.94 1 ...\n", + "9781 0 1 0 0 0 ... 0 109999999990457.1 1 ...\n", + "9912 1 1 0 1 0 ... 1 109999999991962.19 1 ...\n", + "9782 0 1 0 0 1 ... 1 109999999992326.25 1 ...\n", + "9907 0 1 0 1 0 ... 1 109999999994440.22 1 ...\n", + "9786 0 0 0 1 1 ... 1 109999999995036.31 1 ...\n", + "9822 0 1 0 1 1 ... 0 109999999995407.66 1 ...\n", + "9998 1 0 0 1 1 ... 0 109999999996474.47 1 ...\n", + "9759 0 0 0 0 0 ... 1 109999999996482.03 1 ...\n", + "9857 0 1 0 1 1 ... 1 109999999997069.28 1 ...\n", + "9888 0 0 0 0 0 ... 1 109999999997417.1 1 ...\n", + "9787 0 0 0 1 1 ... 1 109999999997465.81 1 ...\n", + "9984 1 0 0 1 1 ... 1 109999999998183.9 1 ...\n", + "9824 0 0 0 0 1 ... 0 110000000002509.78 1 ...\n", + "9880 0 0 0 1 1 ... 0 119999999994284.12 1 ...\n", + "9896 0 0 1 0 0 ... 1 119999999996226.88 1 ...\n", + "9897 0 0 1 0 1 ... 1 119999999996933.16 1 ...\n", + "9827 0 1 1 0 1 ... 1 119999999998250.31 1 ...\n", + "9990 0 1 0 1 1 ... 0 119999999998963.47 1 ...\n", + "9956 0 1 0 1 0 ... 1 120000000005857.94 1 ...\n", + "9933 0 1 0 0 1 ... 1 129999999999847.38 1 ...\n", + "9980 0 1 0 1 0 ... 1 150000000002493.03 1 ...\n", + "['BINARY', 9999 rows, 10000 samples, 49 variables]\n" + ] + } + ], + "source": [ + "## run dwave quantum annealing\n", + "num_shots = 10000\n", + "\n", + "sampler = BraketDWaveSampler(('amazon-braket-481358cc730d','qubo'),'arn:aws:braket:::device/qpu/d-wave/Advantage_system1')\n", + "sampler = EmbeddingComposite(sampler)\n", + "response = sampler.sample(model, num_reads=num_shots)\n", + "\n", + "# print results\n", + "print(response)" + ] + }, + { + "cell_type": "markdown", + "id": "fa774596", + "metadata": {}, + "source": [ + "## 3.1 Evaluate the results" + ] + }, + { + "cell_type": "markdown", + "id": "440cc5dc", + "metadata": {}, + "source": [ + "With the response, we can decode the binary array results into the optimal price results" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "c9e4edbc", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "([12, 10, 13, 12, 13, 16, 19],\n", + " array([0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,\n", + " 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,\n", + " 0, 0, 0, 0, 1], dtype=int8),\n", + " -12656.015625)" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def decoder_price_response(response, n_days, price_options):\n", + " opt_price, energy = response.record.sample[response.record.energy.argmin()], response.record.energy.min()\n", + " prices = []\n", + " for i in range(n_days):\n", + " price_i = opt_price[i*len(price_options): (i+1)*len(price_options)]\n", + " assert price_i.sum()==1\n", + " prices.append(price_options[price_i.argmax()])\n", + " return prices, opt_price, energy\n", + "\n", + "opt_decoded_prices, opt_prices, energy =decoder_price_response(response, len(a), price_levels)\n", + "opt_decoded_prices, opt_prices, energy" + ] + }, + { + "cell_type": "markdown", + "id": "cbd4d901", + "metadata": {}, + "source": [ + "The optimized price path and corresponding demand curve is plot below, respectively. The optimal price level is higher than the past 7 days, which results in the demand decreasing." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "e8c5b283", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "plt.rcParams.update({'font.size': 18})\n", + "plt.figure(figsize=(10,8))\n", + "plt.plot(range(1,8),opt_decoded_prices)\n", + "plt.xlabel('Day')\n", + "plt.ylabel('Price ($)')\n", + "plt.savefig('price_path.png')" + ] + }, + { + "cell_type": "markdown", + "id": "3cb7e9d7", + "metadata": {}, + "source": [ + "__now, Let's get the demand of each day and the total revenue__" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "46b3aceb", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "([185.94625963144793,\n", + " 175.81348574612934,\n", + " 157.99134281226168,\n", + " 147.97640607429904,\n", + " 138.06442038250634,\n", + " 120.33139363114194,\n", + " 95.84307132770529],\n", + " 13360.252420786914)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "opt_d, max_rev = get_demands_rev(a,b,p_data, opt_decoded_prices)\n", + "opt_d, max_rev" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "51cf25d2", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "plt.rcParams.update({'font.size': 18})\n", + "plt.figure(figsize=(10,8))\n", + "plt.plot(range(1,8),opt_d)\n", + "plt.xlabel('Day')\n", + "plt.ylabel('Demand')\n", + "plt.savefig('demand_path.png')" + ] + }, + { + "cell_type": "markdown", + "id": "995deca7", + "metadata": {}, + "source": [ + "__Finally, let's get the overall uncertainty of the demand predictions, here we simply use demand variance to indicate the uncertainty__" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "58a30355", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "704.2370868054443" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "overall_variance = get_overall_variance(data_x, p_data, opt_decoded_prices, sigma)\n", + "overall_variance" + ] + }, + { + "cell_type": "markdown", + "id": "f4b9b007", + "metadata": {}, + "source": [ + "__We can also derive the standard deviation of the revenue based on the variance of demand__\n", + "\n", + "$$std(R)=\\sqrt{(\\sum_{t=T}^{T+n-1}var(\\hat{d}_t)*p^2)}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "8e856169", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "367.83167074590745" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def get_overall_revenue_variance(data_x, hist_p, p, sigma):\n", + " all_p = hist_p + p\n", + " t = len(p)\n", + " var = 0\n", + " for i in range(t):\n", + " var += get_variance(data_x, all_p[i+1:i+1+t], sigma) * (p[i]**2)\n", + "\n", + " return var\n", + "\n", + "revenue_variance = get_overall_revenue_variance(data_x, p_data, opt_decoded_prices, sigma)\n", + "np.sqrt(revenue_variance)" + ] + }, + { + "cell_type": "markdown", + "id": "e812bb27", + "metadata": {}, + "source": [ + "__We can investigate the value of the penality terms to see if any equality constraints are voilated. The penalty is close to zero showing that all the constraints are complied__" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "9c7281cc", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-0.0002910185303335311" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "penalty = max_rev - beta*overall_variance + energy\n", + "penalty" + ] + }, + { + "cell_type": "markdown", + "id": "1d76fe84", + "metadata": {}, + "source": [ + "For comparison, to assess the quality of this optimized result, we also iterate (by brute-force search) through all the $7^7=823,543$ possible price solutions to obtain the energy for each one, which takes more than 5 minutes to run on a standard ml.m5.2xlarge AWS instance. We plot the distribution of the energies of all the 823,543 possible solutions as shown below, where the red line represents our optimized result obtained from the quantum annealer. We can see that although the optimized result from the quantum annealer is not the global optimum with minimum cost, it is close-to-optimal and of good quality. 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"775000\n", + "776000\n", + "777000\n", + "778000\n", + "779000\n", + "780000\n", + "781000\n", + "782000\n", + "783000\n", + "784000\n", + "785000\n", + "786000\n", + "787000\n", + "788000\n", + "789000\n", + "790000\n", + "791000\n", + "792000\n", + "793000\n", + "794000\n", + "795000\n", + "796000\n", + "797000\n", + "798000\n", + "799000\n", + "800000\n", + "801000\n", + "802000\n", + "803000\n", + "804000\n", + "805000\n", + "806000\n", + "807000\n", + "808000\n", + "809000\n", + "810000\n", + "811000\n", + "812000\n", + "813000\n", + "814000\n", + "815000\n", + "816000\n", + "817000\n", + "818000\n", + "819000\n", + "820000\n", + "821000\n", + "822000\n", + "823000\n" + ] + } + ], + "source": [ + "all_rev=[]\n", + "all_var=[]\n", + "all_energy=[]\n", + "i=0\n", + "for p_t1 in price_levels:\n", + " for p_t2 in price_levels:\n", + " for p_t3 in price_levels:\n", + " for p_t4 in price_levels:\n", + " for p_t5 in price_levels:\n", + " for p_t6 in price_levels:\n", + " for p_t7 in price_levels:\n", + " if i%1000==0:\n", + " print(i)\n", + " _, sample_rev = get_demands_rev(a,b,p_data, [p_t1,p_t2,p_t3,p_t4,p_t5,p_t6,p_t7])\n", + " sample_overall_variance = get_overall_variance(data_x, p_data, [p_t1,p_t2,p_t3,p_t4,p_t5,p_t6,p_t7], sigma)\n", + " all_rev.append(sample_rev)\n", + " all_var.append(sample_overall_variance)\n", + " all_energy.append(-(sample_rev-beta*sample_overall_variance))\n", + " i+=1" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "4d5394c7", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "plt.rcParams.update({'font.size': 18})\n", + "plt.figure(figsize=(10,8))\n", + "plt.vlines(energy,0,125000, 'r')\n", + "plt.hist(all_energy,20)\n", + "plt.xlabel('Energy distribution of all possible solutions')\n", + "plt.ylabel('Frequency')\n", + "plt.savefig('result_quality.png')" + ] + }, + { + "cell_type": "markdown", + "id": "70060d44", + "metadata": {}, + "source": [ + "# 4. Trade-off between expected revenue and prediction uncertainty." + ] + }, + { + "cell_type": "markdown", + "id": "9a036ec9", + "metadata": {}, + "source": [ + "Let's first wrap above price optimisation into a single main function for convenience." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "e55a4aee", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(12925.152201999756,\n", + " 708.9643434504553,\n", + " -12216.1875,\n", + " [160.67924800195595,\n", + " 145.95810387141424,\n", + " 148.66838060210074,\n", + " 129.4218983001543,\n", + " 158.66460202317302,\n", + " 149.53560711991358,\n", + " 132.71037020072518],\n", + " [19, 12, 8, 16, 5, 13, 16],\n", + " 359.36452646566903)" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qubo_dynamic_pricing import main\n", + "Ld=1e6\n", + "\n", + "max_revenue, prediction_variance, energy, opt_demand, opt_prices, rev_std = main(\n", + " a = a,\n", + " b = b,\n", + " data_x = data_x,\n", + " selected_hist_prices = p_data,\n", + " price_levels = price_levels,\n", + " Lp = Lp,\n", + " Ld = Ld,\n", + " sigma = sigma ,\n", + " beta=beta,\n", + " vol_bound=None\n", + ")\n", + "max_revenue, prediction_variance, energy, opt_demand, opt_prices, rev_std" + ] + }, + { + "cell_type": "markdown", + "id": "71edac8a", + "metadata": {}, + "source": [ + "In order to investigate the trade-off between the expected revenue and prediction uncertainties, we vary the knob parameter $\\beta$ within a large range of $[1e2,1e9]$ and run multiple experiments on D-Wave with different $\\beta$ values. The scatter plot are shown below, where each dot represents the optimized result of an experiment with x-axis representing its expected revenue and y-axis representing the estimated standard deviation of revenue $std(R)$. The standard deviation of revenue can be derived from the estimated variance of the predicted demand:\n", + "\n", + "$$std(R)=\\sqrt{(\\sum_{t=T}^{T+n-1}var(\\hat{d}_t)*p^2)}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "a2bab81e", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "---\n", + "beta_sample:100.0\n", + "max_revenue:12570.821217355566\n", + "prediction_variance:709.1535902008336\n", + "energy:58344.5390625\n", + "opt_demand:[211.2132712609399, 191.23057526113467, 150.76974010686075, 111.64710090455874, 110.4335108482119, 113.53949847915052, 110.45368052927205]\n", + "opt_prices:[5, 12, 19, 19, 10, 12, 16]\n", + "rev_std: 375.71388263106917\n", + "penalty_term: 0.001259772208868526\n", + "---\n", + "beta_sample:1000.0\n", + "max_revenue:11897.632624523101\n", + "prediction_variance:702.4293109302826\n", + "energy:690531.671875\n", + "opt_demand:[193.16540581130278, 182.28098165894653, 182.0115887610362, 164.6248798227977, 151.5282109438208, 157.58974397197392, 164.54598849881108]\n", + "opt_prices:[10, 10, 8, 13, 13, 8, 8]\n", + "rev_std: 270.65194226099476\n", + "penalty_term: -0.006430759443901479\n", + "---\n", + "beta_sample:10000.0\n", + "max_revenue:12980.87742870795\n", + "prediction_variance:702.8461008421212\n", + "energy:7015480.1328125\n", + "opt_demand:[193.16540581130278, 175.06183547909168, 168.32494666836413, 152.18500341084314, 145.07609647822775, 147.74845142226496, 129.2768226162399]\n", + "opt_prices:[10, 12, 10, 13, 12, 10, 16]\n", + "rev_std: 318.9774967063375\n", + "penalty_term: 0.0018199952319264412\n", + "---\n", + "beta_sample:100000.0\n", + "max_revenue:12474.432120127967\n", + "prediction_variance:702.0711166209728\n", + "energy:70194637.2265625\n", + "opt_demand:[193.16540581130278, 182.28098165894653, 174.79244258118132, 168.98610317976278, 155.25707431390924, 148.02071530458718, 148.75922380801677]\n", + "opt_prices:[10, 10, 10, 10, 13, 12, 10]\n", + "rev_std: 285.54823653014745\n", + "penalty_term: -0.003414645791053772\n", + "---\n", + "beta_sample:1000000.0\n", + "max_revenue:11048.709968551753\n", + "prediction_variance:702.2210055407705\n", + "energy:702209956.828125\n", + "opt_demand:[200.38455199115765, 188.74847757176371, 180.7648230803187, 180.29455641600072, 192.36774221602548, 206.274779314509, 192.91095726008257]\n", + "opt_prices:[8, 10, 10, 8, 5, 5, 12]\n", + "rev_std: 228.85785780239854\n", + "penalty_term: -0.0026769638061523438\n", + "---\n", + "beta_sample:10000000.0\n", + "max_revenue:12106.055342122756\n", + "prediction_variance:702.3198662040747\n", + "energy:7023186555.9921875\n", + "opt_demand:[193.16540581130278, 182.28098165894653, 182.0115887610362, 175.45359909257996, 190.106039532466, 192.41829837194877, 165.69288636051587]\n", + "opt_prices:[10, 10, 8, 10, 5, 8, 16]\n", + "rev_std: 266.81322270209137\n", + "penalty_term: 0.006781578063964844\n", + "---\n", 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0.003971844911575317\n", + "---\n", + "beta_sample:1000000.0\n", + "max_revenue:10938.52635324596\n", + "prediction_variance:703.0612003899821\n", + "energy:703050261.8671875\n", + "opt_demand:[200.38455199115765, 181.52933139190887, 167.07818098764665, 149.806814554409, 166.137314878462, 174.6592144706206, 195.34218187948787]\n", + "opt_prices:[8, 12, 12, 13, 5, 8, 5]\n", + "rev_std: 252.5275553115527\n", + "penalty_term: 0.003558635711669922\n", + "---\n", + "beta_sample:10000000.0\n", + "max_revenue:12125.395253667739\n", + "prediction_variance:702.9457907041048\n", + "energy:7029445781.6484375\n", + "opt_demand:[193.16540581130278, 200.32884710858366, 180.13246309344206, 181.43495673823531, 181.0371325686151, 168.4443431758921, 160.77217560262812]\n", + "opt_prices:[10, 5, 13, 8, 8, 12, 12]\n", + "rev_std: 267.03972255858883\n", + "penalty_term: 0.0026445388793945312\n", + "---\n", + "beta_sample:100000000.0\n", + "max_revenue:12162.929038181705\n", + "prediction_variance:702.6234669958096\n", + "energy:70262334536.65625\n", + "opt_demand:[185.94625963144793, 175.81348574612934, 157.99134281226168, 162.41469843400876, 161.82813147792302, 156.41569085835218, 165.62055200401358]\n", + "opt_prices:[12, 10, 13, 8, 10, 12, 8]\n", + "rev_std: 280.7137323379572\n", + "penalty_term: 0.0043182373046875\n", + "---\n", + "beta_sample:1000000000.0\n", + "max_revenue:12667.795502625071\n", + "prediction_variance:702.2857940306494\n", + "energy:702285781362.8594\n", + "opt_demand:[200.38455199115765, 188.74847757176371, 187.98396926017358, 172.32375996910818, 174.57641161974618, 163.4510698738995, 140.4658316139201]\n", + "opt_prices:[8, 10, 8, 12, 8, 12, 16]\n", + "rev_std: 289.6763784512922\n", + "penalty_term: 0.0054931640625\n", + "---\n", + "beta_sample:100.0\n", + "max_revenue:12399.253327506141\n", + "prediction_variance:706.1235850814901\n", + "energy:58213.1015625\n", + "opt_demand:[211.2132712609399, 187.62100217120727, 172.80300377994413, 142.12586561963255, 157.04129838586414, 126.8290784428085, 136.15050653596137]\n", + "opt_prices:[5, 13, 12, 16, 5, 19, 10]\n", + "rev_std: 330.28601013881905\n", + "penalty_term: -0.0036181428731651977\n", + "---\n", + "beta_sample:1000.0\n", + "max_revenue:12768.956653409954\n", + "prediction_variance:703.054841964221\n", + "energy:690285.8828125\n", + "opt_demand:[185.94625963144793, 164.98476647634706, 151.89967203296325, 149.47072946185642, 152.2128652300999, 149.83808298258688, 146.25921387782523]\n", + "opt_prices:[12, 13, 12, 10, 10, 12, 12]\n", + "rev_std: 308.08639590657435\n", + "penalty_term: -0.002498311107046902\n", + "---\n", + "beta_sample:10000.0\n", + "max_revenue:12946.893792294639\n", + "prediction_variance:703.4892379335616\n", + "energy:7021945.5\n", + "opt_demand:[182.33668654152052, 172.5797377897207, 155.00515256269296, 145.9317525461075, 137.1811267475665, 134.19734187583984, 130.0575942508404]\n", + "opt_prices:[13, 10, 13, 12, 13, 12, 13]\n", + "rev_std: 327.00879692913395\n", + "penalty_term: 0.014456678181886673\n", + "---\n", + "beta_sample:100000.0\n", + "max_revenue:12884.305136873081\n", + "prediction_variance:702.4916228130044\n", + "energy:70236277.9765625\n", + "opt_demand:[193.16540581130278, 189.5001278388014, 188.47908467385338, 181.42597959171735, 168.9283349593571, 164.3295037671134, 128.63802766095915]\n", + "opt_prices:[10, 8, 8, 10, 12, 10, 19]\n", + "rev_std: 306.20396158318704\n", + "penalty_term: 0.00039893388748168945\n", + "---\n", + "beta_sample:1000000.0\n", + "max_revenue:12521.293601400072\n", + "prediction_variance:702.4127612532577\n", + "energy:702400239.9609375\n", + "opt_demand:[193.16540581130278, 171.45226238916428, 172.31034489181036, 166.4950283438739, 165.9242134982543, 166.3805315052315, 153.40612612460205]\n", + "opt_prices:[10, 13, 8, 10, 10, 10, 13]\n", + "rev_std: 283.68916923837827\n", + "penalty_term: 0.001281142234802246\n", + "---\n", + "beta_sample:10000000.0\n", + "max_revenue:12695.923423045606\n", + "prediction_variance:702.9150704666037\n", + "energy:7029138008.734375\n", + "opt_demand:[200.38455199115765, 188.74847757176371, 169.93610381053645, 152.54544709713775, 149.19256623563928, 158.21240843026567, 140.9673212375265]\n", + "opt_prices:[8, 10, 13, 13, 10, 8, 16]\n", + "rev_std: 304.3612950862385\n", + "penalty_term: -0.008238792419433594\n", + "---\n", + "beta_sample:100000000.0\n", + "max_revenue:12954.587965719564\n", + "prediction_variance:702.6340373486921\n", + "energy:70263390780.28906\n", + "opt_demand:[193.16540581130278, 182.28098165894653, 182.0115887610362, 175.45359909257996, 179.27732026268376, 153.84046978330358, 130.86433196054097]\n", + "opt_prices:[10, 10, 8, 10, 8, 16, 16]\n", + "rev_std: 307.31670060403906\n", + "penalty_term: 0.0078125\n", + "---\n", + "beta_sample:1000000000.0\n", + "max_revenue:11477.05591528449\n", + "prediction_variance:701.6709165846278\n", + "energy:701670905107.5703\n", + "opt_demand:[200.38455199115765, 188.74847757176371, 187.98396926017358, 186.7620523288179, 180.29225726552573, 176.14748113921195, 178.01614585978547]\n", + "opt_prices:[8, 10, 8, 8, 10, 10, 8]\n", + "rev_std: 236.0709905568157\n", + "penalty_term: -0.0015869140625\n" + ] + } + ], + "source": [ + "beta_options=[1e2,1e3,1e4,1e5,1e6,1e7,1e8,1e9]\n", + "results = {beta_option:[] for beta_option in beta_options}\n", + "beta_samples = beta_options*6\n", + "\n", + "for beta_i in beta_samples:\n", + " max_revenue, prediction_variance, energy, opt_demand, opt_prices, rev_std = main(\n", + " a = a,\n", + " b = b,\n", + " data_x = data_x,\n", + " selected_hist_prices = p_data,\n", + " price_levels = price_levels,\n", + " Lp = Lp,\n", + " Ld = Ld,\n", + " sigma = sigma ,\n", + " beta=beta_i,\n", + " vol_bound=None\n", + " )\n", + " print('---')\n", + " print(f\"beta_sample:{beta_i}\")\n", + " print(f\"max_revenue:{max_revenue}\")\n", + " print(f\"prediction_variance:{prediction_variance}\")\n", + " print(f\"energy:{energy}\")\n", + " print(f\"opt_demand:{opt_demand}\")\n", + " print(f\"opt_prices:{opt_prices}\")\n", + " print(f\"rev_std: {rev_std}\")\n", + " print(f\"penalty_term: {max_revenue-beta_i*prediction_variance+energy}\")\n", + " results[beta_i].append([energy, max_revenue, prediction_variance, rev_std])" + ] + }, + { + "cell_type": "markdown", + "id": "b2172f27", + "metadata": {}, + "source": [ + "We can see from the plot below that there is Pareto front where the expected revenue cannot be increased without increasing the standard deviation (i.e. uncertainties), and the other way around.\n", + "\n", + "We can see that the expected revenue can vary significantly between 10000 and 13500, while the estimated standard deviation of the revenue (i.e. uncertainty) can change in a large range $[200,380]$ as well. The figure shows that as the expected revenue increases, the estimated standard deviation of the revenue will also increase. This means that if we select a price solution for higher expected revenue, the uncertainties will increase at the same time indicating that the demand estimation model will become less confident about its predictions. This illustrates there is a trade-off between maximizing the revenue and minimizing the uncertainty. High revenue and rewards usually accompany with high uncertainties and risk. In practice, according to different business strategies and needs, we usually need to find an appropriate $\\beta$ to maximize the revenue under an acceptable level of uncertainty." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "d66a8636", + "metadata": {}, + "outputs": [], + "source": [ + "beta_x=[]\n", + "revenue_y=[]\n", + "variance_y=[]\n", + "rev_std_y=[]\n", + "\n", + "for beta_i in beta_options:\n", + " for result in results[beta_i]:\n", + " beta_x.append(beta_i)\n", + " revenue_y.append(result[1])\n", + " variance_y.append(result[2])\n", + " rev_std_y.append(result[3])" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "ad1da38c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# b=300\n", + "import matplotlib.pyplot as plt\n", + "plt.rcParams.update({'font.size': 18})\n", + "plt.figure(figsize=(10,8))\n", + "plt.scatter(revenue_y, rev_std_y)\n", + "plt.xlabel('Revenue')\n", + "plt.ylabel('Revenue standard deviation')\n", + "plt.savefig('tradoff_sigma=10_b=300.png')" + ] + }, + { + "cell_type": "markdown", + "id": "a2b578b7", + "metadata": {}, + "source": [ + "# 5. Conclusion" + ] + }, + { + "cell_type": "markdown", + "id": "3c85c279", + "metadata": {}, + "source": [ + "In this blog, we demonstrate how to leverage a quantum annealer on Amazon Braket to solve a price optimization use case. We showed how to mathematically formulate the problem within the (quantum-ready) QUBO framework, and then subsequently solve the optimization problem on a D-Wave quantum annealer. Our results are promising in terms of both close-to-optimal quality and computational efficiency. Since the QUBO formalism is a generalized framework that can embrace a variety of combinatorial optimization use cases (e.g. scheduling/planning, routing, portfolio management), the proposed solution can be arguably adapted and recycled by customers across other multiple industries. Already today our customers can get quantum-ready, and easily leverage Amazon Braket to help solve their daily combinatorial optimization challenges, and make better business and operation decisions." + ] + }, + { + "cell_type": "markdown", + "id": "bd9a23f8", + "metadata": {}, + "source": [ + "# 6. References:\n", + "1. Glover, F., Kochenberger, G. and Du, Y., 2019. Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models. 4OR, 17(4), pp.335-371.\n", + "2. Kochenberger, G., Hao, J.K., Glover, F., Lewis, M., Lü, Z., Wang, H. and Wang, Y., 2014. The unconstrained binary quadratic programming problem: a survey. Journal of combinatorial optimization, 28(1), pp.58-81.\n", + "3. Anthony, M., Boros, E., Crama, Y. and Gruber, A., 2017. Quadratic reformulations of nonlinear binary optimization problems. Mathematical Programming, 162(1), pp.115-144.\n", + "4. Amazon Web Services. Amazon Braket – Amazon Web Services, 2021. Available at: https://aws.amazon.com/braket/ (Accessed: 15 July, 2021)\n", + "5. Cruz-Santos, W., Venegas-Andraca, S.E. and Lanzagorta, M., 2019. A QUBo formulation of Minimum Multicut problem instances in trees for D-Wave Quantum Annealers. Scientific reports, 9(1), pp.1-12.\n", + "6. Amazon Web Services. A python SDK for interacting with quantum devices via AWS, 2021. Available at: https://github.com/aws/amazon-braket-sdk-python (Accessed: 16 July, 2021) \n", + "7. Amazon Web Services. Amazon SageMaker – Machine Learning – Amazon Web Services, 2021. Available at: https://aws.amazon.com/sagemaker/ (Accessed: 20 July, 2021)\n", + "8. Ben-Tal, A. and Nemirovski, A., 2002. Robust optimization–methodology and applications. Mathematical programming, 92(3), pp.453-480.\n", + "9. Fabozzi, F.J., Kolm, P.N., Pachamanova, D.A. and Focardi, S.M., 2007. Robust portfolio optimization and management. John Wiley & Sons." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2e2f2f72", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "conda_braket", + "language": "python", + "name": "conda_braket" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/price_optimization/qubo_dynamic_pricing.py b/examples/price_optimization/qubo_dynamic_pricing.py new file mode 100644 index 000000000..1681bec69 --- /dev/null +++ b/examples/price_optimization/qubo_dynamic_pricing.py @@ -0,0 +1,255 @@ +from pyqubo import Binary +import numpy as np +import dimod +from braket.ocean_plugin import BraketSampler, BraketDWaveSampler +from dwave.system.composites import EmbeddingComposite + +np.random.seed(0) + +def get_coeffient(expr, mode): + coeffs, consts = expr.compile().to_qubo() + if mode == 'linear': + new_coeffs = {} + for k, v in coeffs.items(): + assert k[0] == k[1] + new_coeffs[k[0]] = v + elif mode == 'quadratic': + new_coeffs = coeffs + else: + raise TypeError(f"unknown mode: {mode}") + + return new_coeffs, consts + + +def get_demand(coeff, b, prices): + assert len(coeff) == len(prices) + d = b + for i in range(len(coeff)): + d += coeff[i]*prices[i] + + return d + + +def get_variance(data_x, p, sigma): + """ + :param data_x (np.array): [n_samples, n_days] + :param p (list): [n_days] + :return: variance + """ + n_samples, t = data_x.shape + ones = np.ones((n_samples, 1), dtype=np.float) + x_mat = np.concatenate([ones, data_x], axis=1) # [n_samples, n_days+1] + x_mat = np.linalg.inv( + np.dot(x_mat.T, x_mat) + ) + p = np.array([1.]+p) + variance = (sigma**2) * (1. + p.dot(x_mat).dot(p)) + return variance + + +def create_program(a,b, p_data, price_levels, data_x, Lp, Ld, sigma, beta, vol_bound): + """ + + :param a (list of int): [7], coefficient + :param b (int): + :param p_data (list of int): [7], past 7 days prices + :param price_levels (list of int): number of price levels + :param data_x (np.array): [nsamples, n_days] + :param L (float): coeff of constraints penalty + :param sigma (float): standard deviation of noise + :param beta (float): coeff of variance + :return: + """ + assert type(a) is list + #assert type(b) is int + assert type(p_data) is list + assert type(price_levels) is list + + t = len(a) + n_level = len(price_levels) + + # variables + x = [] + p = [] + d = [] + + # get p + for i in range(t): + p_i = 0 + for j in range(n_level): + x_ij = Binary(f"X_{i*n_level+j:03d}") + x.append(x_ij) + p_i += x_ij*price_levels[j] + p.append(p_i) + + all_p = p_data + p + + # get d, rev + rev = 0 + for i in range(t): + d_i = get_demand( + coeff=a, + b=b, + prices=all_p[i+1:i+1+t] + ) + d.append(d_i) + rev += d_i * p[i] + # minus variance + rev -= beta * get_variance(data_x, all_p[i+1:i+1+t], sigma) + # add inequaliry constraints + if vol_bound: + _, d_const = get_coeffient(d_i, 'linear') + rev -= inequality_penalty( + demand=d_i, + demand_name=f'demand{i}', + vol_bounday=vol_bound, + d_const=d_const, + Ld=Ld + ) + + # add equalty constraints + for i in range(t): + penalty = x[i*n_level] + for j in range(1, n_level): + penalty += x[i*n_level+j] + penalty = ((penalty-1)**2)*Lp + rev -= penalty + + return rev, d + + +def construct_slack(n, name): + e = 0 + slack = 0 + while n >= 2**e: + n -= 2**e + slack += (2**e) * Binary(f"{name}_{e}") + e += 1 + + slack += n * Binary(f"{name}_{e}") + return slack + + +def inequality_penalty(demand, demand_name, vol_bounday, d_const, Ld): + rhs = vol_bounday - d_const + assert rhs <= 0 + n = -rhs + slack = construct_slack(n, demand_name) + return ((demand-vol_bounday-slack)**2)*Ld + + +def main( + a, + b, + data_x, + selected_hist_prices, + price_levels, + Lp, + Ld, + sigma, + beta, + vol_bound, + dwave=True +): + """ + + :param a: list of int, coeff + :param b: int, const + :param data_x: training set of x + :param selected_hist_prices: list, last n days prices + :param price_levels: list of int, options of prices + :param Lp: int, coeff of price constraints penalty + :param Ld: int, coeff of demand constraints penalty + :param sigma: float, stand deviation of noise + :param beta: float, coeff of variance penalty + :param vol_bound: float, boundary of demand + :return: + """ + obj, demands = create_program( + a=a, + b=b, + p_data=selected_hist_prices, + price_levels=price_levels, + data_x=data_x, + Lp=Lp, + Ld=Ld, + sigma=sigma, + beta=beta, + vol_bound=vol_bound + ) + + # qubo solver + response = dwave_solver(obj) if dwave else qubo_solver(obj) + # get optimal prices + opt_prices, _, energy = decoder_price_response(response, len(a), price_levels) + opt_demand, max_revenue = get_demands_rev(a, b, selected_hist_prices, opt_prices) + prediction_variance = get_overall_variance(data_x, selected_hist_prices, opt_prices, sigma) + revenue_variance = get_overall_revenue_variance(data_x, selected_hist_prices, opt_prices, sigma) + + return max_revenue, prediction_variance, energy, opt_demand, opt_prices, np.sqrt(revenue_variance) + + +def qubo_solver(obj): + model = (-obj).compile().to_bqm() + num_shots = 100 + + sampler = dimod.SimulatedAnnealingSampler() + response = sampler.sample(model, num_reads=num_shots) + return response + + +def dwave_solver(obj): + model = (-obj).compile().to_bqm() + num_shots = 10000 + + sampler = BraketDWaveSampler(('amazon-braket-481358cc730d', 'qubo'), + 'arn:aws:braket:::device/qpu/d-wave/Advantage_system1') + sampler = EmbeddingComposite(sampler) + response = sampler.sample(model, num_reads=num_shots) + return response + + +def decoder_price_response(response, n_days, price_options): + opt_price, energy = response.record.sample[response.record.energy.argmin()], response.record.energy.min() + prices = [] + for i in range(n_days): + price_i = opt_price[i*len(price_options): (i+1)*len(price_options)] + assert price_i.sum()==1 + prices.append(price_options[price_i.argmax()]) + return prices, opt_price, energy + + +def get_demands_rev(a, b, hist_p, p): + all_p = hist_p + p + t = len(a) + d = [] + revenue = 0 + for i in range(t): + d_i = get_demand( + coeff=a, + b=b, + prices=all_p[i+1:i+1+t] + ) + d.append(d_i) + revenue += d_i * p[i] + return d, revenue + + +def get_overall_variance(data_x, hist_p, p, sigma): + all_p = hist_p + p + t = len(p) + var = 0 + for i in range(t): + var += get_variance(data_x, all_p[i+1:i+1+t], sigma) + + return var + + +def get_overall_revenue_variance(data_x, hist_p, p, sigma): + all_p = hist_p + p + t = len(p) + var = 0 + for i in range(t): + var += get_variance(data_x, all_p[i+1:i+1+t], sigma) * (p[i]**2) + + return var From fd99991b177c9a7291ef2008e145461b1d03c332 Mon Sep 17 00:00:00 2001 From: feng shi Date: Wed, 1 Dec 2021 22:08:26 +0000 Subject: [PATCH 02/13] Add S3 environment setting --- .../price_optimization/QUBO-Pricing.ipynb | 20986 ++++++++-------- .../qubo_dynamic_pricing.py | 2 +- 2 files changed, 10515 insertions(+), 10473 deletions(-) diff --git a/examples/price_optimization/QUBO-Pricing.ipynb b/examples/price_optimization/QUBO-Pricing.ipynb index eaf34d3e2..76b882d06 100644 --- a/examples/price_optimization/QUBO-Pricing.ipynb +++ b/examples/price_optimization/QUBO-Pricing.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "63297199", + "id": "5eb1203e", "metadata": {}, "source": [ "# Using quantum annealing on Amazon Braket for price optimization\n", @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "3d96a889", + "id": "ecdbe31f", "metadata": {}, "source": [ "# Table of content\n", @@ -35,7 +35,7 @@ }, { "cell_type": "markdown", - "id": "cbe832a9", + "id": "4de37df8", "metadata": {}, "source": [ "We start by importing important libraries related to Amazon braket and" @@ -44,7 +44,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "d5ea8de1", + "id": "a2820991", "metadata": {}, "outputs": [ { @@ -53,8 +53,8 @@ "text": [ "Requirement already satisfied: sklearn in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (0.0)\n", "Requirement already satisfied: scikit-learn in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from sklearn) (1.0.1)\n", - "Requirement already satisfied: threadpoolctl>=2.0.0 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (3.0.0)\n", "Requirement already satisfied: scipy>=1.1.0 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.5.2)\n", + "Requirement already satisfied: threadpoolctl>=2.0.0 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (3.0.0)\n", "Requirement already satisfied: numpy>=1.14.6 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.19.2)\n", "Requirement already satisfied: joblib>=0.11 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.1.0)\n" ] @@ -67,7 +67,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "a76144e6", + "id": "e07925ae", "metadata": {}, "outputs": [], "source": [ @@ -94,7 +94,48 @@ }, { "cell_type": "markdown", - "id": "b6eb73b1", + "id": "3902f38c", + "metadata": {}, + "source": [ + "__NOTE__: Enter your S3 bucket and key below. " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "8fbfb24b", + "metadata": {}, + "outputs": [], + "source": [ + "# Enter the S3 bucket you created during onboarding in the code below\n", + "my_bucket = \"amazon-braket-Your-Bucket-Name\" # the name of the bucket\n", + "my_prefix = \"Your-Folder-Name\" # the name of the folder in the bucket\n", + "s3_folder = (my_bucket, my_prefix)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "5a1a0cd6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Device: Device('name': Advantage_system4.1, 'arn': arn:aws:braket:::device/qpu/d-wave/Advantage_system4)\n" + ] + } + ], + "source": [ + "# session and device\n", + "device = AwsDevice(\"arn:aws:braket:::device/qpu/d-wave/Advantage_system4\")\n", + "print('Device:', device)" + ] + }, + { + "cell_type": "markdown", + "id": "eaed10f7", "metadata": {}, "source": [ "# 1. Demand model" @@ -102,7 +143,7 @@ }, { "cell_type": "markdown", - "id": "7e4472cd", + "id": "e6ffce04", "metadata": {}, "source": [ "The usual goal of price optimization is to maximize the revenue in the next certain period, where the revenue can usually be represented by a function of demand and price: \n", @@ -116,7 +157,7 @@ }, { "cell_type": "markdown", - "id": "50714538", + "id": "9f0cfee4", "metadata": {}, "source": [ "## 1.1 Create training dataset" @@ -124,7 +165,7 @@ }, { "cell_type": "markdown", - "id": "f0d07a51", + "id": "65b9ad30", "metadata": {}, "source": [ "For simplicity, we create a dummy dataset on historical demand and price observations so that a demand estimation model can be trained. \n", @@ -141,8 +182,8 @@ }, { "cell_type": "code", - "execution_count": 3, - "id": "846bf53a", + "execution_count": 5, + "id": "f367cc06", "metadata": { "scrolled": true }, @@ -217,7 +258,7 @@ }, { "cell_type": "markdown", - "id": "7d08dd0c", + "id": "a2e76585", "metadata": {}, "source": [ "## 1.2. Fit the demand model" @@ -225,7 +266,7 @@ }, { "cell_type": "markdown", - "id": "34981246", + "id": "bf76f8d4", "metadata": {}, "source": [ "By using the created training dataset, we simply using sklearn to fit a linear demand model. This fitted linear demand model will be used for the following price optimization problem. We round the model coefficents to integer for simplicity to fit with the below QUBO format (quadratic unconstrained binary optimization). " @@ -233,8 +274,8 @@ }, { "cell_type": "code", - "execution_count": 4, - "id": "552b9579", + "execution_count": 6, + "id": "9a7052bb", "metadata": {}, "outputs": [ { @@ -265,7 +306,7 @@ }, { "cell_type": "markdown", - "id": "22311927", + "id": "d5e39096", "metadata": {}, "source": [ "# 2. Price optimization with QUBO" @@ -273,7 +314,7 @@ }, { "cell_type": "markdown", - "id": "26841444", + "id": "4ff66481", "metadata": {}, "source": [ "In this blog, we leverage a general-purpose mathematical framework: Quadratic Unconstrained Binary Optimization (QUBO), which has been recently proposed as an effective framework that is able to generalize across a large variety of combinatorial optimization use cases in industries [2, 3]. We take this price optimization as an example and showcase how to formulate it into QUBO framework considering prediction uncertainties as well as equality constraints." @@ -281,7 +322,7 @@ }, { "cell_type": "markdown", - "id": "4fa6625c", + "id": "d2e51ab6", "metadata": {}, "source": [ "The formal definition of QUBO is expressed as an optimization problem, Minimize:\n", @@ -290,7 +331,7 @@ }, { "cell_type": "markdown", - "id": "0305adc8", + "id": "61516668", "metadata": {}, "source": [ "Where $x$ is a vector of binary variables representing the decision variables of the combinatorial optimization. $Q$ is a squared matrix of constants inherently encoding the context and constraints of the optimization problems. $Q$ is commonly assumed to be symmetric or upper triangular without loss of generality. The goal is to find the optimal values of the binary decision variables $x$ that minimize the objective $H$.\n", @@ -300,7 +341,7 @@ }, { "cell_type": "markdown", - "id": "201247df", + "id": "308e19ca", "metadata": {}, "source": [ "## 2.1 Construct objective function" @@ -308,7 +349,7 @@ }, { "cell_type": "markdown", - "id": "e6e63f90", + "id": "f9b43ce8", "metadata": {}, "source": [ "Assuming tomorrow is day $T$, then the goal of our price optimization is to find the optimal prices $p_t, t\\in[T, T+1, \\ldots, T+n-1]$ in the next $n$ days in order to maximize the revenue in next $n$ days. Based on the demand model we showed above where the demand at a day is correlated with the latest $n$ days' price, we can construct objective function as below:\n", @@ -322,8 +363,8 @@ }, { "cell_type": "code", - "execution_count": 5, - "id": "ecd62532", + "execution_count": 7, + "id": "75a3ed9f", "metadata": {}, "outputs": [ { @@ -332,7 +373,7 @@ "[10, 8, 8, 5, 5, 8, 8]" ] }, - "execution_count": 5, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -344,7 +385,7 @@ }, { "cell_type": "markdown", - "id": "ffb31756", + "id": "6e227359", "metadata": {}, "source": [ "Now, let's construct the objective function which is the total revenue $R$ in the next $n$ days.\n", @@ -356,8 +397,8 @@ }, { "cell_type": "code", - "execution_count": 6, - "id": "74e05aef", + "execution_count": 8, + "id": "61d3e818", "metadata": {}, "outputs": [ { @@ -379,7 +420,7 @@ " (Binary(X_048)*Num(19.000000)+Binary(X_047)*Num(16.000000)+Binary(X_046)*Num(13.000000)+Binary(X_045)*Num(12.000000)+Binary(X_044)*Num(10.000000)+Binary(X_042)*Num(5.000000)+Binary(X_043)*Num(8.000000))]" ] }, - "execution_count": 6, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -406,7 +447,7 @@ }, { "cell_type": "markdown", - "id": "1d79c0d2", + "id": "8314d7be", "metadata": {}, "source": [ "Next, we can input the price variables into our fitted model to estimate the demand, and then use the demand together with price to represent revenue $R$." @@ -414,8 +455,8 @@ }, { "cell_type": "code", - "execution_count": 7, - "id": "df83ba8c", + "execution_count": 9, + "id": "ece4710c", "metadata": {}, "outputs": [ { @@ -461,7 +502,7 @@ }, { "cell_type": "markdown", - "id": "c6aa7c69", + "id": "f5bf5be9", "metadata": {}, "source": [ "## 2.2 Add penalty for prediction uncertainty" @@ -469,7 +510,7 @@ }, { "cell_type": "markdown", - "id": "6f65701b", + "id": "ef843b0b", "metadata": {}, "source": [ "In optimisation, we usually desire to reduce the risk while maximizing the reward, which means we want to reduce the estimated uncertainty/variance of the predicted demands. Therefore, we add a penalty term in the objective function to represent the uncertainty of the predicted demand. The uncertainty of the predicted demand $d_t$ can be represented by its estimated variance.\n", @@ -491,8 +532,8 @@ }, { "cell_type": "code", - "execution_count": 8, - "id": "e5b620b2", + "execution_count": 10, + "id": "780f571a", "metadata": {}, "outputs": [ { @@ -501,7 +542,7 @@ 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] }, - "execution_count": 8, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } @@ -539,7 +580,7 @@ }, { "cell_type": "markdown", - "id": "8d1518cb", + "id": "eb9dae80", "metadata": {}, "source": [ "## 2.3 Add penalty for equality constraints" @@ -547,7 +588,7 @@ }, { "cell_type": "markdown", - "id": "5d26aea8", + "id": "6dacd8cf", "metadata": {}, "source": [ "As we mentioned above that price can only take one option per day, this means that one and only one of the binary variables in a day must be $1$ and others must be $0$. 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] }, - "execution_count": 9, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } @@ -589,7 +630,7 @@ }, { "cell_type": "markdown", - "id": "b961659b", + "id": "07d925f4", "metadata": {}, "source": [ "# 3. Solve QUBO with Braket" @@ -597,7 +638,7 @@ }, { "cell_type": "markdown", - "id": "97fe4b9b", + "id": "3a30c93d", "metadata": {}, "source": [ "Now we have transformed to the total objective function which:\n", @@ -613,7 +654,7 @@ }, { "cell_type": "markdown", - "id": "836ade85", + "id": "ff888617", "metadata": {}, "source": [ "Amazon Braket provides access to quantum annealers from D-Wave Systems Inc. which are specifically designed to solve QUBO problems. A quantum annealer is a hardware implementation of Quantum Annealing (QA) which is a generic algorithm to solve combinatorial optimization problems by taking advantage of quantum fluctuations to escape local minima in complex energy landscapes by effect of tunnelling through barriers separating local minima [5]. Through a simple Amazon Braket API call, the formatted QUBO problem can be embedded to the hardwired topology of the machine and submitted to machine. In turn, the quantum annealer performs an annealing process and obtains a result. However, because of the sparsity of the underlying chip, one typically faces a certain overhead in embedding the original QUBO problem to the D-Wave hardware, because (typically) one logical binary variable maps onto several physical qubits, in order to effectively distill the connectivity of the original QUBO problem. For more details, we refer to the Amazon Braket tutorial notebook available here (https://github.com/aws/amazon-braket-examples/blob/main/examples/quantum_annealing/Dwave_Anatomy.ipynb)." @@ -621,8 +662,8 @@ }, { "cell_type": "code", - "execution_count": 10, - "id": "36e0a910", + "execution_count": 12, + "id": "97ce4e85", "metadata": {}, "outputs": [], "source": [ @@ -646,8 +687,8 @@ }, { "cell_type": "code", - "execution_count": 11, - "id": "b61df9cd", + "execution_count": 13, + "id": "8b60c6c3", "metadata": {}, "outputs": [ { @@ -656,7 +697,7 @@ "BinaryQuadraticModel({X_005: -10000000002744.719, X_030: -10000000002576.855, X_036: -10000000002155.762, X_006: -10000000003050.883, X_043: -10000000002179.559, X_016: -10000000002371.592, X_034: -10000000004275.291, X_033: -10000000003774.486, X_002: -10000000001934.893, X_037: -10000000002622.238, X_032: -10000000003208.34, X_047: -10000000003896.223, X_041: -10000000004362.69, X_011: -10000000002651.016, X_014: -10000000001276.889, 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"execute_result" } @@ -689,7 +730,7 @@ }, { "cell_type": "markdown", - "id": "c4f14a6b", + "id": "c8f0a3d4", "metadata": {}, "source": [ "We embed and submit the QUBO task to be solved by a quantum annealer at D-wave backend. Similar to classical simulated annealing, we take several independent shots in order to increase our chances for success in finding a high-quality solution to the QUBO problem. The response contains a number of rows. Each row represents the optimization result of a single shot, including the binary decision variables $[x_T,\\cdots,x_{T+n-1}]$, and corresponding energy which is the negative value of objective function, i.e. $H$. Below we show how to submit a QUBO problem to D-Wave and provide a sample response. Here, the key figure of merit is listed in the column labelled with energy, representing the value for the objective function . We can then easily read off the best bit string found." @@ -697,8 +738,8 @@ }, { "cell_type": "code", - "execution_count": 13, - "id": "0f7cb64f", + "execution_count": 16, + "id": "674a30ee", "metadata": { "scrolled": true }, @@ -708,10006 +749,10007 @@ "output_type": "stream", "text": [ " X_000 X_001 X_002 X_003 X_004 ... 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...\n", + "9761 1 0 0 1 0 ... 1 99999999992282.72 1 ...\n", + "9810 0 1 0 0 0 ... 0 99999999993277.06 1 ...\n", + "9755 1 1 0 0 0 ... 0 99999999993963.16 1 ...\n", + "9955 1 1 0 1 0 ... 0 99999999994092.5 1 ...\n", + "9385 0 0 0 0 1 ... 0 99999999996290.84 1 ...\n", + "9623 0 0 0 0 0 ... 1 99999999997566.16 1 ...\n", + "9807 1 0 0 0 1 ... 0 99999999997965.38 1 ...\n", + "9973 0 0 1 0 0 ... 0 99999999998670.03 1 ...\n", + "9306 0 1 1 0 0 ... 0 99999999999454.84 1 ...\n", + "9806 0 1 1 1 0 ... 0 109999999989177.84 1 ...\n", + "9596 0 1 0 0 0 ... 0 109999999993403.06 1 ...\n", + "9670 0 0 0 0 0 ... 0 109999999997403.9 1 ...\n", + "9760 1 1 1 0 0 ... 1 119999999993356.84 1 ...\n", + "9980 0 1 0 0 0 ... 0 119999999999664.4 1 ...\n", + "9994 1 0 0 0 0 ... 0 129999999997768.84 1 ...\n", + "9986 1 0 0 1 0 ... 0 130000000000172.53 1 ...\n", + "['BINARY', 10000 rows, 10000 samples, 49 variables]\n" ] } ], @@ -10715,7 +10757,7 @@ "## run dwave quantum annealing\n", "num_shots = 10000\n", "\n", - "sampler = BraketDWaveSampler(('amazon-braket-481358cc730d','qubo'),'arn:aws:braket:::device/qpu/d-wave/Advantage_system1')\n", + "sampler = BraketDWaveSampler(s3_folder,'arn:aws:braket:::device/qpu/d-wave/Advantage_system4')\n", "sampler = EmbeddingComposite(sampler)\n", "response = sampler.sample(model, num_reads=num_shots)\n", "\n", @@ -10725,7 +10767,7 @@ }, { "cell_type": "markdown", - "id": "fa774596", + "id": "b5581aec", "metadata": {}, "source": [ "## 3.1 Evaluate the results" @@ -10733,7 +10775,7 @@ }, { "cell_type": "markdown", - "id": "440cc5dc", + "id": "2da268f0", "metadata": {}, "source": [ "With the response, we can decode the binary array results into the optimal price results" @@ -10741,21 +10783,21 @@ }, { "cell_type": "code", - "execution_count": 14, - "id": "c9e4edbc", + "execution_count": 17, + "id": "da02622c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "([12, 10, 13, 12, 13, 16, 19],\n", - " array([0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,\n", - " 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,\n", + "([13, 12, 12, 13, 10, 10, 19],\n", + " array([0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,\n", + " 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,\n", " 0, 0, 0, 0, 1], dtype=int8),\n", - " -12656.015625)" + " -12520.765625)" ] }, - "execution_count": 14, + "execution_count": 17, "metadata": {}, "output_type": "execute_result" } @@ -10776,7 +10818,7 @@ }, { "cell_type": "markdown", - "id": "cbd4d901", + "id": "2aa84683", "metadata": {}, "source": [ "The optimized price path and corresponding demand curve is plot below, respectively. The optimal price level is higher than the past 7 days, which results in the demand decreasing." @@ -10784,13 +10826,13 @@ }, { "cell_type": "code", - "execution_count": 15, - "id": "e8c5b283", + "execution_count": 18, + "id": "bbe4d6aa", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -10813,7 +10855,7 @@ }, { "cell_type": "markdown", - "id": "3cb7e9d7", + "id": "2d1b267b", "metadata": {}, "source": [ "__now, Let's get the demand of each day and the total revenue__" @@ -10821,24 +10863,24 @@ }, { "cell_type": "code", - "execution_count": 16, - "id": "46b3aceb", + "execution_count": 19, + "id": "717ef755", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "([185.94625963144793,\n", - " 175.81348574612934,\n", - " 157.99134281226168,\n", - " 147.97640607429904,\n", - " 138.06442038250634,\n", - " 120.33139363114194,\n", - " 95.84307132770529],\n", - " 13360.252420786914)" + "([182.33668654152052,\n", + " 165.36059160986585,\n", + " 152.14722973980318,\n", + " 139.58354691345133,\n", + " 143.67298125412577,\n", + " 148.40960793366366,\n", + " 121.5201742495238],\n", + " 13224.766093729508)" ] }, - "execution_count": 16, + "execution_count": 19, "metadata": {}, "output_type": "execute_result" } @@ -10850,13 +10892,13 @@ }, { "cell_type": "code", - "execution_count": 17, - "id": "51cf25d2", + "execution_count": 20, + "id": "5a12bfe2", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -10879,7 +10921,7 @@ }, { "cell_type": "markdown", - "id": "995deca7", + "id": "de5b6c2d", "metadata": {}, "source": [ "__Finally, let's get the overall uncertainty of the demand predictions, here we simply use demand variance to indicate the uncertainty__" @@ -10887,17 +10929,17 @@ }, { "cell_type": "code", - "execution_count": 18, - "id": "58a30355", + "execution_count": 21, + "id": "b2083cd3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "704.2370868054443" + "703.9977273152239" ] }, - "execution_count": 18, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" } @@ -10909,7 +10951,7 @@ }, { "cell_type": "markdown", - "id": "f4b9b007", + "id": "e226adb8", "metadata": {}, "source": [ "__We can also derive the standard deviation of the revenue based on the variance of demand__\n", @@ -10919,17 +10961,17 @@ }, { "cell_type": "code", - "execution_count": 19, - "id": "8e856169", + "execution_count": 22, + "id": "65d2d48b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "367.83167074590745" + "345.69772474444244" ] }, - "execution_count": 19, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } @@ -10950,7 +10992,7 @@ }, { "cell_type": "markdown", - "id": "e812bb27", + "id": "fae8b436", "metadata": {}, "source": [ "__We can investigate the value of the penality terms to see if any equality constraints are voilated. The penalty is close to zero showing that all the constraints are complied__" @@ -10958,17 +11000,17 @@ }, { "cell_type": "code", - "execution_count": 20, - "id": "9c7281cc", + "execution_count": 23, + "id": "1657334a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "-0.0002910185303335311" + "0.0027414142841735156" ] }, - "execution_count": 20, + "execution_count": 23, "metadata": {}, "output_type": "execute_result" } @@ -10980,7 +11022,7 @@ }, { "cell_type": "markdown", - "id": "1d76fe84", + "id": "fa267458", "metadata": {}, "source": [ "For comparison, to assess the quality of this optimized result, we also iterate (by brute-force search) through all the $7^7=823,543$ possible price solutions to obtain the energy for each one, which takes more than 5 minutes to run on a standard ml.m5.2xlarge AWS instance. We plot the distribution of the energies of all the 823,543 possible solutions as shown below, where the red line represents our optimized result obtained from the quantum annealer. We can see that although the optimized result from the quantum annealer is not the global optimum with minimum cost, it is close-to-optimal and of good quality. " @@ -10988,8 +11030,8 @@ }, { "cell_type": "code", - "execution_count": 21, - "id": "16f98180", + "execution_count": 24, + "id": "dbbe522c", "metadata": { "scrolled": true }, @@ -11849,13 +11891,13 @@ }, { "cell_type": "code", - "execution_count": 22, - "id": "4d5394c7", + "execution_count": 25, + "id": "ad63ad18", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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QlSRJUi8ZZCVJktRLBllJkiT1kkFWkiRJvWSQlSRJUi8ZZCVJktRLBllJkiT1kkFWkiRJvWSQlSRJUi8ZZCVJktRLBllJkiT1kkFWkiRJvWSQlSRJUi8ZZCVJktRLBllJkiT1kkFWkiRJvTTtIJtk30kMRJIkSZqOrWfwnMuT3AC8HzirqlbP8pgkzaGlx144J8dZdeLyOTmOJGnLMZOlBce227cB30jy90lemCSzOC5JkiRpo6YdZKvqpKr6GeBXgHOA/wFcCNyW5C+SLJ3VEUqSJEkjzPjDXlX1b1X1B8ATgFcBtwP/B7gpycVJfifJI2dpnJIkSdIGNvuqBVV1T1WdCfwW8JG2z+cBH6VZevD6JFtt7nEkSZKkrs0KskkekeQlSf4RuA04GPh/wO8DvwvcAJwIvHOK5x+X5PwktySpJKs2cbxdk3w8yZ1J7klyeZL9NzK2Y5LckGRdkq8nOTnJ9gu5b0mSJI1nRkE2ydOSnAh8A/gY8EvAu4CfqapfraqPVNX5VfVs4H3AQVN09VZgf+Bm4M5NHHMX4HPAPsBJwOuBHYCLkjxvxFNOAd4OXA8cBZwPvA64IMkGr3uB9S1JkqQxTPvyW0k+C+wLBLgM+GPgH6rq/imecjnw6in27VJVt7T9fpEm4E3lBGBH4JlVdW37nLOALwGnJdmtqqpt350mYK6oqgM6Y78VOBU4EDh3ofUtSZKk8c3kjOxuNGcjd62q51TV324kxAJcAjxn1I5BiN2U9i37lwCXDsJg+/y7gTOBpwF7dZ5yEE3QfsdQV2cAa2mWQCzEviVJkjSmmQTZJVX1+qq6cZziqlpdVZfN4DhdewDbAFeM2Hdlu+0Gwr2A9cBVQ2NZB1w7VLuQ+pYkSdKYZhJkn5jk16fameTXJ3At2Z3b7e0j9g3algzVr6mq+6ao3ynJogXY94OSHJFkZZKVq1d78zRJkqRhMwmyfwW8YSP7/xh4y8yGM6Xt2u2o8LhuqGbw9ajaUfULqe8HVdXpVbWsqpYtXrx4isNJkiRtuWYSZH8ZuGgj+y+muevXbFrbbrcZsW/boZrB16NqR9UvpL4lSZI0ppkE2ccD39rI/u8APzGz4UzpjnY76m34QVv37fs7aN7iHxUgl9AsDbi/U7tQ+pYkSdKYZhJkvwfsspH9TwF+MLPhTOk6mrfn9xmx71ntdmWn7Wqa17Z3tzDJtsCeQ7ULqW9JkiSNaSZB9nLg8CRPGN7Rth1Gc3evWdNeruoCYL8kz+gcb4f2eDey4VUEzgMKOHqoq8Np1qSes0D7liRJ0pimfUMEmg97/TrwH0lOprnkVAE/T/NBrx1o7ti1SUleDjy5/XYxsCjJG9vvb6uqszvlxwHPBS5OcgpwF014XAIs795UoKquS3IacGSSFcAngKfT3H3rMja8YcGC6VuSJEnjm3aQraprk/w28EGaW64OgliANcDLqmrct8sPBZ491Da44sFlwINBtqpuSrIvcCJwLLAIuAZ4YVVdMqLvo4FVwBHA8nZs7wKOr6r1Q69pIfUtSZKkMczkjCxV9c9JngT8D+CpNCH2K8DFVXXvNPrZb5rH/TLw0jFrHwBObh+96VuSJEnjmVGQBWgD68dncSySJEnS2GbyYS9JkiRp3s0oyCY5MMm/JflOkgdGPH442wOVJEmSuqa9tCDJ62k+uPRd4Mp2K0mSJM2pmayRfS3w78Bzp/PBLkmSJGk2zWRpwROAjxhiJUmSNJ9mEmRvAnac7YFIkiRJ0zGTIHsycGiSR8/2YCRJkqRxzWSN7APAd4AvJ/kAcGvbtoGqOmszxyZJkiRNaSZB9kOdr984RU0BBllJkiRNzEyC7HNmfRSSJEnSNE07yFbVZZMYiCRJkjQdm3WL2iTbJFmSZNFsDUiSJEkax0xvUfsLST4N/AD4GvDLbfvjk3wqyfNmcYySJEnSQ0w7yCbZE7gc2IWhD3RV1XeARwGvmJXRSZIkSVOYyRnZNwN3ALsDxwIZ2v8pYO/NHJckSZK0UTMJsr8CnFFVd9NcZmvY14CdN2tUkiRJ0ibMJMhuC3x/I/t/bIZjkSRJksY2k+vI3gw8cyP79weun9lw9HB35S3f5cBjL5zvYUiSpIeBmZyRPRd4+dCVCQogyR8DLwTOnoWxSZIkSVOayRnZvwaeD1wE3EATYk9Jshh4AvBJ4D2zNkJJkiRphGmfka2q+2mC7J8A9wLrgKcBa4A3AC+uqvWzOUhJkiRp2EzOyFJVPwROaR+SJEnSnNusW9RKkiRJ82XaZ2ST/P44dVV11qarJEmSpJmZydKCD9F8wGv4jl7DN0cwyEqSJGliZhJknzNFP7sArwHWAn+2OYOSJEmSNmXaQbaqLpti16eSfBi4CvgF4DObMzBJkiRpY2b1w15VdR/wEZozs5IkSdLETOKqBfcBSybQryRJkvSgWQ2ySX4SeDVw62z2K0mSJA2byeW3Pj3FrscBuwGLgFdszqAkSZKkTZnJVQt+modeaquA/wJWAO+uqs9t7sAkSZKkjZnJVQuWTmAckiRJ0rR4i1pJkiT1kkFWkiRJvTTtIJtkfZIHpvn44WwMNskOSf40yXVJfpBkTZLPJTkkSYZqd03y8SR3JrknyeVJ9p+i30ckOSbJDUnWJfl6kpOTbD9F/cT6liRJ0nhm8mGvs2ju3PWzwFeALwOhuWLBrsB1wDWzNcCBJI8A/gX4JeDDwLuA7YCDgA8CTwf+d1u7C/A54IfAScD3gcOBi5L8WlVdMtT9KcDrgI8BJ7d9vQ74+STPq6r1nXFMrG9JkiSNbyZB9hzgAOA3quqfujuS/AZwNvAnVfXJWRhf1y8Cvwy8o6qO6RzzPcANwKtogyxwArAj8MyquratOwv4EnBakt2qqtr23YGjgBVVdUCn31uBU4EDgXM745hk35IkSRrTTNbIvgV433CIBaiqjwOnA3+5uQMb4cfa7R1Dx7wfWAPcA9C+Zf8S4NJB0Gzr7gbOBJ4G7NXp4iCaM8rvGDreGcBa4OBBwyT7liRJ0vTMJMjuAdy8kf030Sw7mG1XAd8D3pDkZUme1K5VPQF4JvCmzvi2Aa4Y0ceV7bYbNvcC1rf9P6iq1gHXDtVOsm9JkiRNw0yC7J3ACzay/4U060ZnVVXdSXM29L+AvwNuo1lS8FrggKo6oy3dud3ePqKbQduSTtvOwJqqum+K+p2SLJqDvjeQ5IgkK5OsXL169agSSZKkLdpMguy5wEuTvD/J05Ns1T6enuQDwItp1tFOwt3AF4G/Bn4LOIzmDPC5SZ7f1mzXbkeFx3VDNYOvR9WOqp9k3xuoqtOrallVLVu8ePEUXUiSJG25ZvJhrzcCTwFeCRxC89Y5NKE4wAVtzaxK8nM0Vws4pqr+ptP+tzTh9oz2igJr213bjOhm23a7ttO2Fnj8FIcdrp9k35IkSZqGmdyi9j7gN5O8APgN4KdoAuzNwD9W1cWzO8QHHUMT/s4fGs/aJBcCRwJL+dGHwZbwUIO27tKAO4CfSbLNiCUAS2iWBtzfqZ1U35IkSZqGmZyRBaANrJMKraMMguJWI/Zt3dleR/N2/j4j6p7Vbld22q6mWfO7N3D5oDHJtsCewGc7tZPsW5IkSdOwWbeoTfKUJPsmecxsDWgjrm+3hwyNYUfgpTQfQru5vRTWBcB+SZ7RqduBZk3tjWx4FYHzgAKOHjre4TTrVx9c7zvJviVJkjQ9Mzojm+TFwDtp3soHeD7w6SSPp1nHemxV/f2sjPBH3gH8PnBiu17234DH0YTCnwReW1WDW+EeBzwXuDjJKcBdbd0SYPnghgUAVXVdktOAI5OsAD7Bj+6+dRkPvWHBJPuWJEnSmKYdZJPsR3O71WtpbhX7psG+qvpOkptp7lg1q0G2qm5LsjdwPE2QPBC4tx3HH1fVik7tTUn2BU4EjgUW0dw294UjbiELzRnTVcARwHKaGyy8Czh++Bayk+xbkiRJ45vJGdnjgS/Q3DL2sXSCbOsKmjOns66qbgZeMWbtl2mWHIxT+wBwcvuY174lSZI0npmskV0GnLORs4nfAJ4w8yFJkiRJmzaTILsVU1/kH2AnwEtKSZIkaaJmEmS/DPzKRva/mGbpgSRJkjQxMwmy7wd+O8mhnedXku2SnEpzjdXTZ2uAkiRJ0igzubPXe9tP7Z9B8wGmAv4W+HGaZQcfrCqvjypJkqSJmtF1ZKvq4CT/ABwM7EZzi9p/B86qqn+YxfFJkiRJI00ryCZ5FPAy4CtV9TGa68lKkiRJc266a2Tvo1lS8PMTGIskSZI0tmkF2fbasV8Hfmwyw5EkSZLGM5OrFnwYeHmSbWZ7MJIkSdK4ZvJhr88BvwVcm+Q9wI3A2uGiqvrsZo5NkiRJmtJMguwnO1+/k+byW11p27aa6aAkSZKkTRkryCbZG7ipqv4LeOVkhyRJkiRt2rhnZK8AXg6cW1UfTrIDzd27/rKqrp/Y6CRJkqQpjPthrwx9vw3wu8ATZnc4kiRJ0nhmctWCgeFwK0mSJM2ZzQmykiRJ0rwxyEqSJKmXpnP5rRclGayJ3Y7mElsvS7LniNqqqlM2e3SSJEnSFKYTZH+vfXS9aoraAgyykiRJmphxg+xzJjoKSZIkaZrGCrJVddmkByJJkiRNx0xuUStJ07b02AsnfoxVJy6f+DEkSQuHVy2QJElSLxlkJUmS1EsGWUmSJPWSQVaSJEm9ZJCVJElSLxlkJUmS1EsGWUmSJPWSQVaSJEm9ZJCVJElSLxlkJUmS1EsGWUmSJPWSQVaSJEm91Lsgm+RxSf46yU1J1iVZneQzSX5lqG7XJB9PcmeSe5JcnmT/Kfp8RJJjktzQ9vn1JCcn2X6K+on1LUmSpPFsPd8DmI4kTwYuBXYA3g98FXgMsAewpFO3C/A54IfAScD3gcOBi5L8WlVdMtT1KcDrgI8BJwNPb7//+STPq6r1c9G3JEmSxterIAt8hGbMe1TVNzdSdwKwI/DMqroWIMlZwJeA05LsVlXVtu8OHAWsqKoDBh0kuRU4FTgQOHeO+pYkSdKYerO0IMmvAr8MnFRV30zyyCTbjajbHngJcOkgaAJU1d3AmcDTgL06TzkICPCOoa7OANYCB89F35IkSZqe3gRZ4EXt9mtJLgDuBe5J8tUk3UC4B7ANcMWIPq5st92wuRewHriqW1hV64Brh2on2bckSZKmoU9Bdtd2ewbwOOAVwKHA/cDZSV7Z7t+53d4+oo9B25JO287Amqq6b4r6nZIsmoO+JUmSNA19WiP76Hb7A+A5VXU/QJKPAbcAb03yYWCw3GBUeFzXbrtLErabona4/v4J972BJEcARwA86UlPmqILSZKkLVefzsje227/dhBiAarqTuCfgCfQnLVd2+7aZkQf27bbtZ22tVPUjqqfZN8bqKrTq2pZVS1bvHjxFF1IkiRtufoUZL/Rbr81Yt/gCgaPBe5ov14yom7Q1l0acAfNW/yjAucSmqUB93dqJ9W3JEmSpqFPQXbwgaknjtg3aPsOcB3N2/n7jKh7Vrtd2Wm7mmYe9u4WJtkW2HOodpJ9S5IkaRr6FGQ/TrM+9uAkOwwak/wk8BvAjVV1U3sprAuA/ZI8o1O3A3AYcCMbXkXgPKCAo4eOdzjN+tVzBg2T7FuSJEnT05sPe1XVnUn+BHgfcGWSDwCLgD9st0d2yo8DngtcnOQU4C6a8LgEWD64YUHb73VJTgOOTLIC+AQ/uvvWZTz0hgWT7FuSJElj6k2QheYDUEnWAG8A3kJzjdYrgN+rqn/r1N2UZF/gROBYmqB7DfDCEbeQheaM6SqaqwQsB9YA7wKOH76F7CT7liRJ0vh6FWQBqmoFsGKMui8DLx2zzweAk9vHOPUT61uSJEnj6dMaWUmSJOlBBllJkiT1kkFWkiRJvWSQlSRJUi8ZZCVJktRLBllJkiT1kkFWkiRJvWSQlSRJUi8ZZCVJktRLBllJkiT1kkFWkiRJvWSQlSRJUi8ZZCVJktRLBllJkiT1kkFWkiRJvWSQlSRJUi8ZZCVJktRLBllJkiT1kkFWkiRJvWSQlSRJUi8ZZCVJktRLBllJkiT1kkFWkiRJvWSQlSRJUi8ZZCVJktRLBllJkiT1kkFWkiRJvWSQlSRJUi8ZZCECBEEAACAASURBVCVJktRLBllJkiT1kkFWkiRJvWSQlSRJUi8ZZCVJktRLBllJkiT1kkFWkiRJvWSQlSRJUi/1Osgm2S7JrUkqybtH7N81yceT3JnkniSXJ9l/ir4ekeSYJDckWZfk60lOTrL9FPUT61uSJEmb1usgC7wZ2GnUjiS7AJ8D9gFOAl4P7ABclOR5I55yCvB24HrgKOB84HXABUk2mKdJ9i1JkqTxbD3fA5ipJL8AHA28ATh5RMkJwI7AM6vq2vY5ZwFfAk5LsltVVdu+O03AXFFVB3SOcStwKnAgcO4c9S1JkqQx9PJsYJKtgDOAfwVWjNi/PfAS4NJB0ASoqruBM4GnAXt1nnIQEOAdQ12dAawFDp6LviVJkjS+XgZZ4BhgN+DIKfbvAWwDXDFi35Xtths29wLWA1d1C6tqHXDtUO0k+5YkSdKYehdkk/wU8BfAm6tq1RRlO7fb20fsG7QtGapfU1X3TVG/U5JFc9C3JEmSxtS7IAu8F7iV5sNTU9mu3Y4Kj+uGagZfj6odVT/Jvh+U5IgkK5OsXL169RRPlyRJ2nL1KsgmORh4AfDqqvrvjZSubbfbjNi37VDN4OtRtaPqJ9n3g6rq9KpaVlXLFi9ePMXTJUmStly9uWpBkm1ozsJ+AvhWkqe0uwZv4z+mbVsD3DG0r2vQ1l0acAfwM0m2GbEEYAnN0oD7O7WT6lvSZlh67IUTP8aqE5dP/BiSpPH06Yzso4DFwHLgxs7j0nb/we33hwHX0bydv8+Ifp7Vbld22q6mmYu9u4VJtgX2HKqdZN+SJEkaU5+C7D3Ay0Y8XtPu/9f2+39qL4V1AbBfkmcMOkiyA03QvZENryJwHlA016XtOpxm/eo5g4ZJ9i1JkqTx9WZpQbsm9u+H25Msbb+8uaq6+48DngtcnOQU4C6a8LgEWD64YUHb93VJTgOOTLKCZvnC02nuvnUZD71hwST7liRJ0hh6E2Snq6puSrIvcCJwLLAIuAZ4YVVdMuIpRwOrgCNoli+sAd4FHF9V6+eqb0mSJI2n90G2vZZsptj3ZeClY/bzAM2tbkfd7nZO+5YkSdKm9WmNrCRJkvQgg6wkSZJ6ySArSZKkXjLISpIkqZcMspIkSeolg6wkSZJ6ySArSZKkXjLISpIkqZcMspIkSeolg6wkSZJ6ySArSZKkXjLISpIkqZcMspIkSeolg6wkSZJ6ySArSZKkXjLISpIkqZcMspIkSeolg6wkSZJ6ySArSZKkXjLISpIkqZcMspIkSeolg6wkSZJ6ySArSZKkXjLISpIkqZcMspIkSeolg6wkSZJ6ySArSZKkXjLISpIkqZcMspIkSeolg6wkSZJ6ySArSZKkXjLISpIkqZcMspIkSeolg6wkSZJ6ySArSZKkXjLISpIkqZd6E2STPC3Jm5NcmWR1kh8kuTbJnyXZfkT9rkk+nuTOJPckuTzJ/lP0/YgkxyS5Icm6JF9PcvKofifdtyRJksbTmyAL/AFwDHAz8Gbg9cBXgL8EPpfkUYPCJLsAnwP2AU5qa3cALkryvBF9nwK8HbgeOAo4H3gdcEGSDeZokn1LkiRpfFvP9wCm4e+BE6rq+522v0lyI/BnwKHAu9v2E4AdgWdW1bUASc4CvgSclmS3qqq2fXeagLmiqg4YdJzkVuBU4EDg3M4xJ9m3pAVu6bEXzslxVp24fE6OI0l91pszglW1cijEDpzXbn8WoH3L/iXApYOg2T7/buBM4GnAXp3nHwQEeMdQv2cAa4GDBw2T7FuSJEnT05sguxFPbLffbrd7ANsAV4yovbLddsPmXsB64KpuYVWtA64dqp1k35IkSZqGXgfZJFsBxwM/5Edv0e/cbm8f8ZRB25JO287Amqq6b4r6nZIsmoO+JUmSNA29DrI0b9k/Czi+qr7Stm3XbkeFx3VDNYOvR9WOqp9k3xtIckSSlUlWrl69eoouJEmStly9DbJJ3gIcCZxeVSd0dq1tt9uMeNq2QzWDr0fVjqqfZN8bqKrTq2pZVS1bvHjxFF1IkiRtufp01YIHJXkT8Ebgg8Crh3bf0W6X8FCDtu7SgDuAn0myzYglAEtolgbcPwd9z7tJfxr7o7d8d6L9S5KkLUvvzsgm+XPgz4GzgMMGl7rquI7m7fx9Rjz9We12Zaftapp52HvoONsCew7VTrJvSZIkTUOvgmyS44E3AWcDr6yq9cM17aWwLgD2S/KMznN3AA4DbmTDqwicBxRw9FBXh9OsXz1nLvqWJEnS9PRmaUGS1wJ/AXwNuAT4vSTdkm9X1Sfbr48DngtcnOQU4C6a8LgEWN49i1tV1yU5DTgyyQrgE8DTae6+dRkPvWHBJPuWJEnSmHoTZPnRNVefBHx4xP7LgE8CVNVNSfYFTgSOBRYB1wAvrKpLRjz3aGAVcASwHFgDvIvmaggbnPWdZN+SJEkaX2+CbFUdAhwyjfovAy8ds/YB4OT2Ma99S5IkaTy9WiMrSZIkDRhkJUmS1EsGWUmSJPWSQVaSJEm9ZJCVJElSLxlkJUmS1EsGWUmSJPWSQVaSJEm9ZJCVJElSLxlkJUmS1EsGWUmSJPWSQVaSJEm9ZJCVJElSLxlkJUmS1EsGWUmSJPXS1vM9AEnSQy099sKJH2PVicsnfgxJmiTPyEqSJKmXDLKSJEnqJYOsJEmSeskgK0mSpF4yyEqSJKmXDLKSJEnqJYOsJEmSeskgK0mSpF4yyEqSJKmXDLKSJEnqJYOsJEmSeskgK0mSpF4yyEqSJKmXtp7vAUiS5sfSYy+ck+OsOnH5nBxH0pbHM7KSJEnqJYOsJEmSeskgK0mSpF4yyEqSJKmXDLKSJEnqJYOsJEmSesnLb82BJI8A/gh4FbAUWA38HXB8Vd0zj0OTpImbi8t8eYkvacvkGdm5cQrwduB64CjgfOB1wAVtyJUkSdI0eUZ2wpLsThNeV1TVAZ32W4FTgQOBc+dpeJIkSb1lkJ28g4AA7xhqPwM4ETgYg6wkbRaXL0hbJoPs5O0FrAeu6jZW1bok17b7JUkLnLf0lRYeg+zk7Qysqar7Ruy7HfilJIuq6v45HpckaQHy7LI0vlTVfI/hYS3JzcAjq+pJI/adBbwceGxVfW9o3xHAEe23uwJf2chhdgLWzM6ItRHO89xwnueG8zw3nOe54TzPjXHn+clVtXjSgwHPyM6FtcDjp9i3badmA1V1OnD6OAdIsrKqls1seBqX8zw3nOe54TzPDed5bjjPc2MhzrOXfpq8O4CdkmwzYt8SmmUHLiuQJEmaJoPs5F1NM897dxuTbAvsCaycj0FJkiT1nUF28s4DCjh6qP1wYDvgnFk4xlhLELTZnOe54TzPDed5bjjPc8N5nhsLbp79sNccSPIu4EjgY8AngKfT3Nnr34D9q2r9PA5PkiSplwyycyDJVjRnZI8AltJ84u884PiqunsehyZJktRbBllJkiT1kmtk50GSVyU5J8kNSR5IMuW/JpK8IslFSb6RZF2S1UmuSHJIe6Z31HN+P8l/JLk3ybeTnJlk5PXckuyc5Ky233uTrEzyso2MZ+y+59s05/klST7Y1t6T5I4klyR54Uae4zwz7XneNclfJ/l0ku8lqSRv2kT/zjPTm+e2fmJz8XCe56kk2SHJSUluTnJfkm+1fzOWTFG/YOa/T5I8Mslrkny+/RvxvSTXJPmjJItG1DvP05QmP9QmHkuGnrNw57mqfMzxA1gF/AD4LPD15j/DlLXvBD4KHAccCvwRcDHNB8jeP6L+mHbfpTRLGd4M3A18Cdh+qPZxwC3t/je39Ze2z3/l5vS9EB7TnOdvAV8F3gYcBrwB+HL7ev/MeZ61eT6E5pbNNwKfal/nmzZS7zzPbJ4nNhcP93meYj4fBXy+/dn9EPAq4MT2v8fXgCcs1Pnv24PmA9AF/D3whzSfL7mobTvPeZ6VOf5p4OARj9e3r+8/+jTP8z6hW+KDZp3sI9qv/5mN/A9pI31c2P5RfUKnbSfgHuAqYKtO+6+3PxR/OtTHSW37r3fatmqf/11gh5n2vRAe05lnmg/dDbdtR3NHtftp7r7mPG/+PD8O2LH9ehkbCbLO82bN88Tm4uE+z1PM59HteI8bav8lmr/DZy7E+e/bg+aW7gV8bKg9wOXtXHf/FjvPszv/x7Wv+bV9+nme94nb0h/MPMi+p/2Pv2un7bC27eUj6m8Grh9q+wZw04jal7f9/M5M+15oj82Y55Pb1/0s53l255lNB1nneYbzPMm52JLmuTPWf2xfxxNG7PsKzdmkRy20+e/bg+Z27AWcNmLf3wE/dJ4nNveheadsLe3Jhr7Ms2tkeyLJY5LslOSpSY4E/oDmrfCbOmV7tdsrRnRxJbBbkh3a/n6S5s5iV05R2+1vWn0/zDyx3X6n0+Y8zw3neQYmORdb8DwP7sz4kNuJt23bAz8LC27+++bm9vEHSQ5LsjTJLkn+F/BbwAlVdS84zxPwbOApwD9U1fcGjX2YZ4Nsf3wKWE0TXk+lWSf3a1X1QKdm53Z7+4jn307zL66dx6yF5gdsJn0/LCR5Bs0fz8ur6pbOLud5bjjPMzPJudhS5/lL7Xb/bmP7P+Ld2m//v3a7kOa/V6rqh8BLgC8CZwC30pysORE4qqr+T6fceZ5dh7bbM4faF/w8b72pAo2WZEceereujTm1qv5rMw75GuDHgJ8ElgM/ATx2qGa7dnvfiOevG6qZTu1M6mfFPMzz4LiLgRXAvTRvlXQ5z7M0z5vgPM9snic5F72Y56lsxvy/F3g18N4k29CcLXoyzYdDB1ePmYs5WlDzOZXN/Dm/l+Yt7quBT9O8nlcA705yT1Wd1dY5z7P096Tt5wCafzR8dmj3gp9ng+zM7Qj8+TTqPwLM+H/8VXVV59uzk5wAfDbJHlV1c9s+eNtrG5o/Bl3bDtV0a4cN106379k0p/MMkORxwCdp/rW4vKq+OlTiPM/CPI/BeZ7ZPE9yLvoyz1OZ0fxX1U1JltOcrfpoZ/8KmqsZ/CFwV9u2kOZ/vsxonpM8gSbAnllVxw52JvkI8P9owuwFVXUnzjPM3t+T36O5Msf7q12g2rHg59mlBTNUVauqKtN43LTpXqflwzT/Ujmk03ZHux11Kn4JzcLpO8ashQ1P90+n71kz1/PchthLaN4u/M2q+vSIMud59n+eR3GeZzbPk5yLXszzVDZn/qvqUuCpwO406wmfVFUH0HxKG+CGdruQ5n9ebMY8HwH8OHD+UH/rgX8AHg38QtvsPM/e35NDaT5I96ER+xb8PBtk++tR7fZxnbar2+0+I+p/EfhKtbfErapv0vyAPGtE7aBt5Uz67qskj6U5E7s7TYj91ylKnee54TzPwCTnYkuf52pcX1Wfraqvt8sM9qf51PVX25qFNP99Mwgvo272s3V36zzPjiR70vzj4MKq+tbw/l7Mcy2Ayz5syQ82chkdml/YH59i3wcYusQFsJjmNPy/M/r6bW8c6uNtTH39tjuBR8+074X22Ng8t/sfS/MW4X3AizfRl/M8w3keqt3U5bec55n/PE9sLrakeR7jv8Pg8nyHLMT579uD5oY/BbxnqP2RwBeA/wYe7zzP6py/e/h1jqhZ0PM875O4JT7a/6BvbB83DP7jto8jO3U70qwxORf4U5rT/39G8y+eonkLfKuhvv+43fcZmrdp/oLmGodfZujCwjRv4ayiuTvNX7T1n2mff+iIcY/d90J4jDvPbe3Kdv+5jL7jyU87z7Myz4/p7BtcC/nTnbY9nOdZmeeJzcXDfZ43Mv+fB/6a5q5er2t/bgt434jaBTP/fXrQfKD5lva1/BPwWpq7TX2hbTvJeZ7V+d6WZs3s7QxliT7N87xP5Jb4oFmHUlM8VnXqFtH8i/9qYA3NGpY7aRa9vxZ45BT9H9L+4q+juf7pB+j8K3aodglwdtv/OuAa4Hc3Mvax+57vx7jz3NZOVTd4HOI8z8o8L3WeJz/Pk56Lh/M8b+Q1nEZz+cO1NB/s+ixw0EbqF8z89+kBPJ7mLOGtNHdVHNwl6nAgzvOszvXvtX8//mqM2gU7z2k7kSRJknrFD3tJkiSplwyykiRJ6iWDrCRJknrJICtJkqReMshKkiSplwyykiRJ6iWDrCRJknrJICtpk5Lsl6SSHLKxti1lHPN53M2RZLskpyb5WpIHkqyaxb5XJbl0qO3S2TzGfEvyoSS1qbZN9FFJPjTrg5tl031d0+x7aTsPb5pE/9qyGGS1xeoEkakeP5zvMT5cJTm6DwEwyZ5J3pRk6XyPZZb8b+Ao4DyaO+8cPa+j0cNWG1bflGTP+R6LHt62nu8BSAvA3wKfGNG+fq4H0jOfBR4F/PcMnns0zf21PzSHx5yJPYE/By6lGe98jmU2PB+4rqpeP98D6anDgVfP9yB6YinN784q4NqhfbfR/O54skCbzSArwTVV9ZH5HkRXkkcB/11VC/YPfVWtp7kv9sQleXRV/WAuj7kpC2ks0/AE4GvzPYi+qqr/pl//cFmQqqro3++OFiiXFkhj6K7pSvLiJFcnWZfkm0neluQh/yhM8tQkZ7c197drCN+WZPuhug+1fS9O8oEk3wbuAZ7Y7t8jycVJ7kny3SQfTrJTd61dkp9ojzEykCd5T5L1SZ48xmt9aZL/aF/f15O8GXjkiLpR61XTLhv4zyQ/SHJXkq8keX+SR7Y1BTwZePbQUo6l7f5V7drKn09yUZLvA/851TGHxnRUkq+2Y/9qkqNG1DxkLeeovtv1ex9sd3+mM84PbWwsSbZPckKSm5Pcl+RbSc4anvvu85O8MsmX2vrbkrxh1Oub4jVvneR/J7m+fd3fTfKxJD/XqTmknfefYsN5f9Mm+n5N+7N3e/vz9c0kH5nEUovB3CZ5XpIrk6xt5+6dw78zbf3S9vfr2+283ZzkrUm2G6p7XJJT2v2D+fl8ktcP1f1+kquSfK/9XbslyTlJFndqplw3mub396y2/3uSfCrJz0/j9T+vnevvteP8zyRjn/0dZ/xt3a8m+WSS7ye5N8k1SQ4d8xgj1zxnaM1r+zvxmXb3Bzs/b5eOqu/0s8mf5eHnZ4y/x0l2T3J++3M8+J38TJLl47xuLWyekZVguyQ7jWi/v6ruGmp7EfAa4G+ADwAvBf4EuBN466AoyTOBTwPfA94H3A48A3gdsG+SZ7dnd7o+CXwLeAuwPXB3kqcCl9P8o/PUtp8XAf/SfWJVfTvJPwEHJDmyqr7XGcu2wEHAJVV128YmIslvAv9A83bgm2ne+nsl8OKNPa/jje3zLqCZowdowtNLgG1ozma9HDgFWAP8Vee5qztfP4lm/s5vx7PDGMc+iuaM4/uAH9C85lOTPK6q/mLM8XetAH4SOILmv+2X2/abp3pC+z/Qi4B9gb8HTgaeCvwh8IIky6rqG0NPezXwE8D7aX5eDgb+b5JvVNW5Y4zzHOB3aH5+3kszB68FrkjyK1X1HzTLIEbN+39uou8/Aa6k+dn7L+BngcOA/ZP8XFV9d4zxTccvAL8NnAGcBTyH5nfmZ5M8vz0LTpp/FFwFPIbmNX8V2A84jub367mddzPOB36V5ufiC8B2wG5t/dva/g4GPkzzu3Y8cC/Nz+CvAY9nw5/NqfwrzRy9iea/wZHAZ5PsU1Vf3NgTkxxB8/tyJc1/m3toloG8N8kum1oKMu74k/w68DGavzMn0/yeHAicmeSnq+rPxnid4/gsze/MnwKnt+MC+PYmnjfOz3LXJv8eJ/lxmr8ltHW3ATsBy4BfBC6c0SvUwlFVPnxskQ+a/5HVRh7/3Kld2rbdAyzttAf4IvDNob6/ANwAPHqo/Tfbfg7ptH2obfvIiDH+Xbtv36H289r2D3XaXtC2vWao9n+27b+zifnYiuZt5zXATp32x9D88R8e934j2q4Brh9j7lcBl25kXwGHbeS/2ahx/AB4Yqd9EU3Y+e+h9pHHnqLvQ9q2/casP7xtO2modnnbfvaI598B7Nhp344meFwxxjw+v+3jPCCd9j1o/hFy+bjzPkX/249oe257zDdsqm/atcVjHmvwe/cbQ+3vbNsP7LSd07a9aKj2bW37oZ2f3QLes4lj///tnX+MHVUVxz9fWikBkUKtUhGhLQhFMUADqGCICEglRiBNjOU3SBRCotgIpWoCEqGgJBJ+pIFSirUEMdjFVgRaqyBEClJ+U6BAMZCia1tCpVSalOMf587udPa+92bf7tp95HySyezeOXPnzp1775w599zzfgdsAEa2kJtHmhmvpqU8ys9gMu5nf2/mPsv9dhw+zX575nrX4h+DEwdafrx//wP/WPpEpZ88nK6zb4t7zT5PesfHS5v1jxbytdsy/RiP8Y/oluNfbJ27hWtBELjF4NjMlrNOdJnZa8U/5iPln4HdJX0YIE2DfQ64HRgldwP4aLL6PoQPvsdl8v5F+R9JI3CLw6Nm9nBF9prM+UuA1UB1mvAcYB3QlTmnzGRgT+BWM1tbuse3cUtGHd4G9pB0ZE35Rqynd1q/LgusZO00s824BXIk8PUBlqcuJ+HKy5XlRDP7A77g5RuSquPurVayoJvZu7hlbt+a1wP4WWqLRR5PA4uBI6tTy/3BzDYCSNpO0i6pDT+FP+fD2823CS+aWbWdzkr7k4qy4MrJE2ZWXaR5JV7/Rb1sAt4DDldzd4i38Q+IEySpzbJfXXkGj+N98phibGjAVHy24pbyWJHqehE+G/OVFteuU/7JuJV2rpmtKZVzM/4BsB1u0dxWtNOWW47HeN0ATJH0kSEpebBNCUU2CGCVmS3NbE9lZF/NpBXTq2PSflLaX4Zb1spbN+428PFMPi9V/h+bZF/MyPZJS4P4HOAQpZA3kibglpH56YXVjAlp/0Lm2PMtzi2YiVuX/pr80RZImiZp+5rnF7xiZlv6ec7KTFpR7gmZY0PBeGCNmb2VOfYcsDM+rVmmUZsak0nPXe998vf+bEmmLSQdnfwaN+KWvKId7wLs2m6+TehzH2b2Zrp28QzH4q4mz2Vk1wNvFrKpzX8fd4lYLfdDvk5SVTG8ArdWdgH/lnSXpG9L2nkgZcfb3wjcJ7wRxXixlL7jxZJ0LDdelKlT/qId9Kk3etvK/6uf5GinLbccj83sAdxN5UxgraSHJV0m6YABlzgYFoQiGwT9o5lypcr+GvKW3mOBPot5kiUul1+ORoHK5+LTcIVV9uyUz5wmeVWvl8u7lpXKzP4GTMStTAvx8FULgCcl7VYnj0S1LmpdPpOWK3ejuhuMNQPtWPP6q7AP9Hr1MpYOBe7H/RRn4Na64/D2u46heX80ejZq8HfrDM1m41PR5+KuL1OBpZLuKMmsAg7AXUBuwxXPm4EXJE3sz/WalLuVzOk0Hi8WNMugZvkHo610Ut/pyc/MzgAOxH341wHTgaclXdDGNYNhRiz2CoLBZ1XabzGzpQPIpxu3hO2XObZ/7gQz+6ekRcApkmYAZwDLzSxnhalSLGKalDmWS8tiZu/gC7TuAl/5DtyAK9c/L8Tq5tcPchaWotxly816IKdU56xR/S3nK8DxkkaX3QVK5duA+yAPFq8AX8Xvs7pwq6iP1W3mPQ23Jk4xs5485BEEhsIaC5lnKGkcbgEunmE37g/9mYzsrrjP6VZxS5NVdw6+qGkEMB/4lqRrzOyxJPMeHk/6npTX1/CFQD/AFxy1YhLuElJN24JbSxtRjBdrBzJe1Ch/0b/71Bu99Z6zcJZZj7soVBmsvjNUbRnzBXfPAldLGg0sB2ZJuqHsyhB0HmGRDYLB5wl8wPxumtrfihRipqV1Mk2t/xE4TNIRlcPTm5x6M65ozMZDeNWxxgI8DrwBnFWO4pD8ymqFAWoQ/WFF2pfv+R3yyuRAOEXSJ0tl2R64EFckFpfkXgL2l7RHSXYUeWXlnbSvW9YufFydUU6UNAU4GPi9pZX3g0ThT3pJ2TdS0mdxP9KHzKzOivschbWraimbydC9O/aTdGIl7eK074Ke+L2LgIMlHV+RnZHKthB6fpJ3q3BcqV8VitJuSa5uu23GRZVncAhwDPCn9HHXiDtxP97L5PGjtyL5Jo9qduGa5V+BL+Y8S9LupXM/BPwQVzzvbnYdvO/sLOmw0vnb4f2sSjt9Bwa5LcvDr23VXtNH5mrcr3iH/uYZDC/CIhsE7lN6aoNjXS1eQn0wM5N0Gh7y5WlJc3G/tB2BfYCT8TBB82pk92PcSnGvpOtxRfME3E8Q8laP+3AL0Km4RfeOjEyu3FskXYi/WB+VdDPupnA2Ph33qRrZrJT0CG7tWENv+KrNlXI8Apwj6XLcJ+59YFGxuKhNXgKWS5qNW+ymAYcCl5vZ6yW56/GQQ0uT7PZ4aKqcO8NjqWw/Sta+jcBqM1veoAzzcCv4xWlx0YP4Mz8fDz00cwD31wczWyLpTvx+dpW0mN6QRf/FQ1e1y0JcQblH0k34MzwWX8g4mFblMs8Av05tbxUefmsq8AC+mr1gZipLl6QbgZfxEFvfxOv8tiT3aeABSQvxj8u3cIvfebgiU4SFul8er/hB4HVgNL0RK+bXLPtewH3yMHjj8PBbm3AlsSFm9oak8/APzpWS5uP9dyw+HX4ibpF8rUk2Lcuf+vcF+HN9LD3T/+B19nngiuSi0Iyb8I/ohZKuxdvEVPK6xPMp//MlvYv7OXeb2bKM7FC25dOBC1MbeBmPYnIUPq7eaWab2sw3GC5s67AJscW2rTZah98yYJ8kuzeVcDGlfC5Nx/aupO+FW0Vfwwf8dbjV80pgz5LcPCphbir5HIQvBHkXn9r7Fb7ooWFYIeAn6fgtbdTLyfjU7Hv4S/FyekPjnJmpv3LaDPxl2l06/7fAIZVrfAx3PViPK4o99Ufz0Fy5a/ak4S+7Venaq4DvNcjnDHzB3GZcobkIOLqad0n2+STbEzopV5aUvlN6xq+mc7pxZWKvVvdSt01UZEfiVsuV6b7X49atAzOyDeu2Qd4ndEsoZwAAAapJREFUpja7EVde78A/aPrk0yDtL/Qv/NY83Iq5HFcC/wVcRyWMXZIfn+q1O9Xzq/iipx1LMmPwyBVP4orUJlyZ+SUwriR3Lr1xnDfjC8buAb7c6rnQG35rbCrPOryvLgMmN7rPTPoRuJJZ3M8afAX+dGCHFnVXq/xJ9qgkuwFXEJ8gH+ou2wbxSCrF+LAGuAp3f+ozPibZFek6VrQPGoyn1GzLjc5Pxy5l6/HkIPzD5mW8HW/AI29MB0bV7QuxDd9N6UEHQdBByH9w4e/AJWY2K3P8IvwF80XzBVhBMKyR/2LWbWZ25rYuSxAEnUP4yAbBMKfqN5f8x4qoB0sy8iOB7wDPhBIbBEEQfJAJH9kgGP48KWkZ7j+4Ex7c/0vAb8yDrgMgaTzwBTxM0gT8J1qDIAiC4ANLKLJBMPy5G1deT8P77GrcB/aqitxR+K9hrQV+ama1FnkFQRAEQacSPrJBEARBEARBRxI+skEQBEEQBEFHEopsEARBEARB0JGEIhsEQRAEQRB0JKHIBkEQBEEQBB1JKLJBEARBEARBRxKKbBAEQRAEQdCR/A+yVJmL0EksagAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] @@ -11879,7 +11921,7 @@ }, { "cell_type": "markdown", - "id": "70060d44", + "id": "2af769de", "metadata": {}, "source": [ "# 4. Trade-off between expected revenue and prediction uncertainty." @@ -11887,7 +11929,7 @@ }, { "cell_type": "markdown", - "id": "9a036ec9", + "id": "a6b10fec", "metadata": {}, "source": [ "Let's first wrap above price optimisation into a single main function for convenience." @@ -11895,28 +11937,28 @@ }, { "cell_type": "code", - "execution_count": 25, - "id": "e55a4aee", + "execution_count": 35, + "id": "f89fc742", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "(12925.152201999756,\n", - " 708.9643434504553,\n", - " -12216.1875,\n", - " [160.67924800195595,\n", - " 145.95810387141424,\n", - " 148.66838060210074,\n", - " 129.4218983001543,\n", - " 158.66460202317302,\n", - " 149.53560711991358,\n", - " 132.71037020072518],\n", - " [19, 12, 8, 16, 5, 13, 16],\n", - " 359.36452646566903)" + "(13338.581109728268,\n", + " 703.6300560847318,\n", + " -12634.953125,\n", + " [182.33668654152052,\n", + " 165.36059160986585,\n", + " 159.36637591965803,\n", + " 156.8797620960508,\n", + " 152.12745944263415,\n", + " 147.77084364608078,\n", + " 116.98084569202341],\n", + " [13, 12, 10, 10, 12, 12, 19],\n", + " 341.94199709111217)" ] }, - "execution_count": 25, + "execution_count": 35, "metadata": {}, "output_type": "execute_result" } @@ -11942,7 +11984,7 @@ }, { "cell_type": "markdown", - "id": "71edac8a", + "id": "56faf584", "metadata": {}, "source": [ "In order to investigate the trade-off between the expected revenue and prediction uncertainties, we vary the knob parameter $\\beta$ within a large range of $[1e2,1e9]$ and run multiple experiments on D-Wave with different $\\beta$ values. The scatter plot are shown below, where each dot represents the optimized result of an experiment with x-axis representing its expected revenue and y-axis representing the estimated standard deviation of revenue $std(R)$. The standard deviation of revenue can be derived from the estimated variance of the predicted demand:\n", @@ -11952,8 +11994,8 @@ }, { "cell_type": "code", - "execution_count": 26, - "id": "a2bab81e", + "execution_count": 36, + "id": "c899d278", "metadata": { "scrolled": true }, @@ -11964,436 +12006,436 @@ "text": [ "---\n", "beta_sample:100.0\n", - "max_revenue:12570.821217355566\n", - "prediction_variance:709.1535902008336\n", - "energy:58344.5390625\n", - "opt_demand:[211.2132712609399, 191.23057526113467, 150.76974010686075, 111.64710090455874, 110.4335108482119, 113.53949847915052, 110.45368052927205]\n", - "opt_prices:[5, 12, 19, 19, 10, 12, 16]\n", - "rev_std: 375.71388263106917\n", - "penalty_term: 0.001259772208868526\n", + "max_revenue:13344.971150411837\n", + "prediction_variance:705.3216713996405\n", + "energy:57187.1875\n", + "opt_demand:[182.33668654152052, 179.79888396957557, 150.6439292057279, 156.64118153572883, 148.8564279708053, 130.57018515611858, 105.12477557318046]\n", + "opt_prices:[13, 8, 16, 8, 12, 16, 19]\n", + "rev_std: 364.1707583850488\n", + "penalty_term: -0.008489552208629902\n", "---\n", "beta_sample:1000.0\n", - "max_revenue:11897.632624523101\n", - "prediction_variance:702.4293109302826\n", - "energy:690531.671875\n", - "opt_demand:[193.16540581130278, 182.28098165894653, 182.0115887610362, 164.6248798227977, 151.5282109438208, 157.58974397197392, 164.54598849881108]\n", - "opt_prices:[10, 10, 8, 13, 13, 8, 8]\n", - "rev_std: 270.65194226099476\n", - "penalty_term: -0.006430759443901479\n", + "max_revenue:13078.512262531649\n", + "prediction_variance:702.8956246094274\n", + "energy:689817.109375\n", + "opt_demand:[193.16540581130278, 189.5001278388014, 174.04079231414366, 168.49098776608298, 164.20272014093717, 140.96094702759993, 122.50346515166794]\n", + "opt_prices:[10, 8, 12, 10, 10, 16, 16]\n", + "rev_std: 320.1714516345594\n", + "penalty_term: -0.0029718957375735044\n", "---\n", "beta_sample:10000.0\n", - "max_revenue:12980.87742870795\n", - "prediction_variance:702.8461008421212\n", - "energy:7015480.1328125\n", - "opt_demand:[193.16540581130278, 175.06183547909168, 168.32494666836413, 152.18500341084314, 145.07609647822775, 147.74845142226496, 129.2768226162399]\n", - "opt_prices:[10, 12, 10, 13, 12, 10, 16]\n", - "rev_std: 318.9774967063375\n", - "penalty_term: 0.0018199952319264412\n", + "max_revenue:11847.00605735832\n", + "prediction_variance:702.2879419564052\n", + "energy:7011032.40625\n", + "opt_demand:[185.94625963144793, 175.81348574612934, 161.6009159021891, 165.64844639041735, 172.03346790734656, 179.36613265907062, 178.19207178387035]\n", + "opt_prices:[12, 10, 12, 8, 8, 8, 10]\n", + "rev_std: 261.2157278976442\n", + "penalty_term: -0.007256694138050079\n", "---\n", "beta_sample:100000.0\n", - "max_revenue:12474.432120127967\n", - "prediction_variance:702.0711166209728\n", - "energy:70194637.2265625\n", - "opt_demand:[193.16540581130278, 182.28098165894653, 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157.98487904469658]\n", + "opt_prices:[10, 5, 8, 10, 10, 10, 13]\n", + "rev_std: 256.93398684116414\n", + "penalty_term: 0.0101470947265625\n", "---\n", "beta_sample:1000000000.0\n", - "max_revenue:11477.05591528449\n", - "prediction_variance:701.6709165846278\n", - "energy:701670905107.5703\n", - "opt_demand:[200.38455199115765, 188.74847757176371, 187.98396926017358, 186.7620523288179, 180.29225726552573, 176.14748113921195, 178.01614585978547]\n", - "opt_prices:[8, 10, 8, 8, 10, 10, 8]\n", - "rev_std: 236.0709905568157\n", - "penalty_term: -0.0015869140625\n" + "max_revenue:12396.538139042514\n", + "prediction_variance:702.4360114890887\n", + "energy:702435999092.5469\n", + "opt_demand:[185.94625963144793, 175.81348574612934, 176.0392082618988, 164.14514585634205, 163.8240909001321, 169.13248986074478, 156.74553244194385]\n", + "opt_prices:[12, 10, 8, 12, 10, 8, 13]\n", + "rev_std: 280.6743822723691\n", + "penalty_term: -0.0037841796875\n" ] } ], @@ -12429,7 +12471,7 @@ }, { "cell_type": "markdown", - "id": "b2172f27", + "id": "2937d192", "metadata": {}, "source": [ "We can see from the plot below that there is Pareto front where the expected revenue cannot be increased without increasing the standard deviation (i.e. uncertainties), and the other way around.\n", @@ -12439,8 +12481,8 @@ }, { "cell_type": "code", - "execution_count": 27, - "id": "d66a8636", + "execution_count": 37, + "id": "650d95d3", "metadata": {}, "outputs": [], "source": [ @@ -12459,13 +12501,13 @@ }, { "cell_type": "code", - "execution_count": 28, - "id": "ad1da38c", + "execution_count": 38, + "id": "595c046d", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -12489,7 +12531,7 @@ }, { "cell_type": "markdown", - "id": "a2b578b7", + "id": "fdfe1f51", "metadata": {}, "source": [ "# 5. Conclusion" @@ -12497,7 +12539,7 @@ }, { "cell_type": "markdown", - "id": "3c85c279", + "id": "1c4fced3", "metadata": {}, "source": [ "In this blog, we demonstrate how to leverage a quantum annealer on Amazon Braket to solve a price optimization use case. We showed how to mathematically formulate the problem within the (quantum-ready) QUBO framework, and then subsequently solve the optimization problem on a D-Wave quantum annealer. Our results are promising in terms of both close-to-optimal quality and computational efficiency. Since the QUBO formalism is a generalized framework that can embrace a variety of combinatorial optimization use cases (e.g. scheduling/planning, routing, portfolio management), the proposed solution can be arguably adapted and recycled by customers across other multiple industries. Already today our customers can get quantum-ready, and easily leverage Amazon Braket to help solve their daily combinatorial optimization challenges, and make better business and operation decisions." @@ -12505,7 +12547,7 @@ }, { "cell_type": "markdown", - "id": "bd9a23f8", + "id": "1e71d3d8", "metadata": {}, "source": [ "# 6. References:\n", @@ -12523,7 +12565,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2e2f2f72", + "id": "c6feedec", "metadata": {}, "outputs": [], "source": [] diff --git a/examples/price_optimization/qubo_dynamic_pricing.py b/examples/price_optimization/qubo_dynamic_pricing.py index 1681bec69..6a0525aae 100644 --- a/examples/price_optimization/qubo_dynamic_pricing.py +++ b/examples/price_optimization/qubo_dynamic_pricing.py @@ -203,7 +203,7 @@ def dwave_solver(obj): num_shots = 10000 sampler = BraketDWaveSampler(('amazon-braket-481358cc730d', 'qubo'), - 'arn:aws:braket:::device/qpu/d-wave/Advantage_system1') + 'arn:aws:braket:::device/qpu/d-wave/Advantage_system4') sampler = EmbeddingComposite(sampler) response = sampler.sample(model, num_reads=num_shots) return response From 200b252edd31ea6105ee83906cce37abd9509954 Mon Sep 17 00:00:00 2001 From: FengShi0705 Date: Wed, 1 Dec 2021 22:11:45 +0000 Subject: [PATCH 03/13] Move to quantum annealing folder --- .../{ => quantum_annealing}/price_optimization/QUBO-Pricing.ipynb | 0 .../price_optimization/qubo_dynamic_pricing.py | 0 2 files changed, 0 insertions(+), 0 deletions(-) rename examples/{ => quantum_annealing}/price_optimization/QUBO-Pricing.ipynb (100%) rename examples/{ => quantum_annealing}/price_optimization/qubo_dynamic_pricing.py (100%) diff --git a/examples/price_optimization/QUBO-Pricing.ipynb b/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb similarity index 100% rename from examples/price_optimization/QUBO-Pricing.ipynb rename to examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb diff --git a/examples/price_optimization/qubo_dynamic_pricing.py b/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py similarity index 100% rename from examples/price_optimization/qubo_dynamic_pricing.py rename to examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py From 6c7438fd404c94c4f58bfeb835f96a6e99af1a66 Mon Sep 17 00:00:00 2001 From: feng shi Date: Fri, 3 Dec 2021 21:47:33 +0000 Subject: [PATCH 04/13] Setting S3 folder in script, remove blog reference --- .../price_optimization/QUBO-Pricing.ipynb | 20932 ++++++++-------- .../qubo_dynamic_pricing.py | 7 +- 2 files changed, 10471 insertions(+), 10468 deletions(-) diff --git a/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb b/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb index 76b882d06..0af7e7f0b 100644 --- a/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb +++ b/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb @@ -2,19 +2,19 @@ "cells": [ { "cell_type": "markdown", - "id": "5eb1203e", + "id": "7db71c1a", "metadata": {}, "source": [ "# Using quantum annealing on Amazon Braket for price optimization\n", "\n", "Combinatorial Optimization is one of the most important fields in optimization. Practical applications can be found in virtually every industry. Prominent examples include supply chain optimization in transport and logistics, portfolio management in finance, and the optimization of clinical trials in healthcare, among many others. It is also one of the most active research topics in operation research and computer science. However, many practical combinatorial optimization problems are NP-hard and require massive computation costs to find solution of good quality. \n", "\n", - "In this blog post, we demonstrate how a quantum annealer on Amazon Braket can be used for price optimization taking into consideration the trade-off between maximizing revenue and minimizing risk. We showcase how to formulate this problem as a quadratic unconstrained binary optimization problem (QUBO) and use D-Wave Systems Inc. Advantage quantum annealer on Amazon Braket to find close-to-optimal solutions. Overall, this blog demonstrates that customers can easily leverage quantum computing through Amazon Braket to solve difficult combinatorial optimization challenges in their daily decision-making process." + "In this notebook, we demonstrate how a quantum annealer on Amazon Braket can be used for price optimization taking into consideration the trade-off between maximizing revenue and minimizing risk. We showcase how to formulate this problem as a quadratic unconstrained binary optimization problem (QUBO) and use D-Wave Systems Inc. Advantage quantum annealer on Amazon Braket to find close-to-optimal solutions. Overall, this notebook demonstrates that customers can easily leverage quantum computing through Amazon Braket to solve difficult combinatorial optimization challenges in their daily decision-making process." ] }, { "cell_type": "markdown", - "id": "ecdbe31f", + "id": "115f30aa", "metadata": {}, "source": [ "# Table of content\n", @@ -35,7 +35,7 @@ }, { "cell_type": "markdown", - "id": "4de37df8", + "id": "df21764a", "metadata": {}, "source": [ "We start by importing important libraries related to Amazon braket and" @@ -44,7 +44,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "a2820991", + "id": "d87b667a", "metadata": {}, "outputs": [ { @@ -53,10 +53,10 @@ "text": [ "Requirement already satisfied: sklearn in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (0.0)\n", "Requirement already satisfied: scikit-learn in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from sklearn) (1.0.1)\n", + "Requirement already satisfied: joblib>=0.11 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.1.0)\n", "Requirement already satisfied: scipy>=1.1.0 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.5.2)\n", - "Requirement already satisfied: threadpoolctl>=2.0.0 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (3.0.0)\n", "Requirement already satisfied: numpy>=1.14.6 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.19.2)\n", - "Requirement already satisfied: joblib>=0.11 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.1.0)\n" + "Requirement already satisfied: threadpoolctl>=2.0.0 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (3.0.0)\n" ] } ], @@ -67,7 +67,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "e07925ae", + "id": "0d861ad7", "metadata": {}, "outputs": [], "source": [ @@ -94,7 +94,7 @@ }, { "cell_type": "markdown", - "id": "3902f38c", + "id": "d9125a9d", "metadata": {}, "source": [ "__NOTE__: Enter your S3 bucket and key below. " @@ -103,7 +103,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "8fbfb24b", + "id": "9d95206b", "metadata": {}, "outputs": [], "source": [ @@ -115,8 +115,8 @@ }, { "cell_type": "code", - "execution_count": 4, - "id": "5a1a0cd6", + "execution_count": 5, + "id": "096e6b68", "metadata": {}, "outputs": [ { @@ -135,7 +135,7 @@ }, { "cell_type": "markdown", - "id": "eaed10f7", + "id": "100a23e0", "metadata": {}, "source": [ "# 1. Demand model" @@ -143,7 +143,7 @@ }, { "cell_type": "markdown", - "id": "e6ffce04", + "id": "359646ca", "metadata": {}, "source": [ "The usual goal of price optimization is to maximize the revenue in the next certain period, where the revenue can usually be represented by a function of demand and price: \n", @@ -157,7 +157,7 @@ }, { "cell_type": "markdown", - "id": "9f0cfee4", + "id": "a20fc0ee", "metadata": {}, "source": [ "## 1.1 Create training dataset" @@ -165,7 +165,7 @@ }, { "cell_type": "markdown", - "id": "65b9ad30", + "id": "a9deb8e4", "metadata": {}, "source": [ "For simplicity, we create a dummy dataset on historical demand and price observations so that a demand estimation model can be trained. \n", @@ -182,8 +182,8 @@ }, { "cell_type": "code", - "execution_count": 5, - "id": "f367cc06", + "execution_count": 6, + "id": "16b1f48a", "metadata": { "scrolled": true }, @@ -258,7 +258,7 @@ }, { "cell_type": "markdown", - "id": "a2e76585", + "id": "302e1103", "metadata": {}, "source": [ "## 1.2. Fit the demand model" @@ -266,7 +266,7 @@ }, { "cell_type": "markdown", - "id": "bf76f8d4", + "id": "6b87f767", "metadata": {}, "source": [ "By using the created training dataset, we simply using sklearn to fit a linear demand model. This fitted linear demand model will be used for the following price optimization problem. We round the model coefficents to integer for simplicity to fit with the below QUBO format (quadratic unconstrained binary optimization). " @@ -274,8 +274,8 @@ }, { "cell_type": "code", - "execution_count": 6, - "id": "9a7052bb", + "execution_count": 7, + "id": "da72c96b", "metadata": {}, "outputs": [ { @@ -306,7 +306,7 @@ }, { "cell_type": "markdown", - "id": "d5e39096", + "id": "a8cbe45b", "metadata": {}, "source": [ "# 2. Price optimization with QUBO" @@ -314,15 +314,15 @@ }, { "cell_type": "markdown", - "id": "4ff66481", + "id": "bf96e228", "metadata": {}, "source": [ - "In this blog, we leverage a general-purpose mathematical framework: Quadratic Unconstrained Binary Optimization (QUBO), which has been recently proposed as an effective framework that is able to generalize across a large variety of combinatorial optimization use cases in industries [2, 3]. We take this price optimization as an example and showcase how to formulate it into QUBO framework considering prediction uncertainties as well as equality constraints." + "In this notebook, we leverage a general-purpose mathematical framework: Quadratic Unconstrained Binary Optimization (QUBO), which has been recently proposed as an effective framework that is able to generalize across a large variety of combinatorial optimization use cases in industries [2, 3]. We take this price optimization as an example and showcase how to formulate it into QUBO framework considering prediction uncertainties as well as equality constraints." ] }, { "cell_type": "markdown", - "id": "d2e51ab6", + "id": "d6d45322", "metadata": {}, "source": [ "The formal definition of QUBO is expressed as an optimization problem, Minimize:\n", @@ -331,7 +331,7 @@ }, { "cell_type": "markdown", - "id": "61516668", + "id": "45a87632", "metadata": {}, "source": [ "Where $x$ is a vector of binary variables representing the decision variables of the combinatorial optimization. $Q$ is a squared matrix of constants inherently encoding the context and constraints of the optimization problems. $Q$ is commonly assumed to be symmetric or upper triangular without loss of generality. The goal is to find the optimal values of the binary decision variables $x$ that minimize the objective $H$.\n", @@ -341,7 +341,7 @@ }, { "cell_type": "markdown", - "id": "308e19ca", + "id": "a7753b90", "metadata": {}, "source": [ "## 2.1 Construct objective function" @@ -349,7 +349,7 @@ }, { "cell_type": "markdown", - "id": "f9b43ce8", + "id": "e083a37b", "metadata": {}, "source": [ "Assuming tomorrow is day $T$, then the goal of our price optimization is to find the optimal prices $p_t, t\\in[T, T+1, \\ldots, T+n-1]$ in the next $n$ days in order to maximize the revenue in next $n$ days. Based on the demand model we showed above where the demand at a day is correlated with the latest $n$ days' price, we can construct objective function as below:\n", @@ -363,8 +363,8 @@ }, { "cell_type": "code", - "execution_count": 7, - "id": "75a3ed9f", + "execution_count": 8, + "id": "8243b21d", "metadata": {}, "outputs": [ { @@ -373,7 +373,7 @@ "[10, 8, 8, 5, 5, 8, 8]" ] }, - "execution_count": 7, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -385,7 +385,7 @@ }, { "cell_type": "markdown", - "id": "6e227359", + "id": "18802866", "metadata": {}, "source": [ "Now, let's construct the objective function which is the total revenue $R$ in the next $n$ days.\n", @@ -397,8 +397,8 @@ }, { "cell_type": "code", - "execution_count": 8, - "id": "61d3e818", + "execution_count": 9, + "id": "adbadd2e", "metadata": {}, "outputs": [ { @@ -420,7 +420,7 @@ " (Binary(X_048)*Num(19.000000)+Binary(X_047)*Num(16.000000)+Binary(X_046)*Num(13.000000)+Binary(X_045)*Num(12.000000)+Binary(X_044)*Num(10.000000)+Binary(X_042)*Num(5.000000)+Binary(X_043)*Num(8.000000))]" ] }, - "execution_count": 8, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -447,7 +447,7 @@ }, { "cell_type": "markdown", - "id": "8314d7be", + "id": "19373b02", "metadata": {}, "source": [ "Next, we can input the price variables into our fitted model to estimate the demand, and then use the demand together with price to represent revenue $R$." @@ -455,8 +455,8 @@ }, { "cell_type": "code", - "execution_count": 9, - "id": "ece4710c", + "execution_count": 10, + "id": "43cb9f33", "metadata": {}, "outputs": [ { @@ -502,7 +502,7 @@ }, { "cell_type": "markdown", - "id": "f5bf5be9", + "id": "d9a5e5b8", "metadata": {}, "source": [ "## 2.2 Add penalty for prediction uncertainty" @@ -510,7 +510,7 @@ }, { "cell_type": "markdown", - "id": "ef843b0b", + "id": "f4a146fa", "metadata": {}, "source": [ "In optimisation, we usually desire to reduce the risk while maximizing the reward, which means we want to reduce the estimated uncertainty/variance of the predicted demands. Therefore, we add a penalty term in the objective function to represent the uncertainty of the predicted demand. The uncertainty of the predicted demand $d_t$ can be represented by its estimated variance.\n", @@ -532,8 +532,8 @@ }, { "cell_type": "code", - "execution_count": 10, - "id": "780f571a", + "execution_count": 11, + "id": "a912ae7e", "metadata": {}, "outputs": [ { @@ -542,7 +542,7 @@ 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] }, - "execution_count": 10, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } @@ -580,7 +580,7 @@ }, { "cell_type": "markdown", - "id": "eb9dae80", + "id": "9f23641a", "metadata": {}, "source": [ "## 2.3 Add penalty for equality constraints" @@ -588,7 +588,7 @@ }, { "cell_type": "markdown", - "id": "6dacd8cf", + "id": "20ad0481", "metadata": {}, "source": [ "As we mentioned above that price can only take one option per day, this means that one and only one of the binary variables in a day must be $1$ and others must be $0$. 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] }, - "execution_count": 11, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } @@ -630,7 +630,7 @@ }, { "cell_type": "markdown", - "id": "07d925f4", + "id": "18603c19", "metadata": {}, "source": [ "# 3. Solve QUBO with Braket" @@ -638,7 +638,7 @@ }, { "cell_type": "markdown", - "id": "3a30c93d", + "id": "b847c8f9", "metadata": {}, "source": [ "Now we have transformed to the total objective function which:\n", @@ -654,7 +654,7 @@ }, { "cell_type": "markdown", - "id": "ff888617", + "id": "53911f70", "metadata": {}, "source": [ "Amazon Braket provides access to quantum annealers from D-Wave Systems Inc. which are specifically designed to solve QUBO problems. A quantum annealer is a hardware implementation of Quantum Annealing (QA) which is a generic algorithm to solve combinatorial optimization problems by taking advantage of quantum fluctuations to escape local minima in complex energy landscapes by effect of tunnelling through barriers separating local minima [5]. Through a simple Amazon Braket API call, the formatted QUBO problem can be embedded to the hardwired topology of the machine and submitted to machine. In turn, the quantum annealer performs an annealing process and obtains a result. However, because of the sparsity of the underlying chip, one typically faces a certain overhead in embedding the original QUBO problem to the D-Wave hardware, because (typically) one logical binary variable maps onto several physical qubits, in order to effectively distill the connectivity of the original QUBO problem. For more details, we refer to the Amazon Braket tutorial notebook available here (https://github.com/aws/amazon-braket-examples/blob/main/examples/quantum_annealing/Dwave_Anatomy.ipynb)." @@ -662,8 +662,8 @@ }, { "cell_type": "code", - "execution_count": 12, - "id": "97ce4e85", + "execution_count": 13, + "id": "105323af", "metadata": {}, "outputs": [], "source": [ @@ -687,8 +687,8 @@ }, { "cell_type": "code", - "execution_count": 13, - "id": "8b60c6c3", + "execution_count": 14, + "id": "6b6ee53c", "metadata": {}, "outputs": [ { @@ -697,7 +697,7 @@ "BinaryQuadraticModel({X_005: -10000000002744.719, X_030: -10000000002576.855, X_036: -10000000002155.762, X_006: -10000000003050.883, X_043: -10000000002179.559, X_016: -10000000002371.592, X_034: -10000000004275.291, X_033: -10000000003774.486, X_002: -10000000001934.893, X_037: -10000000002622.238, X_032: -10000000003208.34, X_047: -10000000003896.223, X_041: -10000000004362.69, X_011: -10000000002651.016, X_014: -10000000001276.889, 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"execute_result" } @@ -730,7 +730,7 @@ }, { "cell_type": "markdown", - "id": "c8f0a3d4", + "id": "f61d635c", "metadata": {}, "source": [ "We embed and submit the QUBO task to be solved by a quantum annealer at D-wave backend. Similar to classical simulated annealing, we take several independent shots in order to increase our chances for success in finding a high-quality solution to the QUBO problem. The response contains a number of rows. Each row represents the optimization result of a single shot, including the binary decision variables $[x_T,\\cdots,x_{T+n-1}]$, and corresponding energy which is the negative value of objective function, i.e. $H$. Below we show how to submit a QUBO problem to D-Wave and provide a sample response. Here, the key figure of merit is listed in the column labelled with energy, representing the value for the objective function . We can then easily read off the best bit string found." @@ -739,7 +739,7 @@ { "cell_type": "code", "execution_count": 16, - "id": "674a30ee", + "id": "ee123eac", "metadata": { "scrolled": true }, @@ -749,10006 +749,10006 @@ "output_type": "stream", "text": [ " X_000 X_001 X_002 X_003 X_004 ... 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1 ...\n", + "9416 0 0 1 0 1 ... 0 79999999996491.9 1 ...\n", + "9782 0 1 0 0 0 ... 1 79999999996670.44 1 ...\n", + "9417 0 0 1 0 0 ... 0 79999999996683.31 1 ...\n", + "9702 0 0 1 0 0 ... 0 79999999996721.12 1 ...\n", + "9889 1 0 0 0 0 ... 1 79999999997080.47 1 ...\n", + "9399 0 0 1 0 0 ... 0 79999999997362.47 1 ...\n", + "9562 0 0 0 1 1 ... 0 79999999997588.53 1 ...\n", + "9920 0 0 0 0 1 ... 0 79999999997624.34 1 ...\n", + "9851 0 0 1 0 0 ... 1 79999999997864.94 1 ...\n", + "9693 0 0 0 1 0 ... 0 79999999998482.34 1 ...\n", + "9967 0 0 1 0 0 ... 1 79999999999897.94 1 ...\n", + "9481 1 0 0 0 0 ... 0 80000000001523.19 1 ...\n", + "9781 0 0 0 0 0 ... 0 80000000004300.66 1 ...\n", + "9731 0 0 0 0 0 ... 0 89999999990887.84 1 ...\n", + "9752 0 0 0 1 0 ... 0 89999999992994.9 1 ...\n", + "9948 0 0 1 0 0 ... 0 89999999993050.72 1 ...\n", + "9926 1 0 0 0 0 ... 0 89999999993302.1 1 ...\n", + "9949 1 0 0 0 0 ... 0 89999999993581.56 1 ...\n", + "9801 0 0 1 0 0 ... 0 89999999994340.81 1 ...\n", + "9833 0 0 1 0 0 ... 0 89999999995397.94 1 ...\n", + "9907 0 0 0 1 0 ... 0 89999999995931.97 1 ...\n", + "9977 1 0 0 1 0 ... 0 89999999999482.62 1 ...\n", + "9925 0 0 1 0 0 ... 0 89999999999985.6 1 ...\n", + "9700 0 0 0 0 1 ... 1 90000000000062.97 1 ...\n", + "9963 0 0 0 0 0 ... 1 90000000000377.4 1 ...\n", + "9701 0 0 0 1 0 ... 0 90000000002155.78 1 ...\n", + "9992 0 1 1 1 0 ... 0 99999999991573.28 1 ...\n", + "9915 0 0 0 0 0 ... 0 99999999995320.72 1 ...\n", + "9946 0 1 0 0 0 ... 0 99999999997008.69 1 ...\n", + "9861 0 0 1 0 0 ... 0 99999999999712.4 1 ...\n", + "9984 0 0 1 0 0 ... 0 109999999993272.66 1 ...\n", + "9983 1 0 0 0 0 ... 0 109999999997625.06 1 ...\n", + "9965 0 1 0 0 0 ... 1 120000000002667.9 1 ...\n", "['BINARY', 10000 rows, 10000 samples, 49 variables]\n" ] } @@ -10767,7 +10767,7 @@ }, { "cell_type": "markdown", - "id": "b5581aec", + "id": "67df526f", "metadata": {}, "source": [ "## 3.1 Evaluate the results" @@ -10775,7 +10775,7 @@ }, { "cell_type": "markdown", - "id": "2da268f0", + "id": "7fc33e70", "metadata": {}, "source": [ "With the response, we can decode the binary array results into the optimal price results" @@ -10784,17 +10784,17 @@ { "cell_type": "code", "execution_count": 17, - "id": "da02622c", + "id": "e73bafd5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "([13, 12, 12, 13, 10, 10, 19],\n", - " array([0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,\n", - " 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,\n", + "([13, 13, 13, 12, 8, 16, 19],\n", + " array([0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,\n", + " 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,\n", " 0, 0, 0, 0, 1], dtype=int8),\n", - " -12520.765625)" + " -12690.9375)" ] }, "execution_count": 17, @@ -10818,7 +10818,7 @@ }, { "cell_type": "markdown", - "id": "2aa84683", + "id": "626bb099", "metadata": {}, "source": [ "The optimized price path and corresponding demand curve is plot below, respectively. The optimal price level is higher than the past 7 days, which results in the demand decreasing." @@ -10827,12 +10827,12 @@ { "cell_type": "code", "execution_count": 18, - "id": "bbe4d6aa", + "id": "da89ecaa", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -10855,7 +10855,7 @@ }, { "cell_type": "markdown", - "id": "2d1b267b", + "id": "d9e89561", "metadata": {}, "source": [ "__now, Let's get the demand of each day and the total revenue__" @@ -10864,20 +10864,20 @@ { "cell_type": "code", "execution_count": 19, - "id": "717ef755", + "id": "7bac09eb", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "([182.33668654152052,\n", - " 165.36059160986585,\n", - " 152.14722973980318,\n", - " 139.58354691345133,\n", - " 143.67298125412577,\n", - " 148.40960793366366,\n", - " 121.5201742495238],\n", - " 13224.766093729508)" + " 161.75101851993844,\n", + " 145.30390869346718,\n", + " 136.97318179740145,\n", + " 149.09503161262904,\n", + " 133.2779083933537,\n", + " 108.67908278844949],\n", + " 13395.87852055809)" ] }, "execution_count": 19, @@ -10893,12 +10893,12 @@ { "cell_type": "code", "execution_count": 20, - "id": "5a12bfe2", + "id": "3e2a6a19", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -10921,7 +10921,7 @@ }, { "cell_type": "markdown", - "id": "de5b6c2d", + "id": "73d15c61", "metadata": {}, "source": [ "__Finally, let's get the overall uncertainty of the demand predictions, here we simply use demand variance to indicate the uncertainty__" @@ -10930,13 +10930,13 @@ { "cell_type": "code", "execution_count": 21, - "id": "b2083cd3", + "id": "4d956f71", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "703.9977273152239" + "704.9419334213342" ] }, "execution_count": 21, @@ -10951,7 +10951,7 @@ }, { "cell_type": "markdown", - "id": "e226adb8", + "id": "055079f6", "metadata": {}, "source": [ "__We can also derive the standard deviation of the revenue based on the variance of demand__\n", @@ -10962,13 +10962,13 @@ { "cell_type": "code", "execution_count": 22, - "id": "65d2d48b", + "id": "5a077566", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "345.69772474444244" + "366.50526804215906" ] }, "execution_count": 22, @@ -10992,7 +10992,7 @@ }, { "cell_type": "markdown", - "id": "fae8b436", + "id": "c1e09f07", "metadata": {}, "source": [ "__We can investigate the value of the penality terms to see if any equality constraints are voilated. The penalty is close to zero showing that all the constraints are complied__" @@ -11001,13 +11001,13 @@ { "cell_type": "code", "execution_count": 23, - "id": "1657334a", + "id": "b6f4ee49", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "0.0027414142841735156" + "-0.0009128632445936091" ] }, "execution_count": 23, @@ -11022,7 +11022,7 @@ }, { "cell_type": "markdown", - "id": "fa267458", + "id": "7ced7d24", "metadata": {}, "source": [ "For comparison, to assess the quality of this optimized result, we also iterate (by brute-force search) through all the $7^7=823,543$ possible price solutions to obtain the energy for each one, which takes more than 5 minutes to run on a standard ml.m5.2xlarge AWS instance. We plot the distribution of the energies of all the 823,543 possible solutions as shown below, where the red line represents our optimized result obtained from the quantum annealer. We can see that although the optimized result from the quantum annealer is not the global optimum with minimum cost, it is close-to-optimal and of good quality. " @@ -11031,7 +11031,7 @@ { "cell_type": "code", "execution_count": 24, - "id": "dbbe522c", + "id": "c72602b6", "metadata": { "scrolled": true }, @@ -11892,12 +11892,12 @@ { "cell_type": "code", "execution_count": 25, - "id": "ad63ad18", + "id": "1d471924", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -11921,7 +11921,7 @@ }, { "cell_type": "markdown", - "id": "2af769de", + "id": "af3d95a0", "metadata": {}, "source": [ "# 4. Trade-off between expected revenue and prediction uncertainty." @@ -11929,7 +11929,7 @@ }, { "cell_type": "markdown", - "id": "a6b10fec", + "id": "28089133", "metadata": {}, "source": [ "Let's first wrap above price optimisation into a single main function for convenience." @@ -11937,28 +11937,28 @@ }, { "cell_type": "code", - "execution_count": 35, - "id": "f89fc742", + "execution_count": 26, + "id": "984b3a9c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "(13338.581109728268,\n", - " 703.6300560847318,\n", - " -12634.953125,\n", - " [182.33668654152052,\n", - " 165.36059160986585,\n", - " 159.36637591965803,\n", - " 156.8797620960508,\n", - " 152.12745944263415,\n", - " 147.77084364608078,\n", - " 116.98084569202341],\n", - " [13, 12, 10, 10, 12, 12, 19],\n", - " 341.94199709111217)" + "(13385.557029586926,\n", + " 704.6026346946801,\n", + " -12680.953125,\n", + " [185.94625963144793,\n", + " 175.81348574612934,\n", + " 157.99134281226168,\n", + " 162.41469843400876,\n", + " 169.04727765777784,\n", + " 137.61617514167745,\n", + " 109.25139281908908],\n", + " [12, 10, 13, 8, 8, 19, 19],\n", + " 357.04970370024245)" ] }, - "execution_count": 35, + "execution_count": 26, "metadata": {}, "output_type": "execute_result" } @@ -11977,14 +11977,15 @@ " Ld = Ld,\n", " sigma = sigma ,\n", " beta=beta,\n", - " vol_bound=None\n", + " vol_bound=None,\n", + " s3_folder=s3_folder\n", ")\n", "max_revenue, prediction_variance, energy, opt_demand, opt_prices, rev_std" ] }, { "cell_type": "markdown", - "id": "56faf584", + "id": "adec78ac", "metadata": {}, "source": [ "In order to investigate the trade-off between the expected revenue and prediction uncertainties, we vary the knob parameter $\\beta$ within a large range of $[1e2,1e9]$ and run multiple experiments on D-Wave with different $\\beta$ values. The scatter plot are shown below, where each dot represents the optimized result of an experiment with x-axis representing its expected revenue and y-axis representing the estimated standard deviation of revenue $std(R)$. The standard deviation of revenue can be derived from the estimated variance of the predicted demand:\n", @@ -11994,8 +11995,8 @@ }, { "cell_type": "code", - "execution_count": 36, - "id": "c899d278", + "execution_count": 27, + "id": "83691475", "metadata": { "scrolled": true }, @@ -12006,436 +12007,436 @@ "text": [ "---\n", "beta_sample:100.0\n", - "max_revenue:13344.971150411837\n", - "prediction_variance:705.3216713996405\n", - "energy:57187.1875\n", - "opt_demand:[182.33668654152052, 179.79888396957557, 150.6439292057279, 156.64118153572883, 148.8564279708053, 130.57018515611858, 105.12477557318046]\n", - "opt_prices:[13, 8, 16, 8, 12, 16, 19]\n", - "rev_std: 364.1707583850488\n", - "penalty_term: -0.008489552208629902\n", + "max_revenue:13291.671898296641\n", + "prediction_variance:704.1931156458986\n", + "energy:57127.640625\n", + "opt_demand:[182.33668654152052, 165.36059160986585, 152.14722973980318, 143.19312000337874, 139.68758303067955, 123.27086373085064, 109.01867880990861]\n", + "opt_prices:[13, 12, 12, 12, 12, 16, 16]\n", + "rev_std: 355.6925164877392\n", + "penalty_term: 0.0009587067761458457\n", "---\n", "beta_sample:1000.0\n", - "max_revenue:13078.512262531649\n", - "prediction_variance:702.8956246094274\n", - "energy:689817.109375\n", - "opt_demand:[193.16540581130278, 189.5001278388014, 174.04079231414366, 168.49098776608298, 164.20272014093717, 140.96094702759993, 122.50346515166794]\n", - "opt_prices:[10, 8, 12, 10, 10, 16, 16]\n", - "rev_std: 320.1714516345594\n", - "penalty_term: -0.0029718957375735044\n", + "max_revenue:12661.267350528498\n", + "prediction_variance:702.2590686281666\n", + "energy:689597.796875\n", + "opt_demand:[193.16540581130278, 189.5001278388014, 188.47908467385338, 181.42597959171735, 165.3187618694297, 150.2670365409225, 137.60803208172922]\n", + "opt_prices:[10, 8, 8, 10, 13, 13, 13]\n", + "rev_std: 289.4392148886471\n", + "penalty_term: -0.004402638063766062\n", "---\n", "beta_sample:10000.0\n", - "max_revenue:11847.00605735832\n", - "prediction_variance:702.2879419564052\n", - "energy:7011032.40625\n", - "opt_demand:[185.94625963144793, 175.81348574612934, 161.6009159021891, 165.64844639041735, 172.03346790734656, 179.36613265907062, 178.19207178387035]\n", - "opt_prices:[12, 10, 12, 8, 8, 8, 10]\n", - "rev_std: 261.2157278976442\n", - "penalty_term: -0.007256694138050079\n", + "max_revenue:11262.938301039747\n", + "prediction_variance:702.010077070336\n", + "energy:7008837.8359375\n", + "opt_demand:[193.16540581130278, 189.5001278388014, 174.04079231414366, 175.7101339459378, 170.67021605375436, 168.59076606630185, 185.70056393570428]\n", + "opt_prices:[10, 8, 12, 8, 10, 10, 5]\n", + "rev_std: 244.68935650750305\n", + "penalty_term: 0.0035351794213056564\n", "---\n", "beta_sample:100000.0\n", - "max_revenue:12277.549797454418\n", - "prediction_variance:702.3964846595861\n", - "energy:70227370.9140625\n", - "opt_demand:[200.38455199115765, 188.74847757176371, 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195.9676237516186, 180.01317281328105, 179.79944100232086, 165.21765714377918, 152.43923911372602, 152.73488900183173]\n", + "opt_prices:[8, 8, 12, 8, 12, 13, 10]\n", + "rev_std: 274.1335026388799\n", + "penalty_term: 0.012939453125\n", "---\n", "beta_sample:100.0\n", - "max_revenue:13123.015287006972\n", - "prediction_variance:704.0082437746344\n", - "energy:57277.8125\n", - "opt_demand:[200.38455199115765, 195.9676237516186, 187.2323189931359, 168.21907146550097, 162.2404440407284, 126.40765229551825, 98.36194358209265]\n", - "opt_prices:[8, 8, 10, 13, 10, 19, 19]\n", - "rev_std: 350.6275902142349\n", - "penalty_term: 0.003409543540328741\n", + "max_revenue:13428.302059160185\n", + "prediction_variance:704.5429695367601\n", + "energy:57025.9921875\n", + "opt_demand:[182.33668654152052, 161.75101851993844, 163.3517741431043, 167.58021393915413, 162.52268232639722, 142.5109452069517, 109.32940407763995]\n", + "opt_prices:[13, 13, 8, 8, 12, 16, 19]\n", + "rev_std: 351.68512469061767\n", + "penalty_term: -0.0027070158248534426\n", "---\n", "beta_sample:1000.0\n", - "max_revenue:13077.213201248951\n", - "prediction_variance:703.3152412323436\n", - "energy:690238.0234375\n", - "opt_demand:[185.94625963144793, 183.03263192598416, 182.506704174716, 184.55581871518916, 170.01967051236727, 144.26600954025398, 120.41156111497642]\n", - "opt_prices:[12, 8, 8, 8, 13, 16, 16]\n", - "rev_std: 319.8066506363613\n", - "penalty_term: -0.004593594698235393\n", + "max_revenue:12686.146173485487\n", + "prediction_variance:702.4741246927732\n", + "energy:689787.9765625\n", + "opt_demand:[200.38455199115765, 195.9676237516186, 194.45146517299077, 174.68656737831816, 168.21282453986578, 155.76397098139327, 133.59348581661482]\n", + "opt_prices:[8, 8, 8, 13, 10, 12, 16]\n", + "rev_std: 294.01822320045846\n", + "penalty_term: -0.001956787775270641\n", "---\n", "beta_sample:10000.0\n", - "max_revenue:11185.01421549005\n", - "prediction_variance:701.6575682454578\n", - "energy:7005390.6640625\n", - "opt_demand:[193.16540581130278, 182.28098165894653, 182.0115887610362, 182.67274527243484, 185.74481617550094, 188.68943500186037, 189.70020738761224]\n", - "opt_prices:[10, 10, 8, 8, 8, 8, 8]\n", - "rev_std: 228.3185934766346\n", - "penalty_term: -0.004176587797701359\n", + "max_revenue:12460.45746762208\n", + "prediction_variance:702.238586248761\n", + "energy:7009925.40625\n", + "opt_demand:[193.16540581130278, 189.5001278388014, 188.47908467385338, 170.5972603219351, 166.4462372699861, 154.61928275136964, 147.2759632921967]\n", + "opt_prices:[10, 8, 8, 13, 10, 12, 12]\n", + "rev_std: 280.6301723807376\n", + "penalty_term: 0.0012300126254558563\n", "---\n", "beta_sample:100000.0\n", - "max_revenue:11714.90903789518\n", - "prediction_variance:702.1839176305133\n", - "energy:70206676.8515625\n", - "opt_demand:[200.38455199115765, 195.9676237516186, 187.2323189931359, 197.09565618492036, 188.11042769199724, 175.5641859215598, 169.84156531183197]\n", - "opt_prices:[8, 8, 10, 5, 10, 12, 10]\n", - "rev_std: 244.71112864636873\n", - "penalty_term: -0.0024509429931640625\n", + "max_revenue:10906.61337332408\n", + "prediction_variance:701.7478807312693\n", + "energy:70163881.4609375\n", + "opt_demand:[200.38455199115765, 195.9676237516186, 187.2323189931359, 179.04779073528323, 171.94168790995423, 175.07152703342604, 190.6011549461458]\n", + "opt_prices:[8, 8, 10, 10, 10, 8, 5]\n", + "rev_std: 227.65734336966304\n", + "penalty_term: 0.0011838972568511963\n", "---\n", "beta_sample:1000000.0\n", - "max_revenue:11111.01302567372\n", - "prediction_variance:701.8582372177341\n", - "energy:701847126.203125\n", - "opt_demand:[200.38455199115765, 195.9676237516186, 187.2323189931359, 179.04779073528323, 179.1608340898091, 192.36774221602548, 188.2269138648719]\n", - "opt_prices:[8, 8, 10, 10, 8, 5, 10]\n", - "rev_std: 227.6815096419856\n", - "penalty_term: -0.0015834569931030273\n", + "max_revenue:10422.132223477654\n", + "prediction_variance:702.4074226628456\n", + "energy:702397000.53125\n", + "opt_demand:[185.94625963144793, 175.81348574612934, 176.0392082618988, 178.58343821605177, 194.8069481754036, 197.24599064106252, 208.73168252197286]\n", + "opt_prices:[12, 10, 8, 8, 5, 8, 5]\n", + "rev_std: 220.84301199423587\n", + "penalty_term: 0.0006278753280639648\n", "---\n", "beta_sample:10000000.0\n", - "max_revenue:11876.503211153971\n", - "prediction_variance:702.7514263104365\n", - "energy:7027502386.6015625\n", - "opt_demand:[182.33668654152052, 172.5797377897207, 173.05301801233009, 176.53878468786024, 193.92365454046376, 189.4545003461959, 176.61926753759982]\n", - "opt_prices:[13, 10, 8, 8, 5, 10, 12]\n", - "rev_std: 258.58897516697846\n", - "penalty_term: 0.000408172607421875\n", + "max_revenue:12794.522636056197\n", + "prediction_variance:702.2224670913383\n", + "energy:7022211876.3828125\n", + "opt_demand:[193.16540581130278, 182.28098165894653, 174.79244258118132, 161.76695699990793, 152.39915149101944, 145.28208276185842, 136.82738773142015]\n", + "opt_prices:[10, 10, 10, 12, 12, 12, 13]\n", + "rev_std: 300.64408668989864\n", + "penalty_term: -0.0079345703125\n", "---\n", "beta_sample:100000000.0\n", - "max_revenue:12033.673076071234\n", - "prediction_variance:702.3630886470199\n", - "energy:70236296831.03906\n", - "opt_demand:[193.16540581130278, 200.32884710858366, 198.18032854307916, 190.38455034042346, 182.28144172378654, 173.44688058475003, 157.98487904469658]\n", - "opt_prices:[10, 5, 8, 10, 10, 10, 13]\n", - "rev_std: 256.93398684116414\n", - "penalty_term: 0.0101470947265625\n", + "max_revenue:11225.412662381104\n", + "prediction_variance:701.8728425144088\n", + "energy:70187273026.03125\n", + "opt_demand:[200.38455199115765, 195.9676237516186, 187.2323189931359, 186.2669369151381, 178.4091838227714, 166.6056151728537, 181.75547017689448]\n", + "opt_prices:[8, 8, 10, 8, 10, 12, 5]\n", + "rev_std: 237.1515609359141\n", + "penalty_term: 0.003021240234375\n", "---\n", "beta_sample:1000000000.0\n", - "max_revenue:12396.538139042514\n", - "prediction_variance:702.4360114890887\n", - "energy:702435999092.5469\n", - "opt_demand:[185.94625963144793, 175.81348574612934, 176.0392082618988, 164.14514585634205, 163.8240909001321, 169.13248986074478, 156.74553244194385]\n", - "opt_prices:[12, 10, 8, 12, 10, 8, 13]\n", - "rev_std: 280.6743822723691\n", - "penalty_term: -0.0037841796875\n" + "max_revenue:11935.362324992222\n", + "prediction_variance:702.212326018176\n", + "energy:702212314082.8125\n", + "opt_demand:[193.16540581130278, 182.28098165894653, 167.57329640132647, 162.5186072669456, 149.28469381477186, 158.36970060791384, 167.1467745436264]\n", + "opt_prices:[10, 10, 12, 10, 13, 8, 8]\n", + "rev_std: 272.64805987855004\n", + "penalty_term: -0.001220703125\n" ] } ], @@ -12455,7 +12456,8 @@ " Ld = Ld,\n", " sigma = sigma ,\n", " beta=beta_i,\n", - " vol_bound=None\n", + " vol_bound=None,\n", + " s3_folder=s3_folder\n", " )\n", " print('---')\n", " print(f\"beta_sample:{beta_i}\")\n", @@ -12471,7 +12473,7 @@ }, { "cell_type": "markdown", - "id": "2937d192", + "id": "7c6f9584", "metadata": {}, "source": [ "We can see from the plot below that there is Pareto front where the expected revenue cannot be increased without increasing the standard deviation (i.e. uncertainties), and the other way around.\n", @@ -12481,8 +12483,8 @@ }, { "cell_type": "code", - "execution_count": 37, - "id": "650d95d3", + "execution_count": 28, + "id": "ab9a050a", "metadata": {}, "outputs": [], "source": [ @@ -12501,13 +12503,13 @@ }, { "cell_type": "code", - "execution_count": 38, - "id": "595c046d", + "execution_count": 29, + "id": "ce52fcf8", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -12531,7 +12533,7 @@ }, { "cell_type": "markdown", - "id": "fdfe1f51", + "id": "4dabcfb4", "metadata": {}, "source": [ "# 5. Conclusion" @@ -12539,15 +12541,15 @@ }, { "cell_type": "markdown", - "id": "1c4fced3", + "id": "2729eeb0", "metadata": {}, "source": [ - "In this blog, we demonstrate how to leverage a quantum annealer on Amazon Braket to solve a price optimization use case. We showed how to mathematically formulate the problem within the (quantum-ready) QUBO framework, and then subsequently solve the optimization problem on a D-Wave quantum annealer. Our results are promising in terms of both close-to-optimal quality and computational efficiency. Since the QUBO formalism is a generalized framework that can embrace a variety of combinatorial optimization use cases (e.g. scheduling/planning, routing, portfolio management), the proposed solution can be arguably adapted and recycled by customers across other multiple industries. Already today our customers can get quantum-ready, and easily leverage Amazon Braket to help solve their daily combinatorial optimization challenges, and make better business and operation decisions." + "In this notebook, we demonstrate how to leverage a quantum annealer on Amazon Braket to solve a price optimization use case. We showed how to mathematically formulate the problem within the (quantum-ready) QUBO framework, and then subsequently solve the optimization problem on a D-Wave quantum annealer. Our results are promising in terms of both close-to-optimal quality and computational efficiency. Since the QUBO formalism is a generalized framework that can embrace a variety of combinatorial optimization use cases (e.g. scheduling/planning, routing, portfolio management), the proposed solution can be arguably adapted and recycled by customers across other multiple industries. Already today our customers can get quantum-ready, and easily leverage Amazon Braket to help solve their daily combinatorial optimization challenges, and make better business and operation decisions." ] }, { "cell_type": "markdown", - "id": "1e71d3d8", + "id": "f794f9b9", "metadata": {}, "source": [ "# 6. References:\n", @@ -12565,7 +12567,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c6feedec", + "id": "c6baafdb", "metadata": {}, "outputs": [], "source": [] diff --git a/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py b/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py index 6a0525aae..9ecdf6168 100644 --- a/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py +++ b/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py @@ -149,6 +149,7 @@ def main( sigma, beta, vol_bound, + s3_folder, dwave=True ): """ @@ -179,7 +180,7 @@ def main( ) # qubo solver - response = dwave_solver(obj) if dwave else qubo_solver(obj) + response = dwave_solver(obj,s3_folder) if dwave else qubo_solver(obj) # get optimal prices opt_prices, _, energy = decoder_price_response(response, len(a), price_levels) opt_demand, max_revenue = get_demands_rev(a, b, selected_hist_prices, opt_prices) @@ -198,11 +199,11 @@ def qubo_solver(obj): return response -def dwave_solver(obj): +def dwave_solver(obj,s3_folder): model = (-obj).compile().to_bqm() num_shots = 10000 - sampler = BraketDWaveSampler(('amazon-braket-481358cc730d', 'qubo'), + sampler = BraketDWaveSampler(s3_folder, 'arn:aws:braket:::device/qpu/d-wave/Advantage_system4') sampler = EmbeddingComposite(sampler) response = sampler.sample(model, num_reads=num_shots) From d3e182139513cc60d7e8525be72f98abd4082365 Mon Sep 17 00:00:00 2001 From: FengShi0705 Date: Mon, 20 Dec 2021 22:48:07 +0000 Subject: [PATCH 05/13] Add covariance function --- .gitignore | 6 ++++++ .../price_optimization/qubo_dynamic_pricing.py | 18 ++++++++++++++++++ 2 files changed, 24 insertions(+) diff --git a/.gitignore b/.gitignore index 8ba78c56e..e75a76fe3 100644 --- a/.gitignore +++ b/.gitignore @@ -136,3 +136,9 @@ dmypy.json # Data intermediates *.pck +.idea/amazon-braket-examples.iml +.idea/inspectionProfiles/profiles_settings.xml +.idea/misc.xml +.idea/modules.xml +.idea/vcs.xml +.idea/workspace.xml diff --git a/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py b/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py index 9ecdf6168..b2b34298d 100644 --- a/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py +++ b/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py @@ -47,6 +47,24 @@ def get_variance(data_x, p, sigma): return variance +def get_covariance(data_x, p1, p2, sigma): + """ + :param data_x (np.array): [n_samples, n_days] + :param p1, p2 (list): [n_days] + :return: variance + """ + n_samples, t = data_x.shape + ones = np.ones((n_samples, 1), dtype=np.float) + x_mat = np.concatenate([ones, data_x], axis=1) # [n_samples, n_days+1] + x_mat = np.linalg.inv( + np.dot(x_mat.T, x_mat) + ) + p1 = np.array([1.] + p1) + p2 = np.array([1.] + p2) + variance = (sigma**2) * (1. + p1.dot(x_mat).dot(p2)) + return variance + + def create_program(a,b, p_data, price_levels, data_x, Lp, Ld, sigma, beta, vol_bound): """ From 27fb36222eb54c02f197161f6d2cf33a6e60a077 Mon Sep 17 00:00:00 2001 From: FengShi0705 Date: Mon, 20 Dec 2021 23:18:06 +0000 Subject: [PATCH 06/13] Add covariance in overall revenue variance --- .../price_optimization/qubo_dynamic_pricing.py | 11 ++++++++++- 1 file changed, 10 insertions(+), 1 deletion(-) diff --git a/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py b/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py index b2b34298d..d6bc51498 100644 --- a/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py +++ b/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py @@ -3,6 +3,7 @@ import dimod from braket.ocean_plugin import BraketSampler, BraketDWaveSampler from dwave.system.composites import EmbeddingComposite +from itertools import combinations np.random.seed(0) @@ -156,7 +157,7 @@ def inequality_penalty(demand, demand_name, vol_bounday, d_const, Ld): return ((demand-vol_bounday-slack)**2)*Ld -def main( +def optimize( a, b, data_x, @@ -271,4 +272,12 @@ def get_overall_revenue_variance(data_x, hist_p, p, sigma): for i in range(t): var += get_variance(data_x, all_p[i+1:i+1+t], sigma) * (p[i]**2) + for i, j in combinations(list(range(t)), 2): + var += get_covariance( + data_x, + all_p[i + 1:i + 1 + t], + all_p[j + 1:j + 1 + t], + sigma + ) * 2 * p[i] * p[j] + return var From 765a15bc415fb3ed551e188b62e76235f8f5e134 Mon Sep 17 00:00:00 2001 From: feng shi Date: Tue, 21 Dec 2021 20:48:15 +0000 Subject: [PATCH 07/13] Update notebook for comments --- .../price_optimization/QUBO-Pricing.ipynb | 11472 ++-------------- 1 file changed, 857 insertions(+), 10615 deletions(-) diff --git a/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb b/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb index 0af7e7f0b..602e01ab9 100644 --- a/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb +++ b/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb @@ -2,26 +2,26 @@ "cells": [ { "cell_type": "markdown", - "id": "7db71c1a", + "id": "ec6267c1", "metadata": {}, "source": [ "# Using quantum annealing on Amazon Braket for price optimization\n", "\n", "Combinatorial Optimization is one of the most important fields in optimization. Practical applications can be found in virtually every industry. Prominent examples include supply chain optimization in transport and logistics, portfolio management in finance, and the optimization of clinical trials in healthcare, among many others. It is also one of the most active research topics in operation research and computer science. However, many practical combinatorial optimization problems are NP-hard and require massive computation costs to find solution of good quality. \n", "\n", - "In this notebook, we demonstrate how a quantum annealer on Amazon Braket can be used for price optimization taking into consideration the trade-off between maximizing revenue and minimizing risk. We showcase how to formulate this problem as a quadratic unconstrained binary optimization problem (QUBO) and use D-Wave Systems Inc. Advantage quantum annealer on Amazon Braket to find close-to-optimal solutions. Overall, this notebook demonstrates that customers can easily leverage quantum computing through Amazon Braket to solve difficult combinatorial optimization challenges in their daily decision-making process." + "In this notebook, we demonstrate how a quantum annealer on Amazon Braket can be used for price optimization taking into consideration the trade-off between maximizing revenue and minimizing risk. We show how to formulate this problem as a quadratic unconstrained binary optimization problem (QUBO) and use the D-Wave Advantage quantum annealer on Amazon Braket to find close-to-optimal solutions. Overall, this notebook demonstrates that customers can easily leverage quantum computing through Amazon Braket to solve difficult combinatorial optimization challenges in their daily decision-making process." ] }, { "cell_type": "markdown", - "id": "115f30aa", + "id": "efbcd2e0", "metadata": {}, "source": [ - "# Table of content\n", + "# Table of contents\n", "### 1. Demand model\n", " 1. Create demand dataset\n", " 2. Fit demand model through linear regression\n", - "### 2. Price optimisation with QUBO\n", + "### 2. Price optimization with QUBO\n", " 1. Construct revenue objective\n", " 2. Add penalty for prediction uncertainty\n", " 3. Add equality constraints\n", @@ -35,16 +35,16 @@ }, { "cell_type": "markdown", - "id": "df21764a", + "id": "336b48d1", "metadata": {}, "source": [ - "We start by importing important libraries related to Amazon braket and" + "We start by importing important libraries related to Amazon braket and installing dependencies." ] }, { "cell_type": "code", "execution_count": 1, - "id": "d87b667a", + "id": "0d12c431", "metadata": {}, "outputs": [ { @@ -53,10 +53,10 @@ "text": [ "Requirement already satisfied: sklearn in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (0.0)\n", "Requirement already satisfied: scikit-learn in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from sklearn) (1.0.1)\n", - "Requirement already satisfied: joblib>=0.11 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.1.0)\n", - "Requirement already satisfied: scipy>=1.1.0 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.5.2)\n", "Requirement already satisfied: numpy>=1.14.6 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.19.2)\n", - "Requirement already satisfied: threadpoolctl>=2.0.0 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (3.0.0)\n" + "Requirement already satisfied: scipy>=1.1.0 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.5.2)\n", + "Requirement already satisfied: threadpoolctl>=2.0.0 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (3.0.0)\n", + "Requirement already satisfied: joblib>=0.11 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.1.0)\n" ] } ], @@ -67,17 +67,17 @@ { "cell_type": "code", "execution_count": 2, - "id": "0d861ad7", + "id": "a22e4613", "metadata": {}, "outputs": [], "source": [ "from braket.aws import AwsDevice\n", "from braket.ocean_plugin import BraketSampler, BraketDWaveSampler\n", - "\n", - "import matplotlib.pyplot as plt\n", + "from pyqubo import Binary\n", "# magic word for producing visualizations in notebook\n", "%matplotlib inline\n", "import time\n", + "import reprlib\n", "from collections import defaultdict\n", "from itertools import combinations\n", "import math\n", @@ -88,13 +88,19 @@ "from dimod.binary_quadratic_model import BinaryQuadraticModel\n", "from dwave.system.composites import EmbeddingComposite\n", "import numpy as np\n", + "from sklearn.linear_model import LinearRegression\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from qubo_dynamic_pricing import optimize\n", "\n", - "np.random.seed(0)" + "np.random.seed(0)\n", + "repr_compact = reprlib.Repr()\n", + "repr_compact.maxother=200" ] }, { "cell_type": "markdown", - "id": "d9125a9d", + "id": "edd2a887", "metadata": {}, "source": [ "__NOTE__: Enter your S3 bucket and key below. " @@ -103,7 +109,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "9d95206b", + "id": "24dfaa49", "metadata": {}, "outputs": [], "source": [ @@ -115,8 +121,8 @@ }, { "cell_type": "code", - "execution_count": 5, - "id": "096e6b68", + "execution_count": 4, + "id": "6fdb286f", "metadata": {}, "outputs": [ { @@ -135,7 +141,7 @@ }, { "cell_type": "markdown", - "id": "100a23e0", + "id": "5e3cd00c", "metadata": {}, "source": [ "# 1. Demand model" @@ -143,21 +149,21 @@ }, { "cell_type": "markdown", - "id": "359646ca", + "id": "f505c4d6", "metadata": {}, "source": [ - "The usual goal of price optimization is to maximize the revenue in the next certain period, where the revenue can usually be represented by a function of demand and price: \n", + "The usual goal of price optimization is to maximize the revenue in the next certain period with respect to the corresponding prices, where the revenue can usually be represented by a function of demand and price: \n", "\n", - "$$R=\\sum_{t=T}^{T+n-1}d_tp_t$$\n", + "$$\\max_{{\\mathbf{p}}} R(\\mathbf{p}) = \\sum_{t=T}^{T+n-1}d_tp_t$$\n", "\n", "where $p_t$ and $d_t$ are the price and demand at day $t$.\n", "\n", - "In order to do price optimization, we need to create a demand model to estimate demand by a function of price: $d_t=f(\\mathbf{p}_t)$, where $\\mathbf{p}$ is a vector of latest prices. In such a way, the revenue objective can be transformed as a function soly depending on price to do optimization $R=\\sum_{t=T}^{T+n-1}f(\\mathbf{p_t})p_t$ " + "In order to do price optimization, we need to create a demand model to estimate demand by a function of price: $d_t=f(\\mathbf{p}_t)$, where $\\mathbf{p}$ is a vector of latest prices. In such a way, the revenue objective can be transformed as a function solely depending on price to do optimization $R=\\sum_{t=T}^{T+n-1}f(\\mathbf{p_t})p_t$." ] }, { "cell_type": "markdown", - "id": "a20fc0ee", + "id": "8167572a", "metadata": {}, "source": [ "## 1.1 Create training dataset" @@ -165,7 +171,7 @@ }, { "cell_type": "markdown", - "id": "a9deb8e4", + "id": "292ff151", "metadata": {}, "source": [ "For simplicity, we create a dummy dataset on historical demand and price observations so that a demand estimation model can be trained. \n", @@ -175,15 +181,15 @@ "Thus the demand at day $t$ would be\n", "$$d_t = \\sum_{i=t-n+1}^{t}a_{i+n-1-t}p_{i} + b + \\varepsilon $$\n", "where $a_j, j\\in [0, 1, \\ldots, n-1]$ is the elasiticity between the price at day $j+t-n+1$ and demand at day $t$, and\n", - "$b$ is the constant.\n", + "$b$ is a constant.\n", "\n", "We use these assumptions to create our dummy training dataset." ] }, { "cell_type": "code", - "execution_count": 6, - "id": "16b1f48a", + "execution_count": 5, + "id": "4d6a38f6", "metadata": { "scrolled": true }, @@ -192,16 +198,19 @@ "name": "stdout", "output_type": "stream", "text": [ - "dataset x:\n", - "[[ 8 10 10 ... 8 10 8]\n", - " [10 10 8 ... 10 8 13]\n", - " [10 8 8 ... 8 13 19]\n", - " ...\n", - " [16 5 10 ... 5 8 10]\n", - " [ 5 10 8 ... 8 10 5]\n", - " [10 8 5 ... 10 5 13]]\n", - "dataset y:\n", - "[176.60983362005817, 166.3135122384355, 122.40886555130055, 139.82753849065216, 136.5494478345374, 139.08672451958816, 171.1141344886614, 149.02456906069798, 153.67576697932017, 185.92865845385478, 218.8935596207448, 199.31303748275712, 191.1192719273116, 149.78503274416957, 132.3689836892222, 128.7844958138008, 143.7904523833443, 153.22628621708824, 163.40219274496187, 178.68599188442033, 188.22129139574835, 169.9991590571518, 162.82599073098172, 185.22470367140997, 180.01027611555656, 178.01057843534466, 191.24586406543554, 178.02900930596007, 196.45336697567134, 185.3003540246204, 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197.3900634281876, 196.44181264703545, 202.7832190240412, 205.6429091413778, 208.89812020628023, 193.14033517959047, 203.0088567910412, 169.6034276346709, 162.2283538460438, 164.07746828269188, 180.43213553233696, 207.5734208909289, 206.11331017346728, 196.27212504403425, 192.8472433886354, 198.01213990808535]\n" + "dataset x first 10 samples:\n", + "[[ 8 10 10 8 8 10 8]\n", + " [10 10 8 8 10 8 13]\n", + " [10 8 8 10 8 13 19]\n", + " [ 8 8 10 8 13 19 8]\n", + " [ 8 10 8 13 19 8 10]\n", + " [10 8 13 19 8 10 8]\n", + " [ 8 13 19 8 10 8 8]\n", + " [13 19 8 10 8 8 16]\n", + " [19 8 10 8 8 16 5]\n", + " [ 8 10 8 8 16 5 5]]\n", + "dataset y first 10 samples:\n", + "[176.60983362005817, 166.3135122384355, 122.40886555130055, 139.82753849065216, 136.5494478345374, 139.08672451958816, 171.1141344886614, 149.02456906069798, 153.67576697932017, 185.92865845385478]\n" ] } ], @@ -209,7 +218,7 @@ "a0=[-0.3, -0.5, -1.0, -2.0, -3.0, -3.3, -3.5] # elasticities in linear demand model\n", "b0=300 # constants in the linear demand model \n", "sigma=10. # the standard deviation of the noise\n", - "price_levels=[5, 8, 10, 12, 13, 16, 19] # the option of price at each day\n", + "price_levels=[5, 8, 10, 12, 13, 16, 19] # predefined possible prices for each day\n", "probabilities=[0.3, 0.3, 0.2, 0.05, 0.05, 0.05, 0.05] # the probabilities of taking a price choice at a day\n", "n_samples=1000 # the number of sample we want to create\n", "\n", @@ -250,15 +259,16 @@ " return data_x, data_y\n", "\n", "data_x, data_y = create_dataset(a0, b0, n_samples, price_levels, probabilities, sigma)\n", - "print(\"dataset x:\")\n", - "print(data_x)\n", - "print(\"dataset y:\")\n", - "print(data_y)" + "\n", + "print(\"dataset x first 10 samples:\")\n", + "print(data_x[:10])\n", + "print(\"dataset y first 10 samples:\")\n", + "print(data_y[:10])" ] }, { "cell_type": "markdown", - "id": "302e1103", + "id": "b19d4409", "metadata": {}, "source": [ "## 1.2. Fit the demand model" @@ -266,16 +276,16 @@ }, { "cell_type": "markdown", - "id": "6b87f767", + "id": "9d1d2c95", "metadata": {}, "source": [ - "By using the created training dataset, we simply using sklearn to fit a linear demand model. This fitted linear demand model will be used for the following price optimization problem. We round the model coefficents to integer for simplicity to fit with the below QUBO format (quadratic unconstrained binary optimization). " + "We use `sklearn` to fit a linear demand model to the training set. This fitted linear demand model will be used for the following price optimization problem." ] }, { "cell_type": "code", - "execution_count": 7, - "id": "da72c96b", + "execution_count": 6, + "id": "6ae94e50", "metadata": {}, "outputs": [ { @@ -288,7 +298,6 @@ } ], "source": [ - "from sklearn.linear_model import LinearRegression\n", "def linear_regression(data_x, data_y):\n", " reg = LinearRegression().fit(data_x, data_y)\n", " a = reg.coef_\n", @@ -306,7 +315,7 @@ }, { "cell_type": "markdown", - "id": "a8cbe45b", + "id": "f33eca0a", "metadata": {}, "source": [ "# 2. Price optimization with QUBO" @@ -314,7 +323,7 @@ }, { "cell_type": "markdown", - "id": "bf96e228", + "id": "5aca76da", "metadata": {}, "source": [ "In this notebook, we leverage a general-purpose mathematical framework: Quadratic Unconstrained Binary Optimization (QUBO), which has been recently proposed as an effective framework that is able to generalize across a large variety of combinatorial optimization use cases in industries [2, 3]. We take this price optimization as an example and showcase how to formulate it into QUBO framework considering prediction uncertainties as well as equality constraints." @@ -322,7 +331,7 @@ }, { "cell_type": "markdown", - "id": "d6d45322", + "id": "3aee7865", "metadata": {}, "source": [ "The formal definition of QUBO is expressed as an optimization problem, Minimize:\n", @@ -331,17 +340,17 @@ }, { "cell_type": "markdown", - "id": "45a87632", + "id": "32b8dbca", "metadata": {}, "source": [ - "Where $x$ is a vector of binary variables representing the decision variables of the combinatorial optimization. $Q$ is a squared matrix of constants inherently encoding the context and constraints of the optimization problems. $Q$ is commonly assumed to be symmetric or upper triangular without loss of generality. The goal is to find the optimal values of the binary decision variables $x$ that minimize the objective $H$.\n", + "where $x$ is a vector of binary variables representing the decision variables of the combinatorial optimization. $Q$ is a squared matrix of constants inherently encoding the context and constraints of the optimization problems. $Q$ is commonly assumed to be symmetric or upper triangular without loss of generality. The goal is to find the optimal values of the binary decision variables $x$ that minimize the objective $H$.\n", "\n", "As shown above, the format of QUBO is strikingly simple, providing a general-purpose framework for a large class of combinatorial optimization problems. Below we show how to transform the objective function together with the constraints into this QUBO format. " ] }, { "cell_type": "markdown", - "id": "a7753b90", + "id": "acf1f460", "metadata": {}, "source": [ "## 2.1 Construct objective function" @@ -349,22 +358,22 @@ }, { "cell_type": "markdown", - "id": "e083a37b", + "id": "00e31bdb", "metadata": {}, "source": [ "Assuming tomorrow is day $T$, then the goal of our price optimization is to find the optimal prices $p_t, t\\in[T, T+1, \\ldots, T+n-1]$ in the next $n$ days in order to maximize the revenue in next $n$ days. Based on the demand model we showed above where the demand at a day is correlated with the latest $n$ days' price, we can construct objective function as below:\n", "\n", - "$maximize$ $R=\\sum_{t=T}^{T+n-1}d_tp_t$\n", + "$$\\max_{{\\mathbf{p}}}R(\\mathbf{p})=\\sum_{t=T}^{T+n-1}d_tp_t$$\n", "\n", "where $d_t$ is represented by our fitted model above: $d_t = \\sum_{i=t-n+1}^{t}a_{i+n-1-t}p_{i} + b $\n", "\n", - "Therefore, we need at least the most recent n day's historical prices. Here we random choose a historical range of $n$ days' prices as the most recent price data. " + "Therefore, we need at least the most recent n days historical prices. Here we randomly choose a historical range of $n$ days' prices as the most recent price data. " ] }, { "cell_type": "code", - "execution_count": 8, - "id": "8243b21d", + "execution_count": 7, + "id": "8a82a02c", "metadata": {}, "outputs": [ { @@ -373,32 +382,33 @@ "[10, 8, 8, 5, 5, 8, 8]" ] }, - "execution_count": 8, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p_data = data_x[np.random.randint(0,n_samples)].tolist()\n", + "\n", "p_data" ] }, { "cell_type": "markdown", - "id": "18802866", + "id": "5d8e7d5e", "metadata": {}, "source": [ - "Now, let's construct the objective function which is the total revenue $R$ in the next $n$ days.\n", + "Now, let's construct the objective function, i.e. the total revenue $R$, for the next $n$ days.\n", "\n", - "First, we need to define the price variable $p_t$. Since the price at each day only has a set of fixed $m$ options $c_k, k \\in [0, 1, \\ldots, m-1]$, we can represent the price $p_t$ at day $t$ as: $$p_t=\\sum_{k=0}^{m-1}c_{k}x_{t,k}, \\;subject\\;to \\sum_{k=0}^{m-1}x_{t,k}=1$$ \n", + "First, we need to define the price variable $p_t$. According to certain business requirements, the possible prices are usually defined to be a set of discrete price values (e.g. \\\\$5.99, \\\\$9.99, \\\\$14.99). This means the price at each day only has a set of fixed available $m$ options $c_k, k \\in [0, 1, \\ldots, m-1]$, we can represent the price $p_t$ at day $t$ as: $$p_t=\\sum_{k=0}^{m-1}c_{k}x_{t,k}, \\textrm{ subject to } \\sum_{k=0}^{m-1}x_{t,k}=1$$ \n", "\n", "where $x_{t,k}$ is a binary variable with $1$ meaning the price at day $t$ takes option $c_k$, and $0$ meaning otherwise. Therefore, we can use binary variables $x_{t,k}$ to represent the price variables $p_t$." ] }, { "cell_type": "code", - "execution_count": 9, - "id": "adbadd2e", + "execution_count": 8, + "id": "f60b6fc2", "metadata": {}, "outputs": [ { @@ -420,18 +430,20 @@ " (Binary(X_048)*Num(19.000000)+Binary(X_047)*Num(16.000000)+Binary(X_046)*Num(13.000000)+Binary(X_045)*Num(12.000000)+Binary(X_044)*Num(10.000000)+Binary(X_042)*Num(5.000000)+Binary(X_043)*Num(8.000000))]" ] }, - "execution_count": 9, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "from pyqubo import Binary\n", + "# here, we use a list to represent the sequence of prices from day T-n to day T+n-1.\n", + "\n", "t = len(a) # next number of days to optimize\n", "n_level = len(price_levels) # number of price options\n", "\n", "x = []\n", "p = []\n", + "\n", "# get p\n", "for i in range(t):\n", " p_i = 0\n", @@ -440,32 +452,43 @@ " x.append(x_ij)\n", " p_i += x_ij*price_levels[j]\n", " p.append(p_i)\n", + " \n", "# plus historical prices\n", "all_p = p_data + p\n", + "\n", "all_p" ] }, { "cell_type": "markdown", - "id": "19373b02", + "id": "44be704a", "metadata": {}, "source": [ - "Next, we can input the price variables into our fitted model to estimate the demand, and then use the demand together with price to represent revenue $R$." + "Next, we can input the price variables into our fitted model to estimate the demand, and then use the demand together with the price to represent the revenue $R$." ] }, { "cell_type": "code", - "execution_count": 10, - "id": "43cb9f33", + "execution_count": 9, + "id": "60be057f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Revenue:\n", - "(((Binary(X_048)*Num(19.000000)+Binary(X_047)*Num(16.000000)+Binary(X_046)*Num(13.000000)+Binary(X_045)*Num(12.000000)+Binary(X_044)*Num(10.000000)+Binary(X_042)*Num(5.000000)+Binary(X_043)*Num(8.000000))*Num(-3.609573)+(Binary(X_041)*Num(19.000000)+Binary(X_040)*Num(16.000000)+Binary(X_039)*Num(13.000000)+Binary(X_038)*Num(12.000000)+Binary(X_037)*Num(10.000000)+Binary(X_035)*Num(5.000000)+Binary(X_036)*Num(8.000000))*Num(-3.233748)+(Binary(X_034)*Num(19.000000)+Binary(X_033)*Num(16.000000)+Binary(X_032)*Num(13.000000)+Binary(X_031)*Num(12.000000)+Binary(X_030)*Num(10.000000)+Binary(X_028)*Num(5.000000)+Binary(X_029)*Num(8.000000))*Num(-2.986190)+(Binary(X_027)*Num(19.000000)+Binary(X_026)*Num(16.000000)+Binary(X_025)*Num(13.000000)+Binary(X_024)*Num(12.000000)+Binary(X_023)*Num(10.000000)+Binary(X_021)*Num(5.000000)+Binary(X_022)*Num(8.000000))*Num(-2.044654)+(Binary(X_020)*Num(19.000000)+Binary(X_019)*Num(16.000000)+Binary(X_018)*Num(13.000000)+Binary(X_017)*Num(12.000000)+Binary(X_016)*Num(10.000000)+Binary(X_014)*Num(5.000000)+Binary(X_015)*Num(8.000000))*Num(-0.883294)+(Binary(X_013)*Num(19.000000)+Binary(X_012)*Num(16.000000)+Binary(X_011)*Num(13.000000)+Binary(X_010)*Num(12.000000)+Binary(X_009)*Num(10.000000)+Binary(X_007)*Num(5.000000)+Binary(X_008)*Num(8.000000))*Num(-0.572344)+(Binary(X_006)*Num(19.000000)+Binary(X_005)*Num(16.000000)+Binary(X_004)*Num(13.000000)+Binary(X_003)*Num(12.000000)+Binary(X_002)*Num(10.000000)+Binary(X_000)*Num(5.000000)+Binary(X_001)*Num(8.000000))*Num(-0.377907)+Num(301.262391))*(Binary(X_048)*Num(19.000000)+Binary(X_047)*Num(16.000000)+Binary(X_046)*Num(13.000000)+Binary(X_045)*Num(12.000000)+Binary(X_044)*Num(10.000000)+Binary(X_042)*Num(5.000000)+Binary(X_043)*Num(8.000000))+((Binary(X_041)*Num(19.000000)+Binary(X_040)*Num(16.000000)+Binary(X_039)*Num(13.000000)+Binary(X_038)*Num(12.000000)+Binary(X_037)*Num(10.000000)+Binary(X_035)*Num(5.000000)+Binary(X_036)*Num(8.000000))*Num(-3.609573)+(Binary(X_034)*Num(19.000000)+Binary(X_033)*Num(16.000000)+Binary(X_032)*Num(13.000000)+Binary(X_031)*Num(12.000000)+Binary(X_030)*Num(10.000000)+Binary(X_028)*Num(5.000000)+Binary(X_029)*Num(8.000000))*Num(-3.233748)+(Binary(X_027)*Num(19.000000)+Binary(X_026)*Num(16.000000)+Binary(X_025)*Num(13.000000)+Binary(X_024)*Num(12.000000)+Binary(X_023)*Num(10.000000)+Binary(X_021)*Num(5.000000)+Binary(X_022)*Num(8.000000))*Num(-2.986190)+(Binary(X_020)*Num(19.000000)+Binary(X_019)*Num(16.000000)+Binary(X_018)*Num(13.000000)+Binary(X_017)*Num(12.000000)+Binary(X_016)*Num(10.000000)+Binary(X_014)*Num(5.000000)+Binary(X_015)*Num(8.000000))*Num(-2.044654)+(Binary(X_013)*Num(19.000000)+Binary(X_012)*Num(16.000000)+Binary(X_011)*Num(13.000000)+Binary(X_010)*Num(12.000000)+Binary(X_009)*Num(10.000000)+Binary(X_007)*Num(5.000000)+Binary(X_008)*Num(8.000000))*Num(-0.883294)+(Binary(X_006)*Num(19.000000)+Binary(X_005)*Num(16.000000)+Binary(X_004)*Num(13.000000)+Binary(X_003)*Num(12.000000)+Binary(X_002)*Num(10.000000)+Binary(X_000)*Num(5.000000)+Binary(X_001)*Num(8.000000))*Num(-0.572344)+Num(298.239131))*(Binary(X_041)*Num(19.000000)+Binary(X_040)*Num(16.000000)+Binary(X_039)*Num(13.000000)+Binary(X_038)*Num(12.000000)+Binary(X_037)*Num(10.000000)+Binary(X_035)*Num(5.000000)+Binary(X_036)*Num(8.000000))+((Binary(X_034)*Num(19.000000)+Binary(X_033)*Num(16.000000)+Binary(X_032)*Num(13.000000)+Binary(X_031)*Num(12.000000)+Binary(X_030)*Num(10.000000)+Binary(X_028)*Num(5.000000)+Binary(X_029)*Num(8.000000))*Num(-3.609573)+(Binary(X_027)*Num(19.000000)+Binary(X_026)*Num(16.000000)+Binary(X_025)*Num(13.000000)+Binary(X_024)*Num(12.000000)+Binary(X_023)*Num(10.000000)+Binary(X_021)*Num(5.000000)+Binary(X_022)*Num(8.000000))*Num(-3.233748)+(Binary(X_020)*Num(19.000000)+Binary(X_019)*Num(16.000000)+Binary(X_018)*Num(13.000000)+Binary(X_017)*Num(12.000000)+Binary(X_016)*Num(10.000000)+Binary(X_014)*Num(5.000000)+Binary(X_015)*Num(8.000000))*Num(-2.986190)+(Binary(X_013)*Num(19.000000)+Binary(X_012)*Num(16.000000)+Binary(X_011)*Num(13.000000)+Binary(X_010)*Num(12.000000)+Binary(X_009)*Num(10.000000)+Binary(X_007)*Num(5.000000)+Binary(X_008)*Num(8.000000))*Num(-2.044654)+(Binary(X_006)*Num(19.000000)+Binary(X_005)*Num(16.000000)+Binary(X_004)*Num(13.000000)+Binary(X_003)*Num(12.000000)+Binary(X_002)*Num(10.000000)+Binary(X_000)*Num(5.000000)+Binary(X_001)*Num(8.000000))*Num(-0.883294)+Num(293.660378))*(Binary(X_034)*Num(19.000000)+Binary(X_033)*Num(16.000000)+Binary(X_032)*Num(13.000000)+Binary(X_031)*Num(12.000000)+Binary(X_030)*Num(10.000000)+Binary(X_028)*Num(5.000000)+Binary(X_029)*Num(8.000000))+((Binary(X_027)*Num(19.000000)+Binary(X_026)*Num(16.000000)+Binary(X_025)*Num(13.000000)+Binary(X_024)*Num(12.000000)+Binary(X_023)*Num(10.000000)+Binary(X_021)*Num(5.000000)+Binary(X_022)*Num(8.000000))*Num(-3.609573)+(Binary(X_020)*Num(19.000000)+Binary(X_019)*Num(16.000000)+Binary(X_018)*Num(13.000000)+Binary(X_017)*Num(12.000000)+Binary(X_016)*Num(10.000000)+Binary(X_014)*Num(5.000000)+Binary(X_015)*Num(8.000000))*Num(-3.233748)+(Binary(X_013)*Num(19.000000)+Binary(X_012)*Num(16.000000)+Binary(X_011)*Num(13.000000)+Binary(X_010)*Num(12.000000)+Binary(X_009)*Num(10.000000)+Binary(X_007)*Num(5.000000)+Binary(X_008)*Num(8.000000))*Num(-2.986190)+(Binary(X_006)*Num(19.000000)+Binary(X_005)*Num(16.000000)+Binary(X_004)*Num(13.000000)+Binary(X_003)*Num(12.000000)+Binary(X_002)*Num(10.000000)+Binary(X_000)*Num(5.000000)+Binary(X_001)*Num(8.000000))*Num(-2.044654)+Num(287.727751))*(Binary(X_027)*Num(19.000000)+Binary(X_026)*Num(16.000000)+Binary(X_025)*Num(13.000000)+Binary(X_024)*Num(12.000000)+Binary(X_023)*Num(10.000000)+Binary(X_021)*Num(5.000000)+Binary(X_022)*Num(8.000000))+((Binary(X_020)*Num(19.000000)+Binary(X_019)*Num(16.000000)+Binary(X_018)*Num(13.000000)+Binary(X_017)*Num(12.000000)+Binary(X_016)*Num(10.000000)+Binary(X_014)*Num(5.000000)+Binary(X_015)*Num(8.000000))*Num(-3.609573)+(Binary(X_013)*Num(19.000000)+Binary(X_012)*Num(16.000000)+Binary(X_011)*Num(13.000000)+Binary(X_010)*Num(12.000000)+Binary(X_009)*Num(10.000000)+Binary(X_007)*Num(5.000000)+Binary(X_008)*Num(8.000000))*Num(-3.233748)+(Binary(X_006)*Num(19.000000)+Binary(X_005)*Num(16.000000)+Binary(X_004)*Num(13.000000)+Binary(X_003)*Num(12.000000)+Binary(X_002)*Num(10.000000)+Binary(X_000)*Num(5.000000)+Binary(X_001)*Num(8.000000))*Num(-2.986190)+Num(273.087556))*(Binary(X_020)*Num(19.000000)+Binary(X_019)*Num(16.000000)+Binary(X_018)*Num(13.000000)+Binary(X_017)*Num(12.000000)+Binary(X_016)*Num(10.000000)+Binary(X_014)*Num(5.000000)+Binary(X_015)*Num(8.000000))+((Binary(X_006)*Num(19.000000)+Binary(X_005)*Num(16.000000)+Binary(X_004)*Num(13.000000)+Binary(X_003)*Num(12.000000)+Binary(X_002)*Num(10.000000)+Binary(X_000)*Num(5.000000)+Binary(X_001)*Num(8.000000))*Num(-3.609573)+Num(229.261137))*(Binary(X_006)*Num(19.000000)+Binary(X_005)*Num(16.000000)+Binary(X_004)*Num(13.000000)+Binary(X_003)*Num(12.000000)+Binary(X_002)*Num(10.000000)+Binary(X_000)*Num(5.000000)+Binary(X_001)*Num(8.000000))+((Binary(X_013)*Num(19.000000)+Binary(X_012)*Num(16.000000)+Binary(X_011)*Num(13.000000)+Binary(X_010)*Num(12.000000)+Binary(X_009)*Num(10.000000)+Binary(X_007)*Num(5.000000)+Binary(X_008)*Num(8.000000))*Num(-3.609573)+(Binary(X_006)*Num(19.000000)+Binary(X_005)*Num(16.000000)+Binary(X_004)*Num(13.000000)+Binary(X_003)*Num(12.000000)+Binary(X_002)*Num(10.000000)+Binary(X_000)*Num(5.000000)+Binary(X_001)*Num(8.000000))*Num(-3.233748)+Num(250.714192))*(Binary(X_013)*Num(19.000000)+Binary(X_012)*Num(16.000000)+Binary(X_011)*Num(13.000000)+Binary(X_010)*Num(12.000000)+Binary(X_009)*Num(10.000000)+Binary(X_007)*Num(5.000000)+Binary(X_008)*Num(8.000000)))\n" + "Revenue:\n" ] + }, + { + "data": { + "text/plain": [ + "'(((Binary(X_048)*Num(19.000000)+Binary(X_047)*Num(16.000000)+Binary(X_046)*Num(13.000000)+Binary(X...m(12.000000)+Binary(X_009)*Num(10.000000)+Binary(X_007)*Num(5.000000)+Binary(X_008)*Num(8.000000)))'" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ @@ -479,30 +502,30 @@ "\n", "# get d, rev\n", "def get_demands_rev(a,b,hist_p, p):\n", + " \"\"\" represent the next n days demands and total revenue, based on:\n", + " 1. the fitted coefficients a,b\n", + " 2. the historical price hist_p\n", + " 3. and the future price decisions represented by binary variable x\n", + " \"\"\"\n", " all_p = hist_p + p\n", " t = len(a)\n", - " d = []\n", - " rev = 0\n", - " for i in range(t):\n", - " d_i = get_demand(\n", + " d = [get_demand(\n", " coeff=a,\n", " b=b,\n", " prices=all_p[i+1:i+1+t]\n", - " )\n", - " #print(f'Demand at T+{i}:')\n", - " #print(d_i,'\\n')\n", - " d.append(d_i)\n", - " rev += d_i * p[i]\n", + " ) for i in range(t)]\n", + " rev = np.dot(d, p)\n", " return d, rev\n", "\n", "d, rev = get_demands_rev(a,b,p_data, p)\n", + "\n", "print('Revenue:')\n", - "print(rev)" + "repr_compact.repr(rev)" ] }, { "cell_type": "markdown", - "id": "d9a5e5b8", + "id": "2c089e12", "metadata": {}, "source": [ "## 2.2 Add penalty for prediction uncertainty" @@ -510,14 +533,14 @@ }, { "cell_type": "markdown", - "id": "f4a146fa", + "id": "676b7ac3", "metadata": {}, "source": [ - "In optimisation, we usually desire to reduce the risk while maximizing the reward, which means we want to reduce the estimated uncertainty/variance of the predicted demands. Therefore, we add a penalty term in the objective function to represent the uncertainty of the predicted demand. The uncertainty of the predicted demand $d_t$ can be represented by its estimated variance.\n", + "In optimization, we usually desire to reduce the risk while maximizing the reward, which means we want to reduce the estimated uncertainty/variance of the predicted demands. Therefore, we add a penalty term in the objective function to represent the uncertainty of the predicted demand. The uncertainty of the predicted demand $d_t$ can be represented by its estimated variance,\n", "\n", "$$H=Revenue-\\beta\\sum_{t=T}^{T+n-1}var(d_t)$$\n", "\n", - "Where $\\beta$ is the regularized parameters to control the effect of risk esitmation. The variance of the demand predictions can be estimated as: $$var(d_t)=\\sigma^2(1+\\vec{p}_t'(\\vec{X}'\\vec{X})^{-1}\\vec{p}_t)$$\n", + "where $\\beta$ is the regularization parameter to control the effect of risk estimation. The variance of the demand predictions can be estimated as [10]: $$var(d_t)=\\sigma^2(1+\\vec{p}_t'(\\vec{X}'\\vec{X})^{-1}\\vec{p}_t)$$\n", "\n", "where $\\vec{p}_t'=[1, p_{t-n+1},p_{t-n+2}, \\ldots,p_{t}]$ is the price vector to estimate demand $d_t$. $\\vec{X}$ are the observations in the training dataset used to fit the demand model, where each row is an observation in the training set.\n", "\n", @@ -532,23 +555,24 @@ }, { "cell_type": "code", - "execution_count": 11, - "id": "a912ae7e", + "execution_count": 10, + "id": "84fe4671", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - 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+ "'((((Binary(X_048)*Num(19.000000)+Binary(X_047)*Num(16.000000)+Binary(X_046)*Num(13.000000)+Binary(...X_001)*Num(8.000000))*Num(-0.000535)+Num(0.016381))+Num(1.000000))*Num(100.000000))*Num(-1.000000))'" ] }, - "execution_count": 11, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta=1.\n", + "\n", "def get_variance(data_x, p, sigma):\n", " \"\"\"\n", " :param data_x (np.array): [n_samples, n_days]\n", @@ -575,12 +599,13 @@ " return var\n", "\n", "objective = rev - beta * get_overall_variance(data_x, p_data, p, sigma)\n", - "objective" + "\n", + "repr_compact.repr(objective)" ] }, { "cell_type": "markdown", - "id": "9f23641a", + "id": "5e07dfcf", "metadata": {}, "source": [ "## 2.3 Add penalty for equality constraints" @@ -588,30 +613,30 @@ }, { "cell_type": "markdown", - "id": "20ad0481", + "id": "647d95b8", "metadata": {}, "source": [ - "As we mentioned above that price can only take one option per day, this means that one and only one of the binary variables in a day must be $1$ and others must be $0$. Formallly, we have equality constraints:\n", + "Since the price can only take one value per day, exactly one of the binary variables in a day must be $1$, and the others must be $0$. Formallly, we have equality constraints:\n", "$$\\sum_{k=0}^{m-1}x_{t,k}=1, \\;t\\in[T, T+1, \\cdots, T+n-1]$$\n", "\n", - "We can easily incorporate this equality constraint into the objective function by substracting a penalty term $H_p$ with large enough coefficients $L_p$. If the solution satisfies these constraints, the penalty term will be 0, otherwise a large penalty will be imposed.\n", + "We can easily incorporate this equality constraint into the objective function by substracting a penalty term $H_p$ with large enough coefficient $L_p$. If the solution satisfies these constraints, the penalty term will be 0, otherwise a large penalty will be imposed.\n", "\n", "$$H_p=L_p\\sum_{t=T}^{t=T+n-1}[(\\sum_{k=0}^{m-1}x_{t,k})-1]^{2}$$" ] }, { "cell_type": "code", - "execution_count": 12, - "id": "ad1dc004", + "execution_count": 11, + "id": "2bdc7ef9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - 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+ "'(((((((((((Binary(X_048)*Num(19.000000)+Binary(X_047)*Num(16.000000)+Binary(X_046)*Num(13.000000)+...nary(X_044)+Binary(X_042)+Binary(X_043))+Num(-1.000000))*Num(10000000000000.000000)*Num(-1.000000))'" ] }, - "execution_count": 12, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } @@ -619,18 +644,17 @@ "source": [ "# add equalty constraints\n", "Lp=1e13\n", + "\n", "for i in range(t):\n", - " penalty = x[i*n_level]\n", - " for j in range(1, n_level):\n", - " penalty += x[i*n_level+j]\n", - " penalty = ((penalty-1)**2)*Lp\n", - " objective -= penalty\n", - "objective" + " penalty_i = ((sum(x[i*n_level:(i+1)*n_level]) - 1)**2)*Lp\n", + " objective -= penalty_i\n", + " \n", + "repr_compact.repr(objective)" ] }, { "cell_type": "markdown", - "id": "18603c19", + "id": "ac0eb6e8", "metadata": {}, "source": [ "# 3. Solve QUBO with Braket" @@ -638,7 +662,7 @@ }, { "cell_type": "markdown", - "id": "b847c8f9", + "id": "fc8330b6", "metadata": {}, "source": [ "Now we have transformed to the total objective function which:\n", @@ -654,7 +678,7 @@ }, { "cell_type": "markdown", - "id": "53911f70", + "id": "814e0eb0", "metadata": {}, "source": [ "Amazon Braket provides access to quantum annealers from D-Wave Systems Inc. which are specifically designed to solve QUBO problems. A quantum annealer is a hardware implementation of Quantum Annealing (QA) which is a generic algorithm to solve combinatorial optimization problems by taking advantage of quantum fluctuations to escape local minima in complex energy landscapes by effect of tunnelling through barriers separating local minima [5]. Through a simple Amazon Braket API call, the formatted QUBO problem can be embedded to the hardwired topology of the machine and submitted to machine. In turn, the quantum annealer performs an annealing process and obtains a result. However, because of the sparsity of the underlying chip, one typically faces a certain overhead in embedding the original QUBO problem to the D-Wave hardware, because (typically) one logical binary variable maps onto several physical qubits, in order to effectively distill the connectivity of the original QUBO problem. For more details, we refer to the Amazon Braket tutorial notebook available here (https://github.com/aws/amazon-braket-examples/blob/main/examples/quantum_annealing/Dwave_Anatomy.ipynb)." @@ -662,55 +686,31 @@ }, { "cell_type": "code", - "execution_count": 13, - "id": "105323af", - "metadata": {}, - "outputs": [], - "source": [ - "from braket.aws import AwsDevice\n", - "from braket.ocean_plugin import BraketSampler, BraketDWaveSampler\n", - "\n", - "import matplotlib.pyplot as plt\n", - "# magic word for producing visualizations in notebook\n", - "%matplotlib inline\n", - "import time\n", - "from collections import defaultdict\n", - "from itertools import combinations\n", - "import math\n", - "import networkx as nx\n", - "import dwave_networkx as dnx\n", - "import minorminer\n", - "import dimod\n", - "from dimod.binary_quadratic_model import BinaryQuadraticModel\n", - "from dwave.system.composites import EmbeddingComposite" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - 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827.5870047578463, ('X_019', 'X_013'): 982.69260742879, ('X_010', 'X_013'): 20000000001664.652, ('X_010', 'X_026'): 572.3665512211251, ('X_026', 'X_013'): 906.2470394334479}, 70000000000715.1, 'BINARY')" + "\"BinaryQuadraticModel({X_005: -10000000002744.719, X_030: -10000000002576.855, X_036: -100000000021...', 'X_026'): 572.3665512211251, ('X_026', 'X_013'): 906.2470394334479}, 70000000000715.1, 'BINARY')\"" ] }, - "execution_count": 14, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model = (-objective).compile().to_bqm()\n", - "model" + "\n", + "repr_compact.repr(model)" ] }, { "cell_type": "code", - "execution_count": 15, - "id": "dc155a00", + "execution_count": 13, + "id": "b78a79d5", "metadata": {}, "outputs": [ { @@ -719,7 +719,7 @@ "49" ] }, - "execution_count": 15, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } @@ -730,10027 +730,220 @@ }, { "cell_type": "markdown", - "id": "f61d635c", + "id": "b3e984dd", "metadata": {}, "source": [ - "We embed and submit the QUBO task to be solved by a quantum annealer at D-wave backend. Similar to classical simulated annealing, we take several independent shots in order to increase our chances for success in finding a high-quality solution to the QUBO problem. The response contains a number of rows. Each row represents the optimization result of a single shot, including the binary decision variables $[x_T,\\cdots,x_{T+n-1}]$, and corresponding energy which is the negative value of objective function, i.e. $H$. Below we show how to submit a QUBO problem to D-Wave and provide a sample response. Here, the key figure of merit is listed in the column labelled with energy, representing the value for the objective function . We can then easily read off the best bit string found." + "We embed and submit the QUBO task to be solved by a quantum annealer at D-wave backend. Similar to classical simulated annealing, we take several independent shots in order to increase our chances for success in finding a high-quality solution to the QUBO problem. The response contains a number of rows. Each row represents the optimization result of a single shot, including the binary decision variables $[x_T,\\cdots,x_{T+n-1}]$, and corresponding energy which is the negative value of objective function, i.e. $H$. Below we show how to submit a QUBO problem to D-Wave and provide a sample response. Here, the key figure of merit is listed in the column labelled with energy, representing the value for the objective function . We can then easily read off the best bit string found.\n", + "\n", + "Each row represents an optimized solution. The columns starting with `X_` shows the value of the binary decision variables $x_{t,k}$ and the `energy` column shows the negative value of objective, i.e. $-H$" ] }, { "cell_type": "code", - "execution_count": 16, - "id": "ee123eac", + "execution_count": 15, + "id": "038d79f6", "metadata": { "scrolled": true }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - " X_000 X_001 X_002 X_003 X_004 ... 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The optimal price level is higher than the past 7 days, which results in the demand decreasing." + "The optimized price path and corresponding demand curve are plotted below, respectively. The optimal price level is higher than the past 7 days, which results in the demand decreasing." ] }, { "cell_type": "code", - "execution_count": 18, - "id": "da89ecaa", + "execution_count": 17, + "id": "6fd69a26", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -10844,7 +1042,6 @@ } ], "source": [ - "import matplotlib.pyplot as plt\n", "plt.rcParams.update({'font.size': 18})\n", "plt.figure(figsize=(10,8))\n", "plt.plot(range(1,8),opt_decoded_prices)\n", @@ -10855,16 +1052,16 @@ }, { "cell_type": "markdown", - "id": "d9e89561", + "id": "7f6dd685", "metadata": {}, "source": [ - "__now, Let's get the demand of each day and the total revenue__" + "Let's also calculate the total revenue, and plot the demand of each day." ] }, { "cell_type": "code", - "execution_count": 19, - "id": "7bac09eb", + "execution_count": 18, + "id": "d54a218a", "metadata": {}, "outputs": [ { @@ -10872,33 +1069,34 @@ "text/plain": [ "([182.33668654152052,\n", " 161.75101851993844,\n", - " 145.30390869346718,\n", - " 136.97318179740145,\n", - " 149.09503161262904,\n", - " 133.2779083933537,\n", - " 108.67908278844949],\n", - " 13395.87852055809)" + " 148.9134817833946,\n", + " 165.47394138330202,\n", + " 167.4983113772031,\n", + " 138.92967848592662,\n", + " 108.20132675236677],\n", + " 13457.943867415815)" ] }, - "execution_count": 19, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "opt_d, max_rev = get_demands_rev(a,b,p_data, opt_decoded_prices)\n", + "\n", "opt_d, max_rev" ] }, { "cell_type": "code", - "execution_count": 20, - "id": "3e2a6a19", + "execution_count": 19, + "id": "81afd216", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -10910,7 +1108,6 @@ } ], "source": [ - "import matplotlib.pyplot as plt\n", "plt.rcParams.update({'font.size': 18})\n", "plt.figure(figsize=(10,8))\n", "plt.plot(range(1,8),opt_d)\n", @@ -10921,108 +1118,144 @@ }, { "cell_type": "markdown", - "id": "73d15c61", + "id": "f98366dd", "metadata": {}, "source": [ - "__Finally, let's get the overall uncertainty of the demand predictions, here we simply use demand variance to indicate the uncertainty__" + "Finally, let's get the overall uncertainty of the demand predictions. Here we simply use the estimated demand variance to indicate the uncertainty." ] }, { "cell_type": "code", - "execution_count": 21, - "id": "4d956f71", + "execution_count": 20, + "id": "f320dffc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "704.9419334213342" + "705.7816180128258" ] }, - "execution_count": 21, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "overall_variance = get_overall_variance(data_x, p_data, opt_decoded_prices, sigma)\n", + "\n", "overall_variance" ] }, { "cell_type": "markdown", - "id": "055079f6", + "id": "cacd0729", "metadata": {}, "source": [ "__We can also derive the standard deviation of the revenue based on the variance of demand__\n", "\n", - "$$std(R)=\\sqrt{(\\sum_{t=T}^{T+n-1}var(\\hat{d}_t)*p^2)}$$" + "$$std(R)=\\sqrt{(\\sum_{t=T}^{T+n-1}var(\\hat{d}_t)*p_t^2) + \\sum_{t_1, t_2\\in [T,\\ldots,T+n-1] \\\\ t_1!=t_2}2p_{t_1}p_{t_2}cov(\\hat{d}_{t_1} \\hat{d}_{t_2}) }$$" + ] + }, + { + "cell_type": "markdown", + "id": "cce0c3dd", + "metadata": {}, + "source": [ + "where $cov(\\hat{d}_{t_1} \\hat{d}_{t_2}) = \\sigma^2(1+\\vec{p}_{t_1}'(\\vec{X}'\\vec{X})^{-1}\\vec{p}_{t_2})$" ] }, { "cell_type": "code", - "execution_count": 22, - "id": "5a077566", + "execution_count": 21, + "id": "10863eec", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "366.50526804215906" + "911.7464747275401" ] }, - "execution_count": 22, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ + "def get_covariance(data_x, p1, p2, sigma):\n", + " \"\"\"\n", + " :param data_x (np.array): [n_samples, n_days]\n", + " :param p1, p2 (list): [n_days]\n", + " :return: variance\n", + " \"\"\"\n", + " n_samples, t = data_x.shape\n", + " ones = np.ones((n_samples, 1), dtype=np.float)\n", + " x_mat = np.concatenate([ones, data_x], axis=1) # [n_samples, n_days+1]\n", + " x_mat = np.linalg.inv(\n", + " np.dot(x_mat.T, x_mat)\n", + " )\n", + " p1 = np.array([1.] + p1)\n", + " p2 = np.array([1.] + p2)\n", + " variance = (sigma**2) * (1. + p1.dot(x_mat).dot(p2))\n", + " return variance\n", + "\n", "def get_overall_revenue_variance(data_x, hist_p, p, sigma):\n", " all_p = hist_p + p\n", " t = len(p)\n", - " var = 0\n", - " for i in range(t):\n", - " var += get_variance(data_x, all_p[i+1:i+1+t], sigma) * (p[i]**2)\n", + " var = sum([get_variance(data_x, all_p[i+1:i+1+t], sigma) * (p[i]**2) for i in range(t)])\n", + " \n", + " # add covariance\n", + " var += sum([\n", + " get_covariance(\n", + " data_x,\n", + " all_p[i + 1:i + 1 + t],\n", + " all_p[j + 1:j + 1 + t],\n", + " sigma\n", + " ) * 2 * p[i] * p[j] for i, j in combinations(list(range(t)), 2) \n", + " ])\n", "\n", " return var\n", "\n", "revenue_variance = get_overall_revenue_variance(data_x, p_data, opt_decoded_prices, sigma)\n", + "\n", "np.sqrt(revenue_variance)" ] }, { "cell_type": "markdown", - "id": "c1e09f07", + "id": "d2eae3d0", "metadata": {}, "source": [ - "__We can investigate the value of the penality terms to see if any equality constraints are voilated. The penalty is close to zero showing that all the constraints are complied__" + "We can investigate the value of the penality terms to see if any equality constraints are violated. The penalty is close to zero showing that all the constraints are satisfied. This small but non-zero value is due to floating point precision." ] }, { "cell_type": "code", - "execution_count": 23, - "id": "b6f4ee49", + "execution_count": 22, + "id": "629c3d58", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "-0.0009128632445936091" + "-0.0018130970111087663" ] }, - "execution_count": 23, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "penalty = max_rev - beta*overall_variance + energy\n", + "\n", "penalty" ] }, { "cell_type": "markdown", - "id": "7ced7d24", + "id": "7e981832", "metadata": {}, "source": [ "For comparison, to assess the quality of this optimized result, we also iterate (by brute-force search) through all the $7^7=823,543$ possible price solutions to obtain the energy for each one, which takes more than 5 minutes to run on a standard ml.m5.2xlarge AWS instance. We plot the distribution of the energies of all the 823,543 possible solutions as shown below, where the red line represents our optimized result obtained from the quantum annealer. We can see that although the optimized result from the quantum annealer is not the global optimum with minimum cost, it is close-to-optimal and of good quality. " @@ -11030,8 +1263,8 @@ }, { "cell_type": "code", - "execution_count": 24, - "id": "c72602b6", + "execution_count": 23, + "id": "34f0bf56", "metadata": { "scrolled": true }, @@ -11872,6 +2105,7 @@ "all_var=[]\n", "all_energy=[]\n", "i=0\n", + "\n", "for p_t1 in price_levels:\n", " for p_t2 in price_levels:\n", " for p_t3 in price_levels:\n", @@ -11881,6 +2115,7 @@ " for p_t7 in price_levels:\n", " if i%1000==0:\n", " print(i)\n", + " \n", " _, sample_rev = get_demands_rev(a,b,p_data, [p_t1,p_t2,p_t3,p_t4,p_t5,p_t6,p_t7])\n", " sample_overall_variance = get_overall_variance(data_x, p_data, [p_t1,p_t2,p_t3,p_t4,p_t5,p_t6,p_t7], sigma)\n", " all_rev.append(sample_rev)\n", @@ -11891,13 +2126,13 @@ }, { "cell_type": "code", - "execution_count": 25, - "id": "1d471924", + "execution_count": 24, + "id": "bba5ae30", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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ZSZIk9ZJBVpIkSb1kkJUkSVIvGWQlSZLUSwZZSZIk9ZJBVpIkSb1kkJUkSVIvGWQlSZLUSwZZSZIk9ZJBVpIkSb1kkJUkSVIvGWQlSZLUSwZZSZIk9ZJBVpIkSb1kkJUkSVIvGWQlSZLUS9MOskn2ncRAJEmSpOnYegbPuTzJDcB7gbOqavUsj0nSHFp67IVzcpxVJy6fk+NIkrYcM1lacGy7fSvwzSQfSfLCJJnFcUmSJEkbNe0gW1UnVdXPAL8MnAP8D+BC4LYkf5lk6ayOUJIkSRphxh/2qqp/rao/BJ4AvBK4Hfg/wE1JLk7yu0keOUvjlCRJkjaw2VctqKp7qupM4LeBD7V9Ph/4MM3Sg9cl2WpzjyNJkiR1bVaQTfKIJC9O8o/AbcDBwP8D/gD4PeAG4ETgHVM8/7gk5ye5JUklWbWJ4+2a5ONJ7kxyT5LLk+y/kbEdk+SGJOuSfCPJyUm2X8h9S5IkaTwzCrJJnpbkROCbwMeAXwTeCfxMVf1KVX2oqs6vqucA7wEOmqKrtwD7AzcDd27imLsAnwf2AU4CXgfsAFyU5PkjnnIK8DbgeuAo4HzgtcAFSTZ43Qusb0mSJI1h2pffSvI5YF8gwGXAnwAfrar7p3jK5cCrpti3S1Xd0vb7JZqAN5UTgB2BZ1XVte1zzgK+DJyWZLeqqrZ9d5qAuaKqDuiM/VbgVOBA4NyF1rckSZLGN5MzsrvRnI3ctaqeW1V/v5EQC3AJ8NxROwYhdlPat+xfDFw6CIPt8+8GzgSeBuzVecpBNEH77UNdnQGspVkCsRD7liRJ0phmEmSXVNXrqurGcYqranVVXTaD43TtAWwDXDFi35XtthsI9wLWA1cNjWUdcO1Q7ULqW5IkSWOaSZB9YpLfmGpnkt+YwLVkd263t4/YN2hbMlS/pqrum6J+pySLFmDfD0pyRJKVSVauXu3N0yRJkobNJMj+NfD6jez/E+DNMxvOlLZrt6PC47qhmsHXo2pH1S+kvh9UVadX1bKqWrZ48eIpDidJkrTlmkmQ/SXgoo3sv5jmrl+zaW273WbEvm2HagZfj6odVb+Q+pYkSdKYZhJkHw98eyP7vwv8xMyGM6U72u2ot+EHbd237++geYt/VIBcQrM04P5O7ULpW5IkSWOaSZD9HrDLRvY/BfjBzIYzpeto3p7fZ8S+Z7fblZ22q2le297dwiTbAnsO1S6kviVJkjSmmQTZy4HDkzxheEfbdhjN3b1mTXu5qguA/ZI8o3O8Hdrj3ciGVxE4Dyjg6KGuDqdZk3rOAu1bkiRJY5r2DRFoPuz1G8C/JzmZ5pJTBTyT5oNeO9DcsWuTkrwMeHL77WJgUZI3tN/fVlVnd8qPA54HXJzkFOAumvC4BFjevalAVV2X5DTgyCQrgE8CT6e5+9ZlbHjDggXTtyRJksY37SBbVdcm+R3g/TS3XB0EsQBrgJdW1bhvlx8KPGeobXDFg8uAB4NsVd2UZF/gROBYYBFwDfDCqrpkRN9HA6uAI4Dl7djeCRxfVeuHXtNC6luSJEljmMkZWarqn5I8CfgfwFNpQuxXgYur6t5p9LPfNI/7FeAlY9Y+AJzcPnrTtyRJksYzoyAL0AbWj8/iWCRJkqSxzeTDXpIkSdK8m1GQTXJgkn9N8t0kD4x4/HC2BypJkiR1TXtpQZLX0Xxw6T+BK9utJEmSNKdmskb2NcC/Ac+bzge7JEmSpNk0k6UFTwA+ZIiVJEnSfJpJkL0J2HG2ByJJkiRNx0yC7MnAoUkePduDkSRJksY1kzWyDwDfBb6S5H3ArW3bBqrqrM0cmyRJkjSlmQTZD3S+fsMUNQUYZCVJkjQxMwmyz531UUiSJEnTNO0gW1WXTWIgkiRJ0nRs1i1qk2yTZEmSRbM1IEmSJGkcM71F7c8n+QzwA+DrwC+17Y9P8ukkz5/FMUqSJEkPMe0gm2RP4HJgF4Y+0FVV3wUeBbx8VkYnSZIkTWEmZ2TfBNwB7A4cC2Ro/6eBvTdzXJIkSdJGzSTI/jJwRlXdTXOZrWFfB3berFFJkiRJmzCTILst8P2N7P+xGY5FkiRJGttMriN7M/CsjezfH7h+ZsPRw93SYy+c7yFIkqSHiZmckT0XeNnQlQkKIMmfAC8Ezp6FsUmSJElTmskZ2b8BXgBcBNxAE2JPSbIYeALwKeBvZ22EkiRJ0gjTPiNbVffTBNk/Be4F1gFPA9YArwdeVFXrZ3OQkiRJ0rCZnJGlqn4InNI+JEmSpDm3WbeolSRJkubLtM/IJvmDceqq6qxNV0mSJEkzM5OlBR+g+YDX8B29hm+OYJCVJEnSxMwkyD53in52AV4NrAX+fHMGJUmSJG3KtINsVV02xa5PJ/kgcBXw88BnN2dgkiRJ0sbM6oe9quo+4EM0Z2YlSZKkiZnEVQvuA5ZMoF9JkiTpQbMaZJP8JPAq4NbZ7FeSJEkaNpPLb31mil2PA3YDFgEv35xBSZIkSZsyk6sW/DQPvdRWAf8FrADeVVWf39yBSZIkSRszk6sWLJ3AOCRJkqRp8Ra1kiRJ6iWDrCRJknpp2kE2yfokD0zz8cPZGGySHZL8WZLrkvwgyZokn09ySJIM1e6a5ONJ7kxyT5LLk+w/Rb+PSHJMkhuSrEvyjSQnJ9l+ivqJ9S1JkqTxzOTDXmfR3LnrZ4GvAl8BQnPFgl2B64BrZmuAA0keAfwz8IvAB4F3AtsBBwHvB54O/O+2dhfg88APgZOA7wOHAxcl+bWqumSo+1OA1wIfA05u+3ot8Mwkz6+q9Z1xTKxvSZIkjW8mQfYc4ADgN6vqE90dSX4TOBv406r61CyMr+sXgF8C3l5Vx3SO+bfADcAraYMscAKwI/Csqrq2rTsL+DJwWpLdqqra9t2Bo4AVVXVAp99bgVOBA4FzO+OYZN+SJEka00zWyL4ZeM9wiAWoqo8DpwN/tbkDG+HH2u0dQ8e8H1gD3APQvmX/YuDSQdBs6+4GzgSeBuzV6eIgmjPKbx863hnAWuDgQcMk+5YkSdL0zCTI7gHcvJH9N9EsO5htVwHfA16f5KVJntSuVT0BeBbwxs74tgGuGNHHle22Gzb3Ata3/T+oqtYB1w7VTrJvSZIkTcNMguydwK9uZP8LadaNzqqqupPmbOh/Af8A3EazpOA1wAFVdUZbunO7vX1EN4O2JZ22nYE1VXXfFPU7JVk0B31vIMkRSVYmWbl69epRJZIkSVu0mQTZc4GXJHlvkqcn2ap9PD3J+4AX0ayjnYS7gS8BfwP8NnAYzRngc5O8oK3Zrt2OCo/rhmoGX4+qHVU/yb43UFWnV9Wyqlq2ePHiKbqQJEnacs3kw15vAJ4CvAI4hOatc2hCcYAL2ppZleTnaK4WcExV/V2n/e9pwu0Z7RUF1ra7thnRzbbtdm2nbS3w+CkOO1w/yb4lSZI0DTO5Re19wG8l+VXgN4GfogmwNwP/WFUXz+4QH3QMTfg7f2g8a5NcCBwJLOVHHwZbwkMN2rpLA+4AfibJNiOWACyhWRpwf6d2Un1LkiRpGmZyRhaANrBOKrSOMgiKW43Yt3Vnex3N2/n7jKh7drtd2Wm7mmbN797A5YPGJNsCewKf69ROsm9JkiRNw2bdojbJU5Lsm+QxszWgjbi+3R4yNIYdgZfQfAjt5vZSWBcA+yV5RqduB5o1tTey4VUEzgMKOHroeIfTrF99cL3vJPuWJEnS9MzojGySFwHvoHkrH+AFwGeSPJ5mHeuxVfWRWRnhj7wd+APgxHa97L8Cj6MJhT8JvKaqBrfCPQ54HnBxklOAu9q6JcDywQ0LAKrquiSnAUcmWQF8kh/dfesyHnrDgkn2LUmSpDFNO8gm2Y/mdqvX0twq9o2DfVX13SQ309yxalaDbFXdlmRv4HiaIHkgcG87jj+pqhWd2puS7AucCBwLLKK5be4LR9xCFpozpquAI4DlNDdYeCdw/PAtZCfZtyRJksY3kzOyxwNfpLll7GPpBNnWFTRnTmddVd0MvHzM2q/QLDkYp/YB4OT2Ma99S5IkaTwzWSO7DDhnI2cTvwk8YeZDkiRJkjZtJkF2K6a+yD/AToCXlJIkSdJEzSTIfgX45Y3sfxHN0gNJkiRpYmYSZN8L/E6SQzvPryTbJTmV5hqrp8/WACVJkqRRZnJnr3e3n9o/g+YDTAX8PfDjNMsO3l9VXh9VkiRJEzWj68hW1cFJPgocDOxGc4vafwPOqqqPzuL4JEmSpJGmFWSTPAp4KfDVqvoYzfVkJUmSpDk33TWy99EsKXjmBMYiSZIkjW1aQba9duw3gB+bzHAkSZKk8czkqgUfBF6WZJvZHowkSZI0rpl82OvzwG8D1yb5W+BGYO1wUVV9bjPHJkmSJE1pJkH2U52v30Fz+a2utG1bzXRQkiRJ0qaMFWST7A3cVFX/BbxiskOSJEmSNm3cM7JXAC8Dzq2qDybZgebuXX9VVddPbHSSJEnSFMb9sFeGvt8G+D3gCbM7HEmSJGk8M7lqwcBwuJUkSZLmzOYEWUmSJGneGGQlSZLUS9O5/NavJxmsid2O5hJbL02y54jaqqpTNnt0kiRJ0hSmE2R/v310vXKK2gIMspIkSZqYcYPscyc6CkmSJGmaxgqyVXXZpAciSZIkTcdMblErSdO29NgLJ36MVScun/gxJEkLh1ctkCRJUi8ZZCVJktRLBllJkiT1kkFWkiRJvWSQlSRJUi8ZZCVJktRLBllJkiT1kkFWkiRJvWSQlSRJUi8ZZCVJktRLBllJkiT1kkFWkiRJvdS7IJvkcUn+JslNSdYlWZ3ks0l+eahu1yQfT3JnknuSXJ5k/yn6fESSY5Lc0Pb5jSQnJ9l+ivqJ9S1JkqTxbD3fA5iOJE8GLgV2AN4LfA14DLAHsKRTtwvweeCHwEnA94HDgYuS/FpVXTLU9SnAa4GPAScDT2+/f2aS51fV+rnoW5IkSePrVZAFPkQz5j2q6lsbqTsB2BF4VlVdC5DkLODLwGlJdquqatt3B44CVlTVAYMOktwKnAocCJw7R31LkiRpTL1ZWpDkV4BfAk6qqm8leWSS7UbUbQ+8GLh0EDQBqupu4EzgacBenaccBAR4+1BXZwBrgYPnom9JkiRNT2+CLPDr7fbrSS4A7gXuSfK1JN1AuAewDXDFiD6ubLfdsLkXsB64qltYVeuAa4dqJ9m3JEmSpqFPQXbXdnsG8Djg5cChwP3A2Ule0e7fud3ePqKPQduSTtvOwJqqum+K+p2SLJqDviVJkjQNfVoj++h2+wPguVV1P0CSjwG3AG9J8kFgsNxgVHhc1267SxK2m6J2uP7+Cfe9gSRHAEcAPOlJT5qiC0mSpC1Xn87I3ttu/34QYgGq6k7gE8ATaM7arm13bTOij23b7dpO29opakfVT7LvDVTV6VW1rKqWLV68eIouJEmStlx9CrLfbLffHrFvcAWDxwJ3tF8vGVE3aOsuDbiD5i3+UYFzCc3SgPs7tZPqW5IkSdPQpyA7+MDUE0fsG7R9F7iO5u38fUbUPbvdruy0XU0zD3t3C5NsC+w5VDvJviVJkjQNfQqyH6dZH3twkh0GjUl+EvhN4Maquqm9FNYFwH5JntGp2wE4DLiRDa8icB5QwNFDxzucZv3qOYOGSfYtSZKk6enNh72q6s4kfwq8B7gyyfuARcAftdsjO+XHAc8DLk5yCnAXTXhcAiwf3LCg7fe6JKcBRyZZAXySH9196zIeesOCSfYtSZKkMfUmyELzAagka4DXA2+muUbrFcDvV9W/dupuSrIvcCJwLE3QvQZ44YhbyEJzxnQVzVUClgNrgHcCxw/fQnaSfUuSJGl8vQqyAFW1AlgxRt1XgJeM2ecDwMntY5z6ifUtSZKk8fRpjawkSZL0IIOsJEmSeskgK0mSpF4yyEqSJKmXDLKSJEnqJYOsJEmSeskgK0mSpF4yyEqSJKmXDLKSJEnqJYOsJEmSeskgK0mSpF4yyEqSJKmXDLKSJEnqJYOsJEmSeskgK0mSpF4yyEqSJKmXDLKSJEnqJYOsJEmSeskgK0mSpF4yyEqSJKmXDLKSJEnqJYOsJEmSeskgK0mSpF4yyEqSJKmXDLKSJEnqJYOsJEmSeskgK0mSpF4yyEqSJKmXDLKSJEnqJbnEbukAACAASURBVIOsJEmSeskgK0mSpF4yyEqSJKmXDLKSJEnqJYOsJEmSeskgK0mSpF4yyEqSJKmXeh1kk2yX5NYkleRdI/bvmuTjSe5Mck+Sy5PsP0Vfj0hyTJIbkqxL8o0kJyfZfor6ifUtSZKkTet1kAXeBOw0akeSXYDPA/sAJwGvA3YALkry/BFPOQV4G3A9cBRwPvBa4IIkG8zTJPuWJEnSeLae7wHMVJKfB44GXg+cPKLkBGBH4FlVdW37nLOALwOnJdmtqqpt350mYK6oqgM6x7gVOBU4EDh3jvqWJEnSGHp5NjDJVsAZwL8AK0bs3x54MXDpIGgCVNXdwJnA04C9Ok85CAjw9qGuzgDWAgfPRd+SJEkaXy+DLHAMsBtw5BT79wC2Aa4Yse/KdtsNm3sB64GruoVVtQ64dqh2kn1LkiRpTL0Lskl+CvhL4E1VtWqKsp3b7e0j9g3algzVr6mq+6ao3ynJojnoW5IkSWPqXZAF3g3cSvPhqals125Hhcd1QzWDr0fVjqqfZN8PSnJEkpVJVq5evXqKp0uSJG25ehVkkxwM/Crwqqr6742Urm2324zYt+1QzeDrUbWj6ifZ94Oq6vSqWlZVyxYvXjzF0yVJkrZcvblqQZJtaM7CfhL4dpKntLsGb+M/pm1bA9wxtK9r0NZdGnAH8DNJthmxBGAJzdKA+zu1k+pb0mZYeuyFEz/GqhOXT/wYkqTx9OmM7KOAxcBy4MbO49J2/8Ht94cB19G8nb/PiH6e3W5XdtquppmLvbuFSbYF9hyqnWTfkiRJGlOfguw9wEtHPF7d7v+X9vtPtJfCugDYL8kzBh0k2YEm6N7IhlcROA8omuvSdh1Os371nEHDJPuWJEnS+HqztKBdE/uR4fYkS9svb66q7v7jgOcBFyc5BbiLJjwuAZYPbljQ9n1dktOAI5OsoFm+8HSau29dxkNvWDDJviVJkjSG3gTZ6aqqm5LsC5wIHAssAq4BXlhVl4x4ytHAKuAImuULa4B3AsdX1fq56luSJEnj6X2Qba8lmyn2fQV4yZj9PEBzq9tRt7ud074lSZK0aX1aIytJkiQ9yCArSZKkXjLISpIkqZcMspIkSeolg6wkSZJ6ySArSZKkXjLISpIkqZcMspIkSeolg6wkSZJ6ySArSZKkXjLISpIkqZcMspIkSeolg6wkSZJ6ySArSZKkXjLISpIkqZcMspIkSeolg6wkSZJ6ySArSZKkXjLISpIkqZcMspIkSeolg6wkSZJ6ySArSZKkXjLISpIkqZcMspIkSeolg6wkSZJ6ySArSZKkXjLISpIkqZcMspIkSeolg6wkSZJ6ySArSZKkXjLISpIkqZcMspIkSeolg6wkSZJ6ySArSZKkXjLISpIkqZcMspIkSeql3gTZJE9L8qYkVyZZneQHSa5N8udJth9Rv2uSjye5M8k9SS5Psv8UfT8iyTFJbkiyLsk3kpw8qt9J9y1JkqTx9CbIAn8IHAPcDLwJeB3wVeCvgM8nedSgMMkuwOeBfYCT2todgIuSPH9E36cAbwOuB44CzgdeC1yQZIM5mmTfkiRJGt/W8z2AafgIcEJVfb/T9ndJbgT+HDgUeFfbfgKwI/CsqroWIMlZwJeB05LsVlXVtu9OEzBXVNUBg46T3AqcChwInNs55iT7lrTALT32wjk5zqoTl8/JcSSpz3pzRrCqVg6F2IHz2u3PArRv2b8YuHQQNNvn3w2cCTwN2Kvz/IOAAG8f6vcMYC1w8KBhkn1LkiRpenoTZDfiie32O+12D2Ab4IoRtVe2227Y3AtYD1zVLayqdcC1Q7WT7FuSJEnT0Osgm2Qr4Hjgh/zoLfqd2+3tI54yaFvSadsZWFNV901Rv1OSRXPQtyRJkqah10GW5i37ZwPHV9VX27bt2u2o8LhuqGbw9ajaUfWT7HsDSY5IsjLJytWrV0/RhSRJ0part0E2yZuBI4HTq+qEzq617XabEU/bdqhm8PWo2lH1k+x7A1V1elUtq6plixcvnqILSZKkLVefrlrwoCRvBN4AvB941dDuO9rtEh5q0NZdGnAH8DNJthmxBGAJzdKA++eg73nX/TT2h2/5TwAOnKNPaEuSJE1X787IJvkL4C+As4DDBpe66riO5u38fUY8/dntdmWn7Wqaedh76DjbAnsO1U6yb0mSJE1Dr4JskuOBNwJnA6+oqvXDNe2lsC4A9kvyjM5zdwAOA25kw6sInAcUcPRQV4fTrF89Zy76liRJ0vT0ZmlBktcAfwl8HbgE+P0k3ZLvVNWn2q+PA54HXJzkFOAumvC4BFjePYtbVdclOQ04MskK4JPA02nuvnUZD71hwST7liRJ0ph6E2T50TVXnwR8cMT+y4BPAVTVTUn2BU4EjgUWAdcAL6yqS0Y892hgFXAEsBxYA7yT5moIG5z1nWTfkiRJGl9vgmxVHQIcMo36rwAvGbP2AeDk9jGvfUuSJGk8vVojK0mSJA0YZCVJktRLBllJkiT1kkFWkiRJvWSQlSRJUi8ZZCVJktRLBllJkiT1kkFWkiRJvWSQlSRJUi8ZZCVJktRLBllJkiT1kkFWkiRJvWSQlSRJUi8ZZCVJktRLBllJkiT10tbzPQBJ0kMtPfbCiR9j1YnLJ34MSZokz8hKkiSplwyykiRJ6iWDrCRJknrJICtJkqReMshKkiSplwyykiRJ6iWDrCRJknrJICtJkqReMshKkiSplwyykiRJ6iWDrCRJknrJICtJkqReMshKkiSpl7ae7wFIkubH0mMvnJPjrDpx+ZwcR9KWxzOykiRJ6iWDrCRJknrJICtJkqReMshKkiSplwyykiRJ6iWDrCRJknrJy2/NgSSPAP4YeCWwFFgN/ANwfFXdM49Dk6SJm4vLfHmJL2nL5BnZuXEK8DbgeuAo4HzgtcAFbciVJEnSNHlGdsKS7E4TXldU1QGd9luBU4EDgXPnaXiSJEm9ZZCdvIOAAG8faj8DOBE4GIOsJG0Wly9IWyaD7OTtBawHruo2VtW6JNe2+yVJC5y39JUWHoPs5O0MrKmq+0bsux34xSSLqur+OR6XJGkB8uyyNL5U1XyP4WEtyc3AI6vqSSP2nQW8DHhsVX1vaN8RwBHtt7sCX93IYXYC1szOiLURzvPccJ7nhvM8N5znueE8z41x5/nJVbV40oMBz8jOhbXA46fYt22nZgNVdTpw+jgHSLKyqpbNbHgal/M8N5znueE8zw3neW44z3NjIc6zl36avDuAnZJsM2LfEpplBy4rkCRJmiaD7ORdTTPPe3cbk2wL7AmsnI9BSZIk9Z1BdvLOAwo4eqj9cGA74JxZOMZYSxC02ZznueE8zw3neW44z3PDeZ4bC26e/bDXHEjyTuBI4GPAJ4Gn09zZ61+B/atq/TwOT5IkqZcMsnMgyVY0Z2SPAJbSfOLvPOD4qrp7HocmSZLUWwZZSZIk9ZJrZOdBklcmOSfJDUkeSDLlvyaSvDzJRUm+mWRdktVJrkhySHumd9Rz/iDJvye5N8l3kpyZZOT13JLsnOSstt97k6xM8tKNjGfsvufbNOf5xUne39bek+SOJJckeeFGnuM8M+153jXJ3yT5TJLvJakkb9xE/84z05vntn5ic/FwnuepJNkhyUlJbk5yX5Jvt38zlkxRv2Dmv0+SPDLJq5N8of0b8b0k1yT54ySLRtQ7z9OUJj/UJh5Lhp6zcOe5qnzM8QNYBfwA+BzwjeY/w5S17wA+DBwHHAr8MXAxzQfI3jui/ph236U0SxneBNwNfBnYfqj2ccAt7f43tfWXts9/xeb0vRAe05znbwNfA94KHAa8HvhK+3r/3HmetXk+hOaWzTcCn25f5xs3Uu88z2yeJzYXD/d5nmI+HwV8of3Z/QDwSuDE9r/H14EnLNT579uD5gPQBXwE+COaz5dc1Lad5zzPyhz/NHDwiMfr2tf3732a53mf0C3xQbNO9hHt1//ERv6HtJE+Lmz/qD6h07YTcA9wFbBVp/032h+KPxvq46S2/Tc6bVu1z/9PYIeZ9r0QHtOZZ5oP3Q23bUdzR7X7ae6+5jxv/jw/Dtix/XoZGwmyzvNmzfPE5uLhPs9TzOfR7XiPG2r/RZq/w2cuxPnv24Pmlu4FfGyoPcDl7Vx3/xY7z7M7/8e1r/k1ffp5nveJ29IfzDzI/m37H3/XTtthbdvLRtTfDFw/1PZN4KYRtS9r+/ndmfa90B6bMc8nt6/72c7z7M4zmw6yzvMM53mSc7ElzXNnrP/Yvo4njNj3VZqzSY9aaPPftwfN7dgLOG3Evn8Afug8T2zuQ/NO2Vrakw19mWfXyPZEksck2SnJU5McCfwhzVvhN3XK9mq3V4zo4kpgtyQ7tP39JM2dxa6corbb37T6fph5Yrv9bqfNeZ4bzvMMTHIutuB5HtyZ8SG3E2/btgd+Fhbc/PfNze3jD5MclmRpkl2S/C/gt4ETqupecJ4n4DnAU4CPVtX3Bo19mGeDbH98GlhNE15PpVkn92tV9UCnZud2e/uI599O8y+uncesheYHbCZ9PywkeQbNH8/Lq+qWzi7neW44zzMzybnYUuf5y+12/25j+z/i3dpv/792u5Dmv1eq6ofAi4EvAWcAt9KcrDkROKqq/k+n3HmeXYe22zOH2hf8PG+9qQKNlmRHHnq3ro05tar+azMO+Wrgx4CfBJYDPwE8dqhmu3Z734jnrxuqmU7tTOpnxTzM8+C4i4EVwL00b5V0Oc+zNM+b4DzPbJ4nORe9mOepbMb8vxt4FfDuJNvQnC16Ms2HQwdXj5mLOVpQ8zmVzfw5v5fmLe6rgc/QvJ6XA+9Kck9VndXWOc+z9Pek7ecAmn80fG5o94KfZ4PszO0I/MU06j8EzPh//FV1Vefbs5OcAHwuyR5VdXPbPnjbaxuaPwZd2w7VdGuHDddOt+/ZNKfzDJDkccCnaP61uLyqvjZU4jzPwjyPwXme2TxPci76Ms9TmdH8V9VNSZbTnK36cGf/CpqrGfwRcFfbtpDmf77MaJ6TPIEmwJ5ZVccOdib5EPD/aMLsBVV1J84zzN7fk9+nuTLHe6tdoNqx4OfZpQUzVFWrqirTeNy06V6n5YM0/1I5pNN2R7sddSp+Cc3C6TvGrIUNT/dPp+9ZM9fz3IbYS2jeLvytqvrMiDLnefZ/nkdxnmc2z5Oci17M81Q2Z/6r6lLgqcDuNOsJn1RVB9B8Shvghna7kOZ/XmzGPB8B/Dhw/lB/64GPAo8Gfr5tdp5n7+/JoTQfpPvAiH0Lfp4Nsv31qHb7uE7b1e12nxH1vwB8tdpb4lbVt2h+QJ49onbQtnImffdVksfSnIndnSbE/ssUpc7z3HCeZ2CSc7Glz3M1rq+qz1XVN9plBvvTfOr6a23NQpr/vhmEl1E3+9m6u3WeZ0eSPWn+cXBhVX17eH8v5rkWwGUftuQHG7mMDs0v7I9Pse99DF3iAlhMcxr+3xh9/bY3DPXxVqa+ftudwKNn2vdCe2xsntv9j6V5i/A+4EWb6Mt5nuE8D9Vu6vJbzvPMf54nNhdb0jyP8d9hcHm+Qxbi/PftQXPDnwL+dqj9kcAXgf8GHu88z+qcv2v4dY6oWdDzPO+TuCU+2v+gb2gfNwz+47aPIzt1O9KsMTkX+DOa0/9/TvMvnqJ5C3yrob7/pN33WZq3af6S5hqHX2HowsI0b+Gsork7zV+29Z9tn3/oiHGP3fdCeIw7z23tynb/uYy+48lPO8+zMs+P6ewbXAv5M522PZznWZnnic3Fw32eNzL/XwD+huauXq9tf24LeM+I2gUz/3160Hyg+Zb2tXwCeA3N3aa+2Lad5DzP6nxvS7Nm9naGskSf5nneJ3JLfNCsQ6kpHqs6dYto/sV/NbCGZg3LnTSL3l8DPHKK/g9pf/HX0Vz/9H10/hU7VLsEOLvtfx1wDfB7Gxn72H3P92PceW5rp6obPA5xnmdlnpc6z5Of50nPxcN5njfyGk6jufzhWpoPdn0OOGgj9Qtm/vv0AB5Pc5bwVpq7Kg7uEnU4EOd5Vuf699u/H389Ru2Cnee0nUiSJEm94oe9JEmS1EsGWUmSJPWSQVaSJEm9ZJCVJElSLxlkJUmS1EsGWUmSJPWSQVaSJEm9ZJCVtElJ9ktSSQ7ZWNuWMo75PO7mSLJdklOTfD3JA0lWzWLfq5JcOtR26WweY74l+UCS2lTbJvqoJB+Y9cHNsum+rmn2vbSdhzdOon9tWQyy2mJ1gshUjx/O9xgfrpIc3YcAmGTPJG9MsnS+xzJL/jdwFHAezZ13jp7X0ehhqw2rb0yy53yPRQ9vW8/3AKQF4O+BT45oXz/XA+mZzwGPAv57Bs89mub+2h+Yw2POxJ7AXwCX0ox3PscyG14AXFdVr5vvgfTU4cCr5nsQPbGU5ndnFXDt0L7baH53PFmgzWaQleCaqvrQfA+iK8mjgP+uqgX7h76q1tPcF3vikjy6qn4wl8fclIU0lml4AvD1+R5EX1XVf9Ovf7gsSFVV9O93RwuUSwukMXTXdCV5UZKrk6xL8q0kb03ykH8UJnlqkrPbmvvbNYRvTbL9UN0H2r4XJ3lfku8A9wBPbPfvkeTiJPck+c8kH0yyU3etXZKfaI8xMpAn+dsk65M8eYzX+pIk/96+vm8keRPwyBF1o9arpl028B9JfpDkriRfTfLeJI9sawp4MvCcoaUcS9v9q9q1lc9MclGS7wP/MdUxh8Z0VJKvtWP/WpKjRtQ8ZC3nqL7b9Xvvb3d/tjPOD2xsLEm2T3JCkpuT3Jfk20nOGp777vOTvCLJl9v625K8ftTrm+I1b53kfye5vn3d/5nkY0l+rlNzSDvvP8WG8/7GTfT96vZn7/b25+tbST40iaUWg7lN8vwkVyZZ287dO4Z/Z9r6pe3v13faebs5yVuSbDdU97gkp7T7B/PzhSSvG6r7gyRXJfle+7t2S5Jzkizu1Ey5bjTN7+9Zbf/3JPl0kmdO4/U/v53r77Xj/I8kY5/9HWf8bd2vJPlUku8nuTfJNUkOHfMYI9c8Z2jNa/s78dl29/s7P2+Xjqrv9LPJn+Xh52eMv8dJdk9yfvtzPPid/GyS5eO8bi1snpGVYLskO41ov7+q7hpq+3Xg1cDfAe8DXgL8KXAn8JZBUZJnAZ8Bvge8B7gdeAbwWmDfJM9pz+50fQr4NvBmYHvg7iRPBS6n+UfnqW0/vw78c/eJVfWdJJ8ADkhyZFV9rzOWbYGDgEuq6raNTUSS3wI+SvN24Jto3vp7BfCijT2v4w3t8y6gmaMHaMLTi4FtaM5mvQw4BVgD/HXnuas7Xz+JZv7Ob8ezwxjHPormjON7gB/QvOZTkzyuqv5yzPF3rQB+EjiC5r/tV9r2m6d6Qvs/0IuAfYGPACcDTwX+CPjVJMuq6ptDT3sV8BPAe2l+Xg4G/m+Sb1bVuWOM8xzgd2l+ft5NMwevAa5I8stV9e80yyBGzft/bKLvPwWupPnZ+y/gZ4HDgP2T/FxV/ecY45uOnwd+BzgDOAt4Ls3vzM8meUF7Fpw0/yi4CngMzWv+GrAfcBzN79fzOu9mnA/8Cs3PxReB7YDd2vq3tv0dDHyQ5nfteOBemp/BXwMez4Y/m1P5F5o5eiPNf4Mjgc8l2aeqvrSxJyY5gub35Uqa/zb30CwDeXeSXTa1FGTc8Sf5DeBjNH9nTqb5PTkQODPJT1fVn4/xOsfxOZrfmT8DTm/HBfCdTTxvnJ/lrk3+PU7y4zR/S2jrbgN2ApYBvwBcOKNXqIWjqnz42CIfNP8jq408/qlTu7RtuwdY2mkP8CXgW0N9fxG4AXj0UPtvtf0c0mn7QNv2oRFj/Id2375D7ee17R/otP1q2/bqodr/2bb/7ibmYyuat53XADt12h9D88d/eNz7jWi7Brh+jLlfBVy6kX0FHLaR/2ajxvED4Imd9kU0Yee/h9pHHnuKvg9p2/Ybs/7wtu2kodrlbfvZI55/B7Bjp307muBxxRjz+IK2j/OAdNr3oPlHyOXjzvsU/W8/ou157TFfv6m+adcWj3mswe/dbw61v6NtP7DTdk7b9utDtW9t2w/t/OwW/P/tnX+MHVUVxz9fWikBkR+1SkWEFhCKYoAGUMEQERAkRiBNjOU3SBRCorURStUEJPJLSST8SAMFWmsJYrCLrQi0Vos0UpCW3wUKFAMpurYlVEqlSTn+ce7sTmfve2/27a7dR84nmczuzJl779y5986Zc889j1ta5P07YAMwsoXcLNLMePVYSqP8DCbifvYPZO6z3G/H4tPsd2XyuwH/GNx3oOXH+/c/8I+lT1T6ydKUz/4t7jX7POkdHy9v1j9ayNduy/RjPMY/oluOf7F17hauBUHgFoPjM1vOOtFlZq8V/5iPlH8G9pD0YYA0DfY54C5glNwN4KPJ6vsIPviekEn7F+V/JI3ALQ6PmdnSiuz1mesXAquB6jTh+cA6oCtzTZmJwF7AnWa2tnSPb+OWjDq8Dewp6eia8o1YT++0fl3mWsnaaWabcQvkSODrAyxPXU7FlZerywfN7A/4gpdvSKqOu3dayYJuZu/ilrn9a+YH8LPUFos0ngYWAEdXp5b7g5ltBJC0naRdUht+Cn/OR7abbhNeNLNqO70m7U8tyoIrJyvMrLpI82q8/ot62QS8Bxyp5u4Qb+MfECdLUptlv67yDJ7A++RxxdjQgEn4bMXt5bEi1fV8fDbmKy3yrlP+ibiV9g4zW1Mq52b8A2A73KK5rWinLbccj/G6AThJ0keGpOTBNiUU2SCAVWa2KLM9lZF9NXOsmF4dnfYT0v4K3LJW3rpxt4GPZ9J5qfL/mCT7Yka2z7E0iM8EDlMKeSNpPG4ZmZNeWM0Yn/YvZM493+Lagum4demvyR9trqTJkraveX3BK2a2pZ/XrMwcK8o9PnNuKBgHrDGztzLnngN2xqc1yzRqU6Mzx3P5vU/+3p8tybSFpGOTX+NG3JJXtONdgN3aTbcJfe7DzN5MeRfPcAzuavJcRnY98GYhm9r893GXiNVyP+QbJVUVw6twa2UX8G9J90r6tqSdB1J2vP2NwH3CG1GMF4voO14sTOdy40WZOuUv2kGfeqO3rfy/+kmOdtpyy/HYzJbgbirnAGslLZV0haSDBlziYFgQimwQ9I9mypUq++vJW3qPB/os5kmWuFx6ORoFKr8Dn4YrrLLnpXRmNkmrml8u7VpWKjP7G7AvbmWah4evmgs8KWn3OmkkqnVRK/vMsVy5G9XdYKwZaMea11+FfaD51UtYOhx4CPdTnIZb607A2+86hub90ejZqMHfrRM0m4FPRV+Au75MAhZJurskswo4CHcBmY0rnrcBL0jatz/5NSl3K5mzaDxezG2WQM3yD0Zb6aS+05OemZ0NHIz78K8DpgJPS7q4jTyDYUYs9gqCwWdV2m8xs0UDSKcbt4QdkDl3YO4CM/unpPnA6ZKmAWcDy8wsZ4WpUiximpA5lzuWxczewRdo3Qu+8h24GVeuf16I1U2vH+QsLEW5y5ab9UBOqc5Zo/pbzleAEyXtWnYXKJVvA+6DPFi8AnwVv8/qwq2iPla3mfZk3Jp4kpn1pCGPIDAU1ljIPENJY3ELcPEMu3F/6M9kZHfDfU63iluarLoz8UVNI4A5wLckXW9mjyeZ9/B40ventL6GLwT6Ab7gqBUTcJeQ6rEtuLW0EcV4sXYg40WN8hf9u0+90VvvOQtnmfW4i0KVweo7Q9WWMV9w9yxwnaRdgWXANZJuLrsyBJ1HWGSDYPBZgQ+Y301T+1uRQsy0tE6mqfU/AkdIOqpyemqTS2/DFY0ZeAivOtZYgCeAN4Bzy1Eckl9ZrTBADaI/LE/78j2/Q16ZHAinS/pkqSzbA1NwRWJBSe4l4EBJe5ZkR5FXVt5J+7pl7cLH1Wnlg5JOAg4Ffm9p5f0gUfiTXlb2jZT0WdyP9BEzq7PiPkdh7apayqYzdO+OAySdUjl2adp3QU/83vnAoZJOrMhOS2WbBz0/ybtVOK7UrwpFafckV7fdNuOSyjM4DDgO+FP6uGvEPbgf7xXy+NFbkXyTRzXLuGb5l+OLOc+VtEfp2g8BP8QVz/ua5YP3nZ0lHVG6fju8n1Vpp+/AILdlefi1rdpr+shcjfsV79DfNIPhRVhkg8B9Ss9ocK6rxUuoD2Zmks7EQ748LekO3C9tR2A/4DQ8TNCsGsn9GLdSPCDpJlzRPBn3E4S81eNB3AJ0Bm7RvTsjkyv3FklT8BfrY5Juw90UzsOn4z5VI5mVkh7FrR1r6A1ftblSjkeB8yVdifvEvQ/MLxYXtclLwDJJM3CL3WTgcOBKM3u9JHcTHnJoUZLdHg9NlXNneDyV7UfJ2rcRWG1myxqUYRZuBb80LS56GH/mF+Ghh6YP4P76YGYLJd2D389ukhbQG7Lov3joqnaZhyso90u6FX+Gx+MLGQfTqlzmGeDXqe2twsNvTQKW4KvZC6ansnRJugV4GQ+x9U28zmcnuU8DSyTNwz8u38ItfhfiikwRFuohebzih4HXgV3pjVgxp2bZ9wYelIfBG4uH39qEK4kNMbM3JF2If3CulDQH779j8OnwU3CL5GtNkmlZ/tS/L8af6+Ppmf4Hr7PPA1clF4Vm3Ip/RM+TdAPeJiaR1yWeT+lfJOld3M+528wWZ2SHsi2fBUxJbeBlPIrJMfi4eo+ZbWoz3WC4sK3DJsQW27baaB1+y4D9kuw+VMLFlNK5PJ3bp3J8b9wq+ho+4K/DrZ5XA3uV5GZRCXNTSecQfCHIu/jU3q/wRQ8NwwoBP0nnb2+jXk7Dp2bfw1+KV9IbGuecTP2Vj03DX6bdpet/CxxWyeNjuOvBelxR7Kk/mofmyuXZcwx/2a1Kea8CvtcgnbPxBXObcYXmEuDYatol2eeTbE/opFxZ0vGd0jN+NV3TjSsTe7e6l7ptoiI7Erdarkz3vR63bh2ckW1Ytw3SPiW1NyXueAAAAahJREFU2Y248no3/kHTJ50Gx/5C/8JvzcKtmMtwJfBfwI1Uwtgl+XGpXrtTPb+KL3rasSQzGo9c8SSuSG3ClZlfAmNLchfQG8d5M75g7H7gy62eC73ht8ak8qzD++piYGKj+8wcPwpXMov7WYOvwJ8K7NCi7mqVP8kek2Q34AriCvKh7rJtEI+kUowPa4BrcfenPuNjkl2e8rGifdBgPKVmW250fTp3OVuPJ4fgHzYv4+14Ax55Yyowqm5fiG34bkoPOgiCDkL+gwt/By4zs2sy5y/BXzBfNF+AFQTDGvkvZs02s3O2dVmCIOgcwkc2CIY5Vb+55D9WRD1YmJEfCXwHeCaU2CAIguCDTPjIBsHw50lJi3H/wZ3w4P5fAn5jHnQdAEnjgC/gYZLG4z/RGgRBEAQfWEKRDYLhz3248nom3mdX4z6w11bkjsF/DWst8FMzq7XIKwiCIAg6lfCRDYIgCIIgCDqS8JENgiAIgiAIOpJQZIMgCIIgCIKOJBTZIAiCIAiCoCMJRTYIgiAIgiDoSEKRDYIgCIIgCDqSUGSDIAiCIAiCjuR/kPyYRc3cxcwAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] @@ -11909,7 +2144,6 @@ } ], "source": [ - "import matplotlib.pyplot as plt\n", "plt.rcParams.update({'font.size': 18})\n", "plt.figure(figsize=(10,8))\n", "plt.vlines(energy,0,125000, 'r')\n", @@ -11921,7 +2155,7 @@ }, { "cell_type": "markdown", - "id": "af3d95a0", + "id": "dd9d8a4e", "metadata": {}, "source": [ "# 4. Trade-off between expected revenue and prediction uncertainty." @@ -11929,45 +2163,44 @@ }, { "cell_type": "markdown", - "id": "28089133", + "id": "e8a417cc", "metadata": {}, "source": [ - "Let's first wrap above price optimisation into a single main function for convenience." + "Let's first wrap the above price optimization into a single optimize function for convenience." ] }, { "cell_type": "code", - "execution_count": 26, - "id": "984b3a9c", + "execution_count": 25, + "id": "01e66782", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "(13385.557029586926,\n", - " 704.6026346946801,\n", - " -12680.953125,\n", + "(13362.364731002446,\n", + " 706.7208258596746,\n", + " -12655.6484375,\n", " [185.94625963144793,\n", - " 175.81348574612934,\n", - " 157.99134281226168,\n", - " 162.41469843400876,\n", - " 169.04727765777784,\n", - " 137.61617514167745,\n", - " 109.25139281908908],\n", - " [12, 10, 13, 8, 8, 19, 19],\n", - " 357.04970370024245)" + " 154.15604720656478,\n", + " 167.46543979322945,\n", + " 155.9292482281557,\n", + " 160.514740479689,\n", + " 130.2613846464788,\n", + " 98.73268259663321],\n", + " [12, 16, 5, 12, 10, 19, 19],\n", + " 931.8876101527734)" ] }, - "execution_count": 26, + "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "from qubo_dynamic_pricing import main\n", "Ld=1e6\n", "\n", - "max_revenue, prediction_variance, energy, opt_demand, opt_prices, rev_std = main(\n", + "max_revenue, prediction_variance, energy, opt_demand, opt_prices, rev_std = optimize(\n", " a = a,\n", " b = b,\n", " data_x = data_x,\n", @@ -11980,23 +2213,32 @@ " vol_bound=None,\n", " s3_folder=s3_folder\n", ")\n", + "\n", "max_revenue, prediction_variance, energy, opt_demand, opt_prices, rev_std" ] }, { "cell_type": "markdown", - "id": "adec78ac", + "id": "6a3d8b01", "metadata": {}, "source": [ - "In order to investigate the trade-off between the expected revenue and prediction uncertainties, we vary the knob parameter $\\beta$ within a large range of $[1e2,1e9]$ and run multiple experiments on D-Wave with different $\\beta$ values. The scatter plot are shown below, where each dot represents the optimized result of an experiment with x-axis representing its expected revenue and y-axis representing the estimated standard deviation of revenue $std(R)$. The standard deviation of revenue can be derived from the estimated variance of the predicted demand:\n", - "\n", - "$$std(R)=\\sqrt{(\\sum_{t=T}^{T+n-1}var(\\hat{d}_t)*p^2)}$$" + "In order to investigate the trade-off between the expected revenue and prediction uncertainties, we vary the hyperparameter $\\beta$ within a large range of $[1e2,1e9]$ and run multiple experiments on D-Wave with different $\\beta$ values. The scatter plot is shown below, where each dot represents the optimized result of an experiment with x-axis representing its expected revenue and y-axis representing the estimated standard deviation of revenue $std(R)$." + ] + }, + { + "cell_type": "markdown", + "id": "05a59edc", + "metadata": {}, + "source": [ + "
\n", + "Caution: Running the following cell will run a substantial amount of tasks for various senarios taking about 30 minutes. Only uncomment it if you are happy to wait.\n", + "
" ] }, { "cell_type": "code", - "execution_count": 27, - "id": "83691475", + "execution_count": 26, + "id": "e83c4ac0", "metadata": { "scrolled": true }, @@ -12007,484 +2249,484 @@ "text": [ "---\n", "beta_sample:100.0\n", - "max_revenue:13291.671898296641\n", - "prediction_variance:704.1931156458986\n", - "energy:57127.640625\n", - "opt_demand:[182.33668654152052, 165.36059160986585, 152.14722973980318, 143.19312000337874, 139.68758303067955, 123.27086373085064, 109.01867880990861]\n", - "opt_prices:[13, 12, 12, 12, 12, 16, 16]\n", - "rev_std: 355.6925164877392\n", - "penalty_term: 0.0009587067761458457\n", + "max_revenue:13142.782268581876\n", + "prediction_variance:703.5502036738326\n", + "energy:57212.2421875\n", + "opt_demand:[182.33668654152052, 179.79888396957557, 165.08222156543758, 155.1378810016535, 155.08534332330055, 154.92897272299166, 125.8542042377626]\n", + "opt_prices:[13, 8, 12, 12, 10, 10, 19]\n", + "rev_std: 840.9865848076566\n", + "penalty_term: 0.004088698617124464\n", "---\n", "beta_sample:1000.0\n", - "max_revenue:12661.267350528498\n", - "prediction_variance:702.2590686281666\n", - "energy:689597.796875\n", - "opt_demand:[193.16540581130278, 189.5001278388014, 188.47908467385338, 181.42597959171735, 165.3187618694297, 150.2670365409225, 137.60803208172922]\n", - "opt_prices:[10, 8, 8, 10, 13, 13, 13]\n", - "rev_std: 289.4392148886471\n", - "penalty_term: -0.004402638063766062\n", + "max_revenue:13198.22244328534\n", + "prediction_variance:702.9415585415351\n", + "energy:689743.3359375\n", + "opt_demand:[193.16540581130278, 182.28098165894653, 163.96372331139906, 159.28485931053694, 157.1272228349854, 151.58799858923842, 122.5817558425566]\n", + "opt_prices:[10, 10, 13, 10, 10, 12, 19]\n", + "rev_std: 841.0012457923974\n", + "penalty_term: -0.0001607497688382864\n", "---\n", "beta_sample:10000.0\n", - "max_revenue:11262.938301039747\n", - "prediction_variance:702.010077070336\n", - "energy:7008837.8359375\n", - "opt_demand:[193.16540581130278, 189.5001278388014, 174.04079231414366, 175.7101339459378, 170.67021605375436, 168.59076606630185, 185.70056393570428]\n", - 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"opt_prices:[12, 8, 8, 8, 8, 12, 5]\n", - "rev_std: 238.91365696777487\n", - "penalty_term: 0.0044097900390625\n", + "max_revenue:12118.204399688242\n", + "prediction_variance:702.0775739077151\n", + "energy:70207745272.57031\n", + "opt_demand:[200.38455199115765, 195.9676237516186, 180.01317281328105, 172.58029482246604, 158.750161230962, 157.2955778843709, 158.3468258146745]\n", + "opt_prices:[8, 8, 12, 10, 12, 10, 10]\n", + "rev_std: 700.5863093976069\n", + "penalty_term: 0.003204345703125\n", "---\n", "beta_sample:1000000000.0\n", - "max_revenue:12261.041891942255\n", - "prediction_variance:702.3029526057086\n", - "energy:702302940344.6797\n", - "opt_demand:[200.38455199115765, 195.9676237516186, 180.01317281328105, 179.79944100232086, 165.21765714377918, 152.43923911372602, 152.73488900183173]\n", - "opt_prices:[8, 8, 12, 8, 12, 13, 10]\n", - "rev_std: 274.1335026388799\n", - "penalty_term: 0.012939453125\n", + "max_revenue:10350.06038481572\n", + "prediction_variance:702.4846362905347\n", + "energy:702484625940.4688\n", + "opt_demand:[211.2132712609399, 205.66886762084437, 203.41003592169682, 198.86839341252983, 187.03144522672824, 197.67896620376422, 196.46329619804368]\n", + "opt_prices:[5, 8, 8, 8, 10, 5, 8]\n", + "rev_std: 520.6166233702603\n", + "penalty_term: -0.0054931640625\n", "---\n", "beta_sample:100.0\n", - "max_revenue:13428.302059160185\n", - "prediction_variance:704.5429695367601\n", - "energy:57025.9921875\n", - "opt_demand:[182.33668654152052, 161.75101851993844, 163.3517741431043, 167.58021393915413, 162.52268232639722, 142.5109452069517, 109.32940407763995]\n", - "opt_prices:[13, 13, 8, 8, 12, 16, 19]\n", - "rev_std: 351.68512469061767\n", - "penalty_term: -0.0027070158248534426\n", + "max_revenue:13101.089112842521\n", + "prediction_variance:703.2120045508508\n", + "energy:57220.109375\n", + "opt_demand:[200.38455199115765, 177.91975830198146, 178.28272539094775, 170.58433540025698, 160.4716545882791, 153.83857764258306, 120.0646260572107]\n", + "opt_prices:[8, 13, 8, 10, 12, 12, 19]\n", + "rev_std: 820.959265376438\n", + "penalty_term: -0.001967242562386673\n", "---\n", "beta_sample:1000.0\n", - "max_revenue:12686.146173485487\n", - "prediction_variance:702.4741246927732\n", - "energy:689787.9765625\n", - "opt_demand:[200.38455199115765, 195.9676237516186, 194.45146517299077, 174.68656737831816, 168.21282453986578, 155.76397098139327, 133.59348581661482]\n", - "opt_prices:[8, 8, 8, 13, 10, 12, 16]\n", - "rev_std: 294.01822320045846\n", - "penalty_term: -0.001956787775270641\n", + "max_revenue:12799.39306175473\n", + "prediction_variance:702.7497978139801\n", + "energy:689950.3984375\n", + "opt_demand:[200.38455199115765, 188.74847757176371, 173.54567690046386, 155.77919505354637, 144.9596103053531, 135.7417005960029, 130.53821386106824]\n", + "opt_prices:[8, 10, 12, 13, 12, 13, 13]\n", + "rev_std: 810.9564396486212\n", + "penalty_term: -0.006314725265838206\n", "---\n", "beta_sample:10000.0\n", - "max_revenue:12460.45746762208\n", - "prediction_variance:702.238586248761\n", - "energy:7009925.40625\n", - "opt_demand:[193.16540581130278, 189.5001278388014, 188.47908467385338, 170.5972603219351, 166.4462372699861, 154.61928275136964, 147.2759632921967]\n", - "opt_prices:[10, 8, 8, 13, 10, 12, 12]\n", - "rev_std: 280.6301723807376\n", - "penalty_term: 0.0012300126254558563\n", + "max_revenue:11668.057902789285\n", + "prediction_variance:702.114905983479\n", + "energy:7009481.0\n", + "opt_demand:[193.16540581130278, 189.5001278388014, 188.47908467385338, 199.47384504135448, 192.31622092125497, 192.94709710762896, 172.9586102534359]\n", + "opt_prices:[10, 8, 8, 5, 10, 8, 13]\n", + "rev_std: 620.5042342568443\n", + "penalty_term: -0.0019320007413625717\n", "---\n", "beta_sample:100000.0\n", - "max_revenue:10906.61337332408\n", - "prediction_variance:701.7478807312693\n", - "energy:70163881.4609375\n", - "opt_demand:[200.38455199115765, 195.9676237516186, 187.2323189931359, 179.04779073528323, 171.94168790995423, 175.07152703342604, 190.6011549461458]\n", - "opt_prices:[8, 8, 10, 10, 10, 8, 5]\n", - "rev_std: 227.65734336966304\n", - "penalty_term: 0.0011838972568511963\n", + "max_revenue:12133.533110080407\n", + "prediction_variance:702.0571376283112\n", + "energy:70193580.234375\n", + "opt_demand:[193.16540581130278, 175.06183547909168, 168.32494666836413, 163.0137226806254, 169.2156327071633, 176.86116017646032, 168.26133247161616]\n", + "opt_prices:[10, 12, 10, 10, 8, 8, 12]\n", + "rev_std: 700.4772829770868\n", + "penalty_term: 0.004653960466384888\n", "---\n", "beta_sample:1000000.0\n", - "max_revenue:10422.132223477654\n", - "prediction_variance:702.4074226628456\n", - "energy:702397000.53125\n", - "opt_demand:[185.94625963144793, 175.81348574612934, 176.0392082618988, 178.58343821605177, 194.8069481754036, 197.24599064106252, 208.73168252197286]\n", - "opt_prices:[12, 10, 8, 8, 5, 8, 5]\n", - "rev_std: 220.84301199423587\n", - "penalty_term: 0.0006278753280639648\n", + "max_revenue:10843.245671844892\n", + "prediction_variance:701.7569277253392\n", + "energy:701746084.4921875\n", + "opt_demand:[193.16540581130278, 182.28098165894653, 182.0115887610362, 175.45359909257996, 179.27732026268376, 182.717054502723, 196.43961960101143]\n", + "opt_prices:[10, 10, 8, 10, 8, 8, 5]\n", + "rev_std: 590.4245277513222\n", + "penalty_term: 0.012520194053649902\n", "---\n", "beta_sample:10000000.0\n", - "max_revenue:12794.522636056197\n", - "prediction_variance:702.2224670913383\n", - "energy:7022211876.3828125\n", - "opt_demand:[193.16540581130278, 182.28098165894653, 174.79244258118132, 161.76695699990793, 152.39915149101944, 145.28208276185842, 136.82738773142015]\n", - "opt_prices:[10, 10, 10, 12, 12, 12, 13]\n", - "rev_std: 300.64408668989864\n", - "penalty_term: -0.0079345703125\n", + "max_revenue:11696.71176176828\n", + "prediction_variance:702.2911264607972\n", + "energy:7022899567.890625\n", + "opt_demand:[200.38455199115765, 188.74847757176371, 173.54567690046386, 166.60791432332866, 154.66085417457893, 173.57685606412835, 173.3708773666939]\n", + "opt_prices:[8, 10, 12, 10, 12, 5, 10]\n", + "rev_std: 670.533082027326\n", + "penalty_term: -0.005584716796875\n", "---\n", "beta_sample:100000000.0\n", - "max_revenue:11225.412662381104\n", - "prediction_variance:701.8728425144088\n", - "energy:70187273026.03125\n", - "opt_demand:[200.38455199115765, 195.9676237516186, 187.2323189931359, 186.2669369151381, 178.4091838227714, 166.6056151728537, 181.75547017689448]\n", - "opt_prices:[8, 8, 10, 8, 10, 12, 5]\n", - "rev_std: 237.1515609359141\n", - "penalty_term: 0.003021240234375\n", + "max_revenue:11259.819536849312\n", + "prediction_variance:701.8711813398561\n", + "energy:70187106874.17188\n", + "opt_demand:[193.16540581130278, 189.5001278388014, 181.2599384939985, 174.95848367890017, 177.39424681992944, 191.22305398600184, 187.4710989807441]\n", + "opt_prices:[10, 8, 10, 10, 8, 5, 10]\n", + "rev_std: 610.443345015263\n", + "penalty_term: 0.00579833984375\n", "---\n", "beta_sample:1000000000.0\n", - "max_revenue:11935.362324992222\n", - "prediction_variance:702.212326018176\n", - "energy:702212314082.8125\n", - "opt_demand:[193.16540581130278, 182.28098165894653, 167.57329640132647, 162.5186072669456, 149.28469381477186, 158.36970060791384, 167.1467745436264]\n", - "opt_prices:[10, 10, 12, 10, 13, 8, 8]\n", - "rev_std: 272.64805987855004\n", - "penalty_term: -0.001220703125\n" + "max_revenue:12094.573836154155\n", + "prediction_variance:702.2972898129863\n", + "energy:702297277718.4141\n", + "opt_demand:[193.16540581130278, 189.5001278388014, 170.43121922421625, 172.4763859895292, 174.9031719840405, 165.79446227107266, 166.27428943744752]\n", + "opt_prices:[10, 8, 13, 8, 8, 12, 10]\n", + "rev_std: 690.5026388893243\n", + "penalty_term: 0.001708984375\n" ] } ], "source": [ - "beta_options=[1e2,1e3,1e4,1e5,1e6,1e7,1e8,1e9]\n", - "results = {beta_option:[] for beta_option in beta_options}\n", - "beta_samples = beta_options*6\n", + "#beta_options=[1e2,1e3,1e4,1e5,1e6,1e7,1e8,1e9]\n", + "#results = {beta_option:[] for beta_option in beta_options}\n", + "#beta_samples = beta_options*6\n", "\n", - "for beta_i in beta_samples:\n", - " max_revenue, prediction_variance, energy, opt_demand, opt_prices, rev_std = main(\n", - " a = a,\n", - " b = b,\n", - " data_x = data_x,\n", - " selected_hist_prices = p_data,\n", - " price_levels = price_levels,\n", - " Lp = Lp,\n", - " Ld = Ld,\n", - " sigma = sigma ,\n", - " beta=beta_i,\n", - " vol_bound=None,\n", - " s3_folder=s3_folder\n", - " )\n", - " print('---')\n", - " print(f\"beta_sample:{beta_i}\")\n", - " print(f\"max_revenue:{max_revenue}\")\n", - " print(f\"prediction_variance:{prediction_variance}\")\n", - " print(f\"energy:{energy}\")\n", - " print(f\"opt_demand:{opt_demand}\")\n", - " print(f\"opt_prices:{opt_prices}\")\n", - " print(f\"rev_std: {rev_std}\")\n", - " print(f\"penalty_term: {max_revenue-beta_i*prediction_variance+energy}\")\n", - " results[beta_i].append([energy, max_revenue, prediction_variance, rev_std])" + "#for beta_i in beta_samples:\n", + "# max_revenue, prediction_variance, energy, opt_demand, opt_prices, rev_std = optimize(\n", + "# a = a,\n", + "# b = b,\n", + "# data_x = data_x,\n", + "# selected_hist_prices = p_data,\n", + "# price_levels = price_levels,\n", + "# Lp = Lp,\n", + "# Ld = Ld,\n", + "# sigma = sigma ,\n", + "# beta=beta_i,\n", + "# vol_bound=None,\n", + "# s3_folder=s3_folder\n", + "# )\n", + "# print('---')\n", + "# print(f\"beta_sample:{beta_i}\")\n", + "# print(f\"max_revenue:{max_revenue}\")\n", + "# print(f\"prediction_variance:{prediction_variance}\")\n", + "# print(f\"energy:{energy}\")\n", + "# print(f\"opt_demand:{opt_demand}\")\n", + "# print(f\"opt_prices:{opt_prices}\")\n", + "# print(f\"rev_std: {rev_std}\")\n", + "# print(f\"penalty_term: {max_revenue-beta_i*prediction_variance+energy}\")\n", + "# results[beta_i].append([energy, max_revenue, prediction_variance, rev_std])" ] }, { "cell_type": "markdown", - "id": "7c6f9584", + "id": "e1ccbf29", "metadata": {}, "source": [ - "We can see from the plot below that there is Pareto front where the expected revenue cannot be increased without increasing the standard deviation (i.e. uncertainties), and the other way around.\n", + "We can see from the plot below that there is a Pareto front [11] where the expected revenue cannot be increased without increasing the standard deviation (i.e. uncertainties), and the other way around.\n", "\n", "We can see that the expected revenue can vary significantly between 10000 and 13500, while the estimated standard deviation of the revenue (i.e. uncertainty) can change in a large range $[200,380]$ as well. The figure shows that as the expected revenue increases, the estimated standard deviation of the revenue will also increase. This means that if we select a price solution for higher expected revenue, the uncertainties will increase at the same time indicating that the demand estimation model will become less confident about its predictions. This illustrates there is a trade-off between maximizing the revenue and minimizing the uncertainty. High revenue and rewards usually accompany with high uncertainties and risk. In practice, according to different business strategies and needs, we usually need to find an appropriate $\\beta$ to maximize the revenue under an acceptable level of uncertainty." ] }, { "cell_type": "code", - "execution_count": 28, - "id": "ab9a050a", + "execution_count": 27, + "id": "7cb3be54", "metadata": {}, "outputs": [], "source": [ @@ -12503,13 +2745,13 @@ }, { "cell_type": "code", - "execution_count": 29, - "id": "ce52fcf8", + "execution_count": 28, + "id": "3e8d10f2", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -12521,8 +2763,6 @@ } ], "source": [ - "# b=300\n", - "import matplotlib.pyplot as plt\n", "plt.rcParams.update({'font.size': 18})\n", "plt.figure(figsize=(10,8))\n", "plt.scatter(revenue_y, rev_std_y)\n", @@ -12533,7 +2773,7 @@ }, { "cell_type": "markdown", - "id": "4dabcfb4", + "id": "8327a32e", "metadata": {}, "source": [ "# 5. Conclusion" @@ -12541,7 +2781,7 @@ }, { "cell_type": "markdown", - "id": "2729eeb0", + "id": "fffaaa75", "metadata": {}, "source": [ "In this notebook, we demonstrate how to leverage a quantum annealer on Amazon Braket to solve a price optimization use case. We showed how to mathematically formulate the problem within the (quantum-ready) QUBO framework, and then subsequently solve the optimization problem on a D-Wave quantum annealer. Our results are promising in terms of both close-to-optimal quality and computational efficiency. Since the QUBO formalism is a generalized framework that can embrace a variety of combinatorial optimization use cases (e.g. scheduling/planning, routing, portfolio management), the proposed solution can be arguably adapted and recycled by customers across other multiple industries. Already today our customers can get quantum-ready, and easily leverage Amazon Braket to help solve their daily combinatorial optimization challenges, and make better business and operation decisions." @@ -12549,7 +2789,7 @@ }, { "cell_type": "markdown", - "id": "f794f9b9", + "id": "8b7f325a", "metadata": {}, "source": [ "# 6. References:\n", @@ -12561,13 +2801,15 @@ "6. Amazon Web Services. A python SDK for interacting with quantum devices via AWS, 2021. Available at: https://github.com/aws/amazon-braket-sdk-python (Accessed: 16 July, 2021) \n", "7. Amazon Web Services. Amazon SageMaker – Machine Learning – Amazon Web Services, 2021. Available at: https://aws.amazon.com/sagemaker/ (Accessed: 20 July, 2021)\n", "8. Ben-Tal, A. and Nemirovski, A., 2002. Robust optimization–methodology and applications. Mathematical programming, 92(3), pp.453-480.\n", - "9. Fabozzi, F.J., Kolm, P.N., Pachamanova, D.A. and Focardi, S.M., 2007. Robust portfolio optimization and management. John Wiley & Sons." + "9. Fabozzi, F.J., Kolm, P.N., Pachamanova, D.A. and Focardi, S.M., 2007. Robust portfolio optimization and management. John Wiley & Sons.\n", + "10. Hyndman, R.J. and Athanasopoulos, G., 2018. Forecasting: principles and practice. OTexts. Available at: https://otexts.com/fpp2/regression-matrices.html (Accessed: 20 July, 2021)\n", + "11. Wikipedia. Pareto front - Wikipedia, 2021. Available at: https://en.wikipedia.org/wiki/Pareto_front (Accessed: 21 Dec, 2021)" ] }, { "cell_type": "code", "execution_count": null, - "id": "c6baafdb", + "id": "98beced0", "metadata": {}, "outputs": [], "source": [] From 2ebe9b8eea2514da498a6252c5ef246a3c454846 Mon Sep 17 00:00:00 2001 From: FengShi0705 Date: Tue, 21 Dec 2021 20:53:30 +0000 Subject: [PATCH 08/13] Clean unnecessary gitignore --- .gitignore | 6 ------ 1 file changed, 6 deletions(-) diff --git a/.gitignore b/.gitignore index e75a76fe3..8ba78c56e 100644 --- a/.gitignore +++ b/.gitignore @@ -136,9 +136,3 @@ dmypy.json # Data intermediates *.pck -.idea/amazon-braket-examples.iml -.idea/inspectionProfiles/profiles_settings.xml -.idea/misc.xml -.idea/modules.xml -.idea/vcs.xml -.idea/workspace.xml From f77eb363a68dcf21dac7bae64734ec416999ad88 Mon Sep 17 00:00:00 2001 From: feng shi Date: Tue, 21 Dec 2021 21:40:00 +0000 Subject: [PATCH 09/13] Correct additional text notes --- .../price_optimization/QUBO-Pricing.ipynb | 144 +++++++++--------- 1 file changed, 72 insertions(+), 72 deletions(-) diff --git a/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb b/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb index 602e01ab9..6effe492a 100644 --- a/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb +++ b/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "ec6267c1", + "id": "29b38ce1", "metadata": {}, "source": [ "# Using quantum annealing on Amazon Braket for price optimization\n", @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "efbcd2e0", + "id": "ea2f87b9", "metadata": {}, "source": [ "# Table of contents\n", @@ -35,7 +35,7 @@ }, { "cell_type": "markdown", - "id": "336b48d1", + "id": "0d4db865", "metadata": {}, "source": [ "We start by importing important libraries related to Amazon braket and installing dependencies." @@ -44,7 +44,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "0d12c431", + "id": "23ca2539", "metadata": {}, "outputs": [ { @@ -67,7 +67,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "a22e4613", + "id": "ed8eb69f", "metadata": {}, "outputs": [], "source": [ @@ -100,7 +100,7 @@ }, { "cell_type": "markdown", - "id": "edd2a887", + "id": "b58b8bf3", "metadata": {}, "source": [ "__NOTE__: Enter your S3 bucket and key below. " @@ -109,7 +109,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "24dfaa49", + "id": "df4045a2", "metadata": {}, "outputs": [], "source": [ @@ -122,7 +122,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "6fdb286f", + "id": "74085aaf", "metadata": {}, "outputs": [ { @@ -141,7 +141,7 @@ }, { "cell_type": "markdown", - "id": "5e3cd00c", + "id": "a01eb6e1", "metadata": {}, "source": [ "# 1. Demand model" @@ -149,7 +149,7 @@ }, { "cell_type": "markdown", - "id": "f505c4d6", + "id": "21708445", "metadata": {}, "source": [ "The usual goal of price optimization is to maximize the revenue in the next certain period with respect to the corresponding prices, where the revenue can usually be represented by a function of demand and price: \n", @@ -163,7 +163,7 @@ }, { "cell_type": "markdown", - "id": "8167572a", + "id": "8b62b878", "metadata": {}, "source": [ "## 1.1 Create training dataset" @@ -171,7 +171,7 @@ }, { "cell_type": "markdown", - "id": "292ff151", + "id": "62b8eec8", "metadata": {}, "source": [ "For simplicity, we create a dummy dataset on historical demand and price observations so that a demand estimation model can be trained. \n", @@ -189,7 +189,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "4d6a38f6", + "id": "da3a43c8", "metadata": { "scrolled": true }, @@ -268,7 +268,7 @@ }, { "cell_type": "markdown", - "id": "b19d4409", + "id": "869e025c", "metadata": {}, "source": [ "## 1.2. Fit the demand model" @@ -276,7 +276,7 @@ }, { "cell_type": "markdown", - "id": "9d1d2c95", + "id": "059f3921", "metadata": {}, "source": [ "We use `sklearn` to fit a linear demand model to the training set. This fitted linear demand model will be used for the following price optimization problem." @@ -285,7 +285,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "6ae94e50", + "id": "1e0822ce", "metadata": {}, "outputs": [ { @@ -315,7 +315,7 @@ }, { "cell_type": "markdown", - "id": "f33eca0a", + "id": "a254a158", "metadata": {}, "source": [ "# 2. Price optimization with QUBO" @@ -323,7 +323,7 @@ }, { "cell_type": "markdown", - "id": "5aca76da", + "id": "9d8d4d22", "metadata": {}, "source": [ "In this notebook, we leverage a general-purpose mathematical framework: Quadratic Unconstrained Binary Optimization (QUBO), which has been recently proposed as an effective framework that is able to generalize across a large variety of combinatorial optimization use cases in industries [2, 3]. We take this price optimization as an example and showcase how to formulate it into QUBO framework considering prediction uncertainties as well as equality constraints." @@ -331,7 +331,7 @@ }, { "cell_type": "markdown", - "id": "3aee7865", + "id": "52ea352c", "metadata": {}, "source": [ "The formal definition of QUBO is expressed as an optimization problem, Minimize:\n", @@ -340,7 +340,7 @@ }, { "cell_type": "markdown", - "id": "32b8dbca", + "id": "80afde02", "metadata": {}, "source": [ "where $x$ is a vector of binary variables representing the decision variables of the combinatorial optimization. $Q$ is a squared matrix of constants inherently encoding the context and constraints of the optimization problems. $Q$ is commonly assumed to be symmetric or upper triangular without loss of generality. The goal is to find the optimal values of the binary decision variables $x$ that minimize the objective $H$.\n", @@ -350,7 +350,7 @@ }, { "cell_type": "markdown", - "id": "acf1f460", + "id": "89e39a72", "metadata": {}, "source": [ "## 2.1 Construct objective function" @@ -358,7 +358,7 @@ }, { "cell_type": "markdown", - "id": "00e31bdb", + "id": "149a3d76", "metadata": {}, "source": [ "Assuming tomorrow is day $T$, then the goal of our price optimization is to find the optimal prices $p_t, t\\in[T, T+1, \\ldots, T+n-1]$ in the next $n$ days in order to maximize the revenue in next $n$ days. Based on the demand model we showed above where the demand at a day is correlated with the latest $n$ days' price, we can construct objective function as below:\n", @@ -373,7 +373,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "8a82a02c", + "id": "1a0fb8cc", "metadata": {}, "outputs": [ { @@ -395,7 +395,7 @@ }, { "cell_type": "markdown", - "id": "5d8e7d5e", + "id": "4e087538", "metadata": {}, "source": [ "Now, let's construct the objective function, i.e. the total revenue $R$, for the next $n$ days.\n", @@ -408,7 +408,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "f60b6fc2", + "id": "a51a2adb", "metadata": {}, "outputs": [ { @@ -461,7 +461,7 @@ }, { "cell_type": "markdown", - "id": "44be704a", + "id": "c2e823ca", "metadata": {}, "source": [ "Next, we can input the price variables into our fitted model to estimate the demand, and then use the demand together with the price to represent the revenue $R$." @@ -470,7 +470,7 @@ { "cell_type": "code", "execution_count": 9, - "id": "60be057f", + "id": "0f9aa7f7", "metadata": {}, "outputs": [ { @@ -525,7 +525,7 @@ }, { "cell_type": "markdown", - "id": "2c089e12", + "id": "082bb482", "metadata": {}, "source": [ "## 2.2 Add penalty for prediction uncertainty" @@ -533,7 +533,7 @@ }, { "cell_type": "markdown", - "id": "676b7ac3", + "id": "b1594642", "metadata": {}, "source": [ "In optimization, we usually desire to reduce the risk while maximizing the reward, which means we want to reduce the estimated uncertainty/variance of the predicted demands. Therefore, we add a penalty term in the objective function to represent the uncertainty of the predicted demand. The uncertainty of the predicted demand $d_t$ can be represented by its estimated variance,\n", @@ -556,7 +556,7 @@ { "cell_type": "code", "execution_count": 10, - "id": "84fe4671", + "id": "aacfe9cf", "metadata": {}, "outputs": [ { @@ -605,7 +605,7 @@ }, { "cell_type": "markdown", - "id": "5e07dfcf", + "id": "f100982e", "metadata": {}, "source": [ "## 2.3 Add penalty for equality constraints" @@ -613,7 +613,7 @@ }, { "cell_type": "markdown", - "id": "647d95b8", + "id": "adfa3518", "metadata": {}, "source": [ "Since the price can only take one value per day, exactly one of the binary variables in a day must be $1$, and the others must be $0$. Formallly, we have equality constraints:\n", @@ -627,7 +627,7 @@ { "cell_type": "code", "execution_count": 11, - "id": "2bdc7ef9", + "id": "eb6f7eb4", "metadata": {}, "outputs": [ { @@ -654,7 +654,7 @@ }, { "cell_type": "markdown", - "id": "ac0eb6e8", + "id": "077a480c", "metadata": {}, "source": [ "# 3. Solve QUBO with Braket" @@ -662,7 +662,7 @@ }, { "cell_type": "markdown", - "id": "fc8330b6", + "id": "f0937957", "metadata": {}, "source": [ "Now we have transformed to the total objective function which:\n", @@ -678,7 +678,7 @@ }, { "cell_type": "markdown", - "id": "814e0eb0", + "id": "062d519c", "metadata": {}, "source": [ "Amazon Braket provides access to quantum annealers from D-Wave Systems Inc. which are specifically designed to solve QUBO problems. A quantum annealer is a hardware implementation of Quantum Annealing (QA) which is a generic algorithm to solve combinatorial optimization problems by taking advantage of quantum fluctuations to escape local minima in complex energy landscapes by effect of tunnelling through barriers separating local minima [5]. Through a simple Amazon Braket API call, the formatted QUBO problem can be embedded to the hardwired topology of the machine and submitted to machine. In turn, the quantum annealer performs an annealing process and obtains a result. However, because of the sparsity of the underlying chip, one typically faces a certain overhead in embedding the original QUBO problem to the D-Wave hardware, because (typically) one logical binary variable maps onto several physical qubits, in order to effectively distill the connectivity of the original QUBO problem. For more details, we refer to the Amazon Braket tutorial notebook available here (https://github.com/aws/amazon-braket-examples/blob/main/examples/quantum_annealing/Dwave_Anatomy.ipynb)." @@ -687,7 +687,7 @@ { "cell_type": "code", "execution_count": 12, - "id": "69ac2301", + "id": "cb43a57f", "metadata": {}, "outputs": [ { @@ -710,7 +710,7 @@ { "cell_type": "code", "execution_count": 13, - "id": "b78a79d5", + "id": "dc1b1808", "metadata": {}, "outputs": [ { @@ -730,18 +730,18 @@ }, { "cell_type": "markdown", - "id": "b3e984dd", + "id": "62c2da91", "metadata": {}, "source": [ "We embed and submit the QUBO task to be solved by a quantum annealer at D-wave backend. Similar to classical simulated annealing, we take several independent shots in order to increase our chances for success in finding a high-quality solution to the QUBO problem. The response contains a number of rows. Each row represents the optimization result of a single shot, including the binary decision variables $[x_T,\\cdots,x_{T+n-1}]$, and corresponding energy which is the negative value of objective function, i.e. $H$. Below we show how to submit a QUBO problem to D-Wave and provide a sample response. Here, the key figure of merit is listed in the column labelled with energy, representing the value for the objective function . We can then easily read off the best bit string found.\n", "\n", - "Each row represents an optimized solution. The columns starting with `X_` shows the value of the binary decision variables $x_{t,k}$ and the `energy` column shows the negative value of objective, i.e. $-H$" + "Each row represents an optimized solution. The columns starting with `X_` show the value of the binary decision variables $x_{t,k}$ and the `energy` column shows the negative value of the objective function, i.e. $-H$" ] }, { "cell_type": "code", "execution_count": 15, - "id": "038d79f6", + "id": "bc8f7ef4", "metadata": { "scrolled": true }, @@ -964,7 +964,7 @@ }, { "cell_type": "markdown", - "id": "6e9fe163", + "id": "47427185", "metadata": {}, "source": [ "## 3.1 Evaluate the results" @@ -972,7 +972,7 @@ }, { "cell_type": "markdown", - "id": "90459742", + "id": "757568f6", "metadata": {}, "source": [ "With the response, we can decode the binary array results into the optimal price results" @@ -981,7 +981,7 @@ { "cell_type": "code", "execution_count": 16, - "id": "9ff6b4ac", + "id": "0b2a51af", "metadata": {}, "outputs": [ { @@ -1016,7 +1016,7 @@ }, { "cell_type": "markdown", - "id": "949865aa", + "id": "2b01ea9a", "metadata": {}, "source": [ "The optimized price path and corresponding demand curve are plotted below, respectively. The optimal price level is higher than the past 7 days, which results in the demand decreasing." @@ -1025,7 +1025,7 @@ { "cell_type": "code", "execution_count": 17, - "id": "6fd69a26", + "id": "a8aeef93", "metadata": {}, "outputs": [ { @@ -1052,7 +1052,7 @@ }, { "cell_type": "markdown", - "id": "7f6dd685", + "id": "c4c90dae", "metadata": {}, "source": [ "Let's also calculate the total revenue, and plot the demand of each day." @@ -1061,7 +1061,7 @@ { "cell_type": "code", "execution_count": 18, - "id": "d54a218a", + "id": "f17ef2ef", "metadata": {}, "outputs": [ { @@ -1091,7 +1091,7 @@ { "cell_type": "code", "execution_count": 19, - "id": "81afd216", + "id": "e69d4068", "metadata": {}, "outputs": [ { @@ -1118,7 +1118,7 @@ }, { "cell_type": "markdown", - "id": "f98366dd", + "id": "de0e1b21", "metadata": {}, "source": [ "Finally, let's get the overall uncertainty of the demand predictions. Here we simply use the estimated demand variance to indicate the uncertainty." @@ -1127,7 +1127,7 @@ { "cell_type": "code", "execution_count": 20, - "id": "f320dffc", + "id": "cddb4b09", "metadata": {}, "outputs": [ { @@ -1149,7 +1149,7 @@ }, { "cell_type": "markdown", - "id": "cacd0729", + "id": "e69f92a7", "metadata": {}, "source": [ "__We can also derive the standard deviation of the revenue based on the variance of demand__\n", @@ -1159,7 +1159,7 @@ }, { "cell_type": "markdown", - "id": "cce0c3dd", + "id": "e68fc702", "metadata": {}, "source": [ "where $cov(\\hat{d}_{t_1} \\hat{d}_{t_2}) = \\sigma^2(1+\\vec{p}_{t_1}'(\\vec{X}'\\vec{X})^{-1}\\vec{p}_{t_2})$" @@ -1168,7 +1168,7 @@ { "cell_type": "code", "execution_count": 21, - "id": "10863eec", + "id": "1d17f745", "metadata": {}, "outputs": [ { @@ -1224,7 +1224,7 @@ }, { "cell_type": "markdown", - "id": "d2eae3d0", + "id": "8a85b0f3", "metadata": {}, "source": [ "We can investigate the value of the penality terms to see if any equality constraints are violated. The penalty is close to zero showing that all the constraints are satisfied. This small but non-zero value is due to floating point precision." @@ -1233,7 +1233,7 @@ { "cell_type": "code", "execution_count": 22, - "id": "629c3d58", + "id": "3d35fbf1", "metadata": {}, "outputs": [ { @@ -1255,7 +1255,7 @@ }, { "cell_type": "markdown", - "id": "7e981832", + "id": "022fffa2", "metadata": {}, "source": [ "For comparison, to assess the quality of this optimized result, we also iterate (by brute-force search) through all the $7^7=823,543$ possible price solutions to obtain the energy for each one, which takes more than 5 minutes to run on a standard ml.m5.2xlarge AWS instance. We plot the distribution of the energies of all the 823,543 possible solutions as shown below, where the red line represents our optimized result obtained from the quantum annealer. We can see that although the optimized result from the quantum annealer is not the global optimum with minimum cost, it is close-to-optimal and of good quality. " @@ -1264,7 +1264,7 @@ { "cell_type": "code", "execution_count": 23, - "id": "34f0bf56", + "id": "af21665e", "metadata": { "scrolled": true }, @@ -2127,7 +2127,7 @@ { "cell_type": "code", "execution_count": 24, - "id": "bba5ae30", + "id": "30a2336e", "metadata": {}, "outputs": [ { @@ -2155,7 +2155,7 @@ }, { "cell_type": "markdown", - "id": "dd9d8a4e", + "id": "2b80e3db", "metadata": {}, "source": [ "# 4. Trade-off between expected revenue and prediction uncertainty." @@ -2163,7 +2163,7 @@ }, { "cell_type": "markdown", - "id": "e8a417cc", + "id": "d757b459", "metadata": {}, "source": [ "Let's first wrap the above price optimization into a single optimize function for convenience." @@ -2172,7 +2172,7 @@ { "cell_type": "code", "execution_count": 25, - "id": "01e66782", + "id": "96d1ab9a", "metadata": {}, "outputs": [ { @@ -2219,7 +2219,7 @@ }, { "cell_type": "markdown", - "id": "6a3d8b01", + "id": "a85545e1", "metadata": {}, "source": [ "In order to investigate the trade-off between the expected revenue and prediction uncertainties, we vary the hyperparameter $\\beta$ within a large range of $[1e2,1e9]$ and run multiple experiments on D-Wave with different $\\beta$ values. The scatter plot is shown below, where each dot represents the optimized result of an experiment with x-axis representing its expected revenue and y-axis representing the estimated standard deviation of revenue $std(R)$." @@ -2227,7 +2227,7 @@ }, { "cell_type": "markdown", - "id": "05a59edc", + "id": "c8517d96", "metadata": {}, "source": [ "
\n", @@ -2238,7 +2238,7 @@ { "cell_type": "code", "execution_count": 26, - "id": "e83c4ac0", + "id": "e6e60108", "metadata": { "scrolled": true }, @@ -2715,7 +2715,7 @@ }, { "cell_type": "markdown", - "id": "e1ccbf29", + "id": "638f0059", "metadata": {}, "source": [ "We can see from the plot below that there is a Pareto front [11] where the expected revenue cannot be increased without increasing the standard deviation (i.e. uncertainties), and the other way around.\n", @@ -2726,7 +2726,7 @@ { "cell_type": "code", "execution_count": 27, - "id": "7cb3be54", + "id": "e8186ab2", "metadata": {}, "outputs": [], "source": [ @@ -2746,7 +2746,7 @@ { "cell_type": "code", "execution_count": 28, - "id": "3e8d10f2", + "id": "f2120d62", "metadata": {}, "outputs": [ { @@ -2773,7 +2773,7 @@ }, { "cell_type": "markdown", - "id": "8327a32e", + "id": "23279bd3", "metadata": {}, "source": [ "# 5. Conclusion" @@ -2781,7 +2781,7 @@ }, { "cell_type": "markdown", - "id": "fffaaa75", + "id": "e60f3591", "metadata": {}, "source": [ "In this notebook, we demonstrate how to leverage a quantum annealer on Amazon Braket to solve a price optimization use case. We showed how to mathematically formulate the problem within the (quantum-ready) QUBO framework, and then subsequently solve the optimization problem on a D-Wave quantum annealer. Our results are promising in terms of both close-to-optimal quality and computational efficiency. Since the QUBO formalism is a generalized framework that can embrace a variety of combinatorial optimization use cases (e.g. scheduling/planning, routing, portfolio management), the proposed solution can be arguably adapted and recycled by customers across other multiple industries. Already today our customers can get quantum-ready, and easily leverage Amazon Braket to help solve their daily combinatorial optimization challenges, and make better business and operation decisions." @@ -2789,7 +2789,7 @@ }, { "cell_type": "markdown", - "id": "8b7f325a", + "id": "7fc1d51c", "metadata": {}, "source": [ "# 6. References:\n", @@ -2809,7 +2809,7 @@ { "cell_type": "code", "execution_count": null, - "id": "98beced0", + "id": "6975ad41", "metadata": {}, "outputs": [], "source": [] From 3a80a4b8281d24a79fab5e71ab1945d0b71d1353 Mon Sep 17 00:00:00 2001 From: feng shi Date: Mon, 27 Dec 2021 13:01:45 +0000 Subject: [PATCH 10/13] Correct notebook results text --- .../price_optimization/QUBO-Pricing.ipynb | 144 +++++++++--------- 1 file changed, 72 insertions(+), 72 deletions(-) diff --git a/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb b/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb index 6effe492a..9d0a55e17 100644 --- a/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb +++ b/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "29b38ce1", + "id": "edd0974e", "metadata": {}, "source": [ "# Using quantum annealing on Amazon Braket for price optimization\n", @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "ea2f87b9", + "id": "5aef5c46", "metadata": {}, "source": [ "# Table of contents\n", @@ -35,7 +35,7 @@ }, { "cell_type": "markdown", - "id": "0d4db865", + "id": "34cd7d9b", "metadata": {}, "source": [ "We start by importing important libraries related to Amazon braket and installing dependencies." @@ -44,7 +44,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "23ca2539", + "id": "36ae1bff", "metadata": {}, "outputs": [ { @@ -67,7 +67,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "ed8eb69f", + "id": "ba7e6e17", "metadata": {}, "outputs": [], "source": [ @@ -100,7 +100,7 @@ }, { "cell_type": "markdown", - "id": "b58b8bf3", + "id": "9a2d83f3", "metadata": {}, "source": [ "__NOTE__: Enter your S3 bucket and key below. " @@ -109,7 +109,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "df4045a2", + "id": "f705556e", "metadata": {}, "outputs": [], "source": [ @@ -122,7 +122,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "74085aaf", + "id": "f9407fdf", "metadata": {}, "outputs": [ { @@ -141,7 +141,7 @@ }, { "cell_type": "markdown", - "id": "a01eb6e1", + "id": "7da0da4b", "metadata": {}, "source": [ "# 1. Demand model" @@ -149,7 +149,7 @@ }, { "cell_type": "markdown", - "id": "21708445", + "id": "7f3156c0", "metadata": {}, "source": [ "The usual goal of price optimization is to maximize the revenue in the next certain period with respect to the corresponding prices, where the revenue can usually be represented by a function of demand and price: \n", @@ -163,7 +163,7 @@ }, { "cell_type": "markdown", - "id": "8b62b878", + "id": "4e328037", "metadata": {}, "source": [ "## 1.1 Create training dataset" @@ -171,7 +171,7 @@ }, { "cell_type": "markdown", - "id": "62b8eec8", + "id": "9656d0b2", "metadata": {}, "source": [ "For simplicity, we create a dummy dataset on historical demand and price observations so that a demand estimation model can be trained. \n", @@ -189,7 +189,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "da3a43c8", + "id": "c443c940", "metadata": { "scrolled": true }, @@ -268,7 +268,7 @@ }, { "cell_type": "markdown", - "id": "869e025c", + "id": "128b6357", "metadata": {}, "source": [ "## 1.2. Fit the demand model" @@ -276,7 +276,7 @@ }, { "cell_type": "markdown", - "id": "059f3921", + "id": "dad040b3", "metadata": {}, "source": [ "We use `sklearn` to fit a linear demand model to the training set. This fitted linear demand model will be used for the following price optimization problem." @@ -285,7 +285,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "1e0822ce", + "id": "9d0f2e1a", "metadata": {}, "outputs": [ { @@ -315,7 +315,7 @@ }, { "cell_type": "markdown", - "id": "a254a158", + "id": "b0fbc444", "metadata": {}, "source": [ "# 2. Price optimization with QUBO" @@ -323,7 +323,7 @@ }, { "cell_type": "markdown", - "id": "9d8d4d22", + "id": "efaea380", "metadata": {}, "source": [ "In this notebook, we leverage a general-purpose mathematical framework: Quadratic Unconstrained Binary Optimization (QUBO), which has been recently proposed as an effective framework that is able to generalize across a large variety of combinatorial optimization use cases in industries [2, 3]. We take this price optimization as an example and showcase how to formulate it into QUBO framework considering prediction uncertainties as well as equality constraints." @@ -331,7 +331,7 @@ }, { "cell_type": "markdown", - "id": "52ea352c", + "id": "a6a8394d", "metadata": {}, "source": [ "The formal definition of QUBO is expressed as an optimization problem, Minimize:\n", @@ -340,7 +340,7 @@ }, { "cell_type": "markdown", - "id": "80afde02", + "id": "bafddc03", "metadata": {}, "source": [ "where $x$ is a vector of binary variables representing the decision variables of the combinatorial optimization. $Q$ is a squared matrix of constants inherently encoding the context and constraints of the optimization problems. $Q$ is commonly assumed to be symmetric or upper triangular without loss of generality. The goal is to find the optimal values of the binary decision variables $x$ that minimize the objective $H$.\n", @@ -350,7 +350,7 @@ }, { "cell_type": "markdown", - "id": "89e39a72", + "id": "3dbc26ac", "metadata": {}, "source": [ "## 2.1 Construct objective function" @@ -358,7 +358,7 @@ }, { "cell_type": "markdown", - "id": "149a3d76", + "id": "99a4ed85", "metadata": {}, "source": [ "Assuming tomorrow is day $T$, then the goal of our price optimization is to find the optimal prices $p_t, t\\in[T, T+1, \\ldots, T+n-1]$ in the next $n$ days in order to maximize the revenue in next $n$ days. Based on the demand model we showed above where the demand at a day is correlated with the latest $n$ days' price, we can construct objective function as below:\n", @@ -373,7 +373,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "1a0fb8cc", + "id": "1374e2e8", "metadata": {}, "outputs": [ { @@ -395,7 +395,7 @@ }, { "cell_type": "markdown", - "id": "4e087538", + "id": "81fe0624", "metadata": {}, "source": [ "Now, let's construct the objective function, i.e. the total revenue $R$, for the next $n$ days.\n", @@ -408,7 +408,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "a51a2adb", + "id": "fdd84340", "metadata": {}, "outputs": [ { @@ -461,7 +461,7 @@ }, { "cell_type": "markdown", - "id": "c2e823ca", + "id": "ced0cdce", "metadata": {}, "source": [ "Next, we can input the price variables into our fitted model to estimate the demand, and then use the demand together with the price to represent the revenue $R$." @@ -470,7 +470,7 @@ { "cell_type": "code", "execution_count": 9, - "id": "0f9aa7f7", + "id": "94cb6355", "metadata": {}, "outputs": [ { @@ -525,7 +525,7 @@ }, { "cell_type": "markdown", - "id": "082bb482", + "id": "fba71f44", "metadata": {}, "source": [ "## 2.2 Add penalty for prediction uncertainty" @@ -533,7 +533,7 @@ }, { "cell_type": "markdown", - "id": "b1594642", + "id": "915245a9", "metadata": {}, "source": [ "In optimization, we usually desire to reduce the risk while maximizing the reward, which means we want to reduce the estimated uncertainty/variance of the predicted demands. Therefore, we add a penalty term in the objective function to represent the uncertainty of the predicted demand. The uncertainty of the predicted demand $d_t$ can be represented by its estimated variance,\n", @@ -556,7 +556,7 @@ { "cell_type": "code", "execution_count": 10, - "id": "aacfe9cf", + "id": "31ac67fd", "metadata": {}, "outputs": [ { @@ -605,7 +605,7 @@ }, { "cell_type": "markdown", - "id": "f100982e", + "id": "2ff48929", "metadata": {}, "source": [ "## 2.3 Add penalty for equality constraints" @@ -613,7 +613,7 @@ }, { "cell_type": "markdown", - "id": "adfa3518", + "id": "03dd90ab", "metadata": {}, "source": [ "Since the price can only take one value per day, exactly one of the binary variables in a day must be $1$, and the others must be $0$. Formallly, we have equality constraints:\n", @@ -627,7 +627,7 @@ { "cell_type": "code", "execution_count": 11, - "id": "eb6f7eb4", + "id": "2688ffc9", "metadata": {}, "outputs": [ { @@ -654,7 +654,7 @@ }, { "cell_type": "markdown", - "id": "077a480c", + "id": "014047a6", "metadata": {}, "source": [ "# 3. Solve QUBO with Braket" @@ -662,7 +662,7 @@ }, { "cell_type": "markdown", - "id": "f0937957", + "id": "19839de1", "metadata": {}, "source": [ "Now we have transformed to the total objective function which:\n", @@ -678,7 +678,7 @@ }, { "cell_type": "markdown", - "id": "062d519c", + "id": "045c86ac", "metadata": {}, "source": [ "Amazon Braket provides access to quantum annealers from D-Wave Systems Inc. which are specifically designed to solve QUBO problems. A quantum annealer is a hardware implementation of Quantum Annealing (QA) which is a generic algorithm to solve combinatorial optimization problems by taking advantage of quantum fluctuations to escape local minima in complex energy landscapes by effect of tunnelling through barriers separating local minima [5]. Through a simple Amazon Braket API call, the formatted QUBO problem can be embedded to the hardwired topology of the machine and submitted to machine. In turn, the quantum annealer performs an annealing process and obtains a result. However, because of the sparsity of the underlying chip, one typically faces a certain overhead in embedding the original QUBO problem to the D-Wave hardware, because (typically) one logical binary variable maps onto several physical qubits, in order to effectively distill the connectivity of the original QUBO problem. For more details, we refer to the Amazon Braket tutorial notebook available here (https://github.com/aws/amazon-braket-examples/blob/main/examples/quantum_annealing/Dwave_Anatomy.ipynb)." @@ -687,7 +687,7 @@ { "cell_type": "code", "execution_count": 12, - "id": "cb43a57f", + "id": "78f7b7e7", "metadata": {}, "outputs": [ { @@ -710,7 +710,7 @@ { "cell_type": "code", "execution_count": 13, - "id": "dc1b1808", + "id": "982c5e27", "metadata": {}, "outputs": [ { @@ -730,7 +730,7 @@ }, { "cell_type": "markdown", - "id": "62c2da91", + "id": "b138ab5d", "metadata": {}, "source": [ "We embed and submit the QUBO task to be solved by a quantum annealer at D-wave backend. Similar to classical simulated annealing, we take several independent shots in order to increase our chances for success in finding a high-quality solution to the QUBO problem. The response contains a number of rows. Each row represents the optimization result of a single shot, including the binary decision variables $[x_T,\\cdots,x_{T+n-1}]$, and corresponding energy which is the negative value of objective function, i.e. $H$. Below we show how to submit a QUBO problem to D-Wave and provide a sample response. Here, the key figure of merit is listed in the column labelled with energy, representing the value for the objective function . We can then easily read off the best bit string found.\n", @@ -741,7 +741,7 @@ { "cell_type": "code", "execution_count": 15, - "id": "bc8f7ef4", + "id": "f690c6d6", "metadata": { "scrolled": true }, @@ -964,7 +964,7 @@ }, { "cell_type": "markdown", - "id": "47427185", + "id": "a1b9ddd8", "metadata": {}, "source": [ "## 3.1 Evaluate the results" @@ -972,7 +972,7 @@ }, { "cell_type": "markdown", - "id": "757568f6", + "id": "2ba24b89", "metadata": {}, "source": [ "With the response, we can decode the binary array results into the optimal price results" @@ -981,7 +981,7 @@ { "cell_type": "code", "execution_count": 16, - "id": "0b2a51af", + "id": "a582d6a2", "metadata": {}, "outputs": [ { @@ -1016,7 +1016,7 @@ }, { "cell_type": "markdown", - "id": "2b01ea9a", + "id": "cb96c9b2", "metadata": {}, "source": [ "The optimized price path and corresponding demand curve are plotted below, respectively. The optimal price level is higher than the past 7 days, which results in the demand decreasing." @@ -1025,7 +1025,7 @@ { "cell_type": "code", "execution_count": 17, - "id": "a8aeef93", + "id": "5f7e78da", "metadata": {}, "outputs": [ { @@ -1052,7 +1052,7 @@ }, { "cell_type": "markdown", - "id": "c4c90dae", + "id": "b06dd1df", "metadata": {}, "source": [ "Let's also calculate the total revenue, and plot the demand of each day." @@ -1061,7 +1061,7 @@ { "cell_type": "code", "execution_count": 18, - "id": "f17ef2ef", + "id": "4d922b80", "metadata": {}, "outputs": [ { @@ -1091,7 +1091,7 @@ { "cell_type": "code", "execution_count": 19, - "id": "e69d4068", + "id": "77b88f14", "metadata": {}, "outputs": [ { @@ -1118,7 +1118,7 @@ }, { "cell_type": "markdown", - "id": "de0e1b21", + "id": "f2cf2845", "metadata": {}, "source": [ "Finally, let's get the overall uncertainty of the demand predictions. Here we simply use the estimated demand variance to indicate the uncertainty." @@ -1127,7 +1127,7 @@ { "cell_type": "code", "execution_count": 20, - "id": "cddb4b09", + "id": "4a24740c", "metadata": {}, "outputs": [ { @@ -1149,7 +1149,7 @@ }, { "cell_type": "markdown", - "id": "e69f92a7", + "id": "8d12e6a0", "metadata": {}, "source": [ "__We can also derive the standard deviation of the revenue based on the variance of demand__\n", @@ -1159,7 +1159,7 @@ }, { "cell_type": "markdown", - "id": "e68fc702", + "id": "90443622", "metadata": {}, "source": [ "where $cov(\\hat{d}_{t_1} \\hat{d}_{t_2}) = \\sigma^2(1+\\vec{p}_{t_1}'(\\vec{X}'\\vec{X})^{-1}\\vec{p}_{t_2})$" @@ -1168,7 +1168,7 @@ { "cell_type": "code", "execution_count": 21, - "id": "1d17f745", + "id": "64009d9d", "metadata": {}, "outputs": [ { @@ -1224,7 +1224,7 @@ }, { "cell_type": "markdown", - "id": "8a85b0f3", + "id": "a4539fa6", "metadata": {}, "source": [ "We can investigate the value of the penality terms to see if any equality constraints are violated. The penalty is close to zero showing that all the constraints are satisfied. This small but non-zero value is due to floating point precision." @@ -1233,7 +1233,7 @@ { "cell_type": "code", "execution_count": 22, - "id": "3d35fbf1", + "id": "aeccb8b2", "metadata": {}, "outputs": [ { @@ -1255,7 +1255,7 @@ }, { "cell_type": "markdown", - "id": "022fffa2", + "id": "b200d0ae", "metadata": {}, "source": [ "For comparison, to assess the quality of this optimized result, we also iterate (by brute-force search) through all the $7^7=823,543$ possible price solutions to obtain the energy for each one, which takes more than 5 minutes to run on a standard ml.m5.2xlarge AWS instance. We plot the distribution of the energies of all the 823,543 possible solutions as shown below, where the red line represents our optimized result obtained from the quantum annealer. We can see that although the optimized result from the quantum annealer is not the global optimum with minimum cost, it is close-to-optimal and of good quality. " @@ -1264,7 +1264,7 @@ { "cell_type": "code", "execution_count": 23, - "id": "af21665e", + "id": "c64a44d0", "metadata": { "scrolled": true }, @@ -2127,7 +2127,7 @@ { "cell_type": "code", "execution_count": 24, - "id": "30a2336e", + "id": "cc17d5f9", "metadata": {}, "outputs": [ { @@ -2155,7 +2155,7 @@ }, { "cell_type": "markdown", - "id": "2b80e3db", + "id": "70ae441a", "metadata": {}, "source": [ "# 4. Trade-off between expected revenue and prediction uncertainty." @@ -2163,7 +2163,7 @@ }, { "cell_type": "markdown", - "id": "d757b459", + "id": "1b0ae4ba", "metadata": {}, "source": [ "Let's first wrap the above price optimization into a single optimize function for convenience." @@ -2172,7 +2172,7 @@ { "cell_type": "code", "execution_count": 25, - "id": "96d1ab9a", + "id": "258c0f2d", "metadata": {}, "outputs": [ { @@ -2219,7 +2219,7 @@ }, { "cell_type": "markdown", - "id": "a85545e1", + "id": "28a35d53", "metadata": {}, "source": [ "In order to investigate the trade-off between the expected revenue and prediction uncertainties, we vary the hyperparameter $\\beta$ within a large range of $[1e2,1e9]$ and run multiple experiments on D-Wave with different $\\beta$ values. The scatter plot is shown below, where each dot represents the optimized result of an experiment with x-axis representing its expected revenue and y-axis representing the estimated standard deviation of revenue $std(R)$." @@ -2227,7 +2227,7 @@ }, { "cell_type": "markdown", - "id": "c8517d96", + "id": "9bd6ff2d", "metadata": {}, "source": [ "
\n", @@ -2238,7 +2238,7 @@ { "cell_type": "code", "execution_count": 26, - "id": "e6e60108", + "id": "24be7ba5", "metadata": { "scrolled": true }, @@ -2715,18 +2715,18 @@ }, { "cell_type": "markdown", - "id": "638f0059", + "id": "8f3a95a0", "metadata": {}, "source": [ "We can see from the plot below that there is a Pareto front [11] where the expected revenue cannot be increased without increasing the standard deviation (i.e. uncertainties), and the other way around.\n", "\n", - "We can see that the expected revenue can vary significantly between 10000 and 13500, while the estimated standard deviation of the revenue (i.e. uncertainty) can change in a large range $[200,380]$ as well. The figure shows that as the expected revenue increases, the estimated standard deviation of the revenue will also increase. This means that if we select a price solution for higher expected revenue, the uncertainties will increase at the same time indicating that the demand estimation model will become less confident about its predictions. This illustrates there is a trade-off between maximizing the revenue and minimizing the uncertainty. High revenue and rewards usually accompany with high uncertainties and risk. In practice, according to different business strategies and needs, we usually need to find an appropriate $\\beta$ to maximize the revenue under an acceptable level of uncertainty." + "We can see that the expected revenue can vary significantly between 10000 and 13500, while the estimated standard deviation of the revenue (i.e. uncertainty) can change in a large range $[550,900]$ as well. The figure shows that as the expected revenue increases, the estimated standard deviation of the revenue will also increase. This means that if we select a price solution for higher expected revenue, the uncertainties will increase at the same time indicating that the demand estimation model will become less confident about its predictions. This illustrates there is a trade-off between maximizing the revenue and minimizing the uncertainty. High revenue and rewards usually accompany with high uncertainties and risk. In practice, according to different business strategies and needs, we usually need to find an appropriate $\\beta$ to maximize the revenue under an acceptable level of uncertainty." ] }, { "cell_type": "code", "execution_count": 27, - "id": "e8186ab2", + "id": "d8bd786d", "metadata": {}, "outputs": [], "source": [ @@ -2746,7 +2746,7 @@ { "cell_type": "code", "execution_count": 28, - "id": "f2120d62", + "id": "fb3ad095", "metadata": {}, "outputs": [ { @@ -2773,7 +2773,7 @@ }, { "cell_type": "markdown", - "id": "23279bd3", + "id": "ebbad1ef", "metadata": {}, "source": [ "# 5. Conclusion" @@ -2781,7 +2781,7 @@ }, { "cell_type": "markdown", - "id": "e60f3591", + "id": "a977be27", "metadata": {}, "source": [ "In this notebook, we demonstrate how to leverage a quantum annealer on Amazon Braket to solve a price optimization use case. We showed how to mathematically formulate the problem within the (quantum-ready) QUBO framework, and then subsequently solve the optimization problem on a D-Wave quantum annealer. Our results are promising in terms of both close-to-optimal quality and computational efficiency. Since the QUBO formalism is a generalized framework that can embrace a variety of combinatorial optimization use cases (e.g. scheduling/planning, routing, portfolio management), the proposed solution can be arguably adapted and recycled by customers across other multiple industries. Already today our customers can get quantum-ready, and easily leverage Amazon Braket to help solve their daily combinatorial optimization challenges, and make better business and operation decisions." @@ -2789,7 +2789,7 @@ }, { "cell_type": "markdown", - "id": "7fc1d51c", + "id": "f0a4ded6", "metadata": {}, "source": [ "# 6. References:\n", @@ -2809,7 +2809,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6975ad41", + "id": "bcd8e68c", "metadata": {}, "outputs": [], "source": [] From 76f82ee4b06d2b2567d18b01443ad673e400dd79 Mon Sep 17 00:00:00 2001 From: feng shi Date: Sat, 12 Feb 2022 20:02:50 +0000 Subject: [PATCH 11/13] add detailed explanation --- .../price_optimization/QUBO-Pricing.ipynb | 162 ++++++++++-------- 1 file changed, 89 insertions(+), 73 deletions(-) diff --git a/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb b/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb index 9d0a55e17..cfd35fd0a 100644 --- a/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb +++ b/examples/quantum_annealing/price_optimization/QUBO-Pricing.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "edd0974e", + "id": "2c5219f3", "metadata": {}, "source": [ "# Using quantum annealing on Amazon Braket for price optimization\n", @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "5aef5c46", + "id": "10f29dc7", "metadata": {}, "source": [ "# Table of contents\n", @@ -35,16 +35,16 @@ }, { "cell_type": "markdown", - "id": "34cd7d9b", + "id": "aed8d388", "metadata": {}, "source": [ - "We start by importing important libraries related to Amazon braket and installing dependencies." + "We start by importing Amazon braket SDK and Dwave SDK to be used for quantum annealing in this use case. In addition, we import sklearn to fit the demand estimation model." ] }, { "cell_type": "code", "execution_count": 1, - "id": "36ae1bff", + "id": "1f31ea86", "metadata": {}, "outputs": [ { @@ -53,8 +53,8 @@ "text": [ "Requirement already satisfied: sklearn in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (0.0)\n", "Requirement already satisfied: scikit-learn in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from sklearn) (1.0.1)\n", - "Requirement already satisfied: numpy>=1.14.6 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.19.2)\n", "Requirement already satisfied: scipy>=1.1.0 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.5.2)\n", + "Requirement already satisfied: numpy>=1.14.6 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.19.2)\n", "Requirement already satisfied: threadpoolctl>=2.0.0 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (3.0.0)\n", "Requirement already satisfied: joblib>=0.11 in /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages (from scikit-learn->sklearn) (1.1.0)\n" ] @@ -67,7 +67,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "ba7e6e17", + "id": "6718da7a", "metadata": {}, "outputs": [], "source": [ @@ -100,7 +100,7 @@ }, { "cell_type": "markdown", - "id": "9a2d83f3", + "id": "61be0cc9", "metadata": {}, "source": [ "__NOTE__: Enter your S3 bucket and key below. " @@ -109,7 +109,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "f705556e", + "id": "ce15ec79", "metadata": {}, "outputs": [], "source": [ @@ -122,7 +122,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "f9407fdf", + "id": "c2fc5e7e", "metadata": {}, "outputs": [ { @@ -141,7 +141,7 @@ }, { "cell_type": "markdown", - "id": "7da0da4b", + "id": "173be395", "metadata": {}, "source": [ "# 1. Demand model" @@ -149,7 +149,7 @@ }, { "cell_type": "markdown", - "id": "7f3156c0", + "id": "5c05da56", "metadata": {}, "source": [ "The usual goal of price optimization is to maximize the revenue in the next certain period with respect to the corresponding prices, where the revenue can usually be represented by a function of demand and price: \n", @@ -163,7 +163,7 @@ }, { "cell_type": "markdown", - "id": "4e328037", + "id": "e7de211f", "metadata": {}, "source": [ "## 1.1 Create training dataset" @@ -171,7 +171,7 @@ }, { "cell_type": "markdown", - "id": "9656d0b2", + "id": "21fe8119", "metadata": {}, "source": [ "For simplicity, we create a dummy dataset on historical demand and price observations so that a demand estimation model can be trained. \n", @@ -189,7 +189,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "c443c940", + "id": "438e6d85", "metadata": { "scrolled": true }, @@ -268,7 +268,7 @@ }, { "cell_type": "markdown", - "id": "128b6357", + "id": "8f68105b", "metadata": {}, "source": [ "## 1.2. Fit the demand model" @@ -276,7 +276,7 @@ }, { "cell_type": "markdown", - "id": "dad040b3", + "id": "31302cb4", "metadata": {}, "source": [ "We use `sklearn` to fit a linear demand model to the training set. This fitted linear demand model will be used for the following price optimization problem." @@ -285,7 +285,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "9d0f2e1a", + "id": "08cdb86d", "metadata": {}, "outputs": [ { @@ -315,7 +315,7 @@ }, { "cell_type": "markdown", - "id": "b0fbc444", + "id": "694b5278", "metadata": {}, "source": [ "# 2. Price optimization with QUBO" @@ -323,7 +323,7 @@ }, { "cell_type": "markdown", - "id": "efaea380", + "id": "c67da567", "metadata": {}, "source": [ "In this notebook, we leverage a general-purpose mathematical framework: Quadratic Unconstrained Binary Optimization (QUBO), which has been recently proposed as an effective framework that is able to generalize across a large variety of combinatorial optimization use cases in industries [2, 3]. We take this price optimization as an example and showcase how to formulate it into QUBO framework considering prediction uncertainties as well as equality constraints." @@ -331,7 +331,7 @@ }, { "cell_type": "markdown", - "id": "a6a8394d", + "id": "2f6135bd", "metadata": {}, "source": [ "The formal definition of QUBO is expressed as an optimization problem, Minimize:\n", @@ -340,7 +340,7 @@ }, { "cell_type": "markdown", - "id": "bafddc03", + "id": "277ac4cc", "metadata": {}, "source": [ "where $x$ is a vector of binary variables representing the decision variables of the combinatorial optimization. $Q$ is a squared matrix of constants inherently encoding the context and constraints of the optimization problems. $Q$ is commonly assumed to be symmetric or upper triangular without loss of generality. The goal is to find the optimal values of the binary decision variables $x$ that minimize the objective $H$.\n", @@ -350,7 +350,7 @@ }, { "cell_type": "markdown", - "id": "3dbc26ac", + "id": "b4ce1392", "metadata": {}, "source": [ "## 2.1 Construct objective function" @@ -358,7 +358,7 @@ }, { "cell_type": "markdown", - "id": "99a4ed85", + "id": "4e5a61db", "metadata": {}, "source": [ "Assuming tomorrow is day $T$, then the goal of our price optimization is to find the optimal prices $p_t, t\\in[T, T+1, \\ldots, T+n-1]$ in the next $n$ days in order to maximize the revenue in next $n$ days. Based on the demand model we showed above where the demand at a day is correlated with the latest $n$ days' price, we can construct objective function as below:\n", @@ -373,7 +373,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "1374e2e8", + "id": "8ab0bc6b", "metadata": {}, "outputs": [ { @@ -395,7 +395,7 @@ }, { "cell_type": "markdown", - "id": "81fe0624", + "id": "8ced72f4", "metadata": {}, "source": [ "Now, let's construct the objective function, i.e. the total revenue $R$, for the next $n$ days.\n", @@ -408,7 +408,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "fdd84340", + "id": "a668a23a", "metadata": {}, "outputs": [ { @@ -461,7 +461,7 @@ }, { "cell_type": "markdown", - "id": "ced0cdce", + "id": "437d5378", "metadata": {}, "source": [ "Next, we can input the price variables into our fitted model to estimate the demand, and then use the demand together with the price to represent the revenue $R$." @@ -470,7 +470,7 @@ { "cell_type": "code", "execution_count": 9, - "id": "94cb6355", + "id": "71dde625", "metadata": {}, "outputs": [ { @@ -525,7 +525,7 @@ }, { "cell_type": "markdown", - "id": "fba71f44", + "id": "88ec1a39", "metadata": {}, "source": [ "## 2.2 Add penalty for prediction uncertainty" @@ -533,7 +533,7 @@ }, { "cell_type": "markdown", - "id": "915245a9", + "id": "05742984", "metadata": {}, "source": [ "In optimization, we usually desire to reduce the risk while maximizing the reward, which means we want to reduce the estimated uncertainty/variance of the predicted demands. Therefore, we add a penalty term in the objective function to represent the uncertainty of the predicted demand. The uncertainty of the predicted demand $d_t$ can be represented by its estimated variance,\n", @@ -556,9 +556,16 @@ { "cell_type": "code", "execution_count": 10, - "id": "31ac67fd", + "id": "6c3d500e", "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Objective with expected revenue and prediction variance:\n" + ] + }, { "data": { "text/plain": [ @@ -600,12 +607,13 @@ "\n", "objective = rev - beta * get_overall_variance(data_x, p_data, p, sigma)\n", "\n", + "print('Objective with expected revenue and prediction variance:')\n", "repr_compact.repr(objective)" ] }, { "cell_type": "markdown", - "id": "2ff48929", + "id": "52a8d37f", "metadata": {}, "source": [ "## 2.3 Add penalty for equality constraints" @@ -613,7 +621,7 @@ }, { "cell_type": "markdown", - "id": "03dd90ab", + "id": "0a92e9af", "metadata": {}, "source": [ "Since the price can only take one value per day, exactly one of the binary variables in a day must be $1$, and the others must be $0$. Formallly, we have equality constraints:\n", @@ -627,9 +635,16 @@ { "cell_type": "code", "execution_count": 11, - "id": "2688ffc9", + "id": "96c8c9be", "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Objective with additional equality constraints:\n" + ] + }, { "data": { "text/plain": [ @@ -649,12 +664,13 @@ " penalty_i = ((sum(x[i*n_level:(i+1)*n_level]) - 1)**2)*Lp\n", " objective -= penalty_i\n", " \n", + "print('Objective with additional equality constraints:')\n", "repr_compact.repr(objective)" ] }, { "cell_type": "markdown", - "id": "014047a6", + "id": "6fbf2237", "metadata": {}, "source": [ "# 3. Solve QUBO with Braket" @@ -662,7 +678,7 @@ }, { "cell_type": "markdown", - "id": "19839de1", + "id": "9edaa67f", "metadata": {}, "source": [ "Now we have transformed to the total objective function which:\n", @@ -678,7 +694,7 @@ }, { "cell_type": "markdown", - "id": "045c86ac", + "id": "2547ec98", "metadata": {}, "source": [ "Amazon Braket provides access to quantum annealers from D-Wave Systems Inc. which are specifically designed to solve QUBO problems. A quantum annealer is a hardware implementation of Quantum Annealing (QA) which is a generic algorithm to solve combinatorial optimization problems by taking advantage of quantum fluctuations to escape local minima in complex energy landscapes by effect of tunnelling through barriers separating local minima [5]. Through a simple Amazon Braket API call, the formatted QUBO problem can be embedded to the hardwired topology of the machine and submitted to machine. In turn, the quantum annealer performs an annealing process and obtains a result. However, because of the sparsity of the underlying chip, one typically faces a certain overhead in embedding the original QUBO problem to the D-Wave hardware, because (typically) one logical binary variable maps onto several physical qubits, in order to effectively distill the connectivity of the original QUBO problem. For more details, we refer to the Amazon Braket tutorial notebook available here (https://github.com/aws/amazon-braket-examples/blob/main/examples/quantum_annealing/Dwave_Anatomy.ipynb)." @@ -687,7 +703,7 @@ { "cell_type": "code", "execution_count": 12, - "id": "78f7b7e7", + "id": "fdfe3dce", "metadata": {}, "outputs": [ { @@ -710,7 +726,7 @@ { "cell_type": "code", "execution_count": 13, - "id": "982c5e27", + "id": "54a70c81", "metadata": {}, "outputs": [ { @@ -730,7 +746,7 @@ }, { "cell_type": "markdown", - "id": "b138ab5d", + "id": "f149c413", "metadata": {}, "source": [ "We embed and submit the QUBO task to be solved by a quantum annealer at D-wave backend. Similar to classical simulated annealing, we take several independent shots in order to increase our chances for success in finding a high-quality solution to the QUBO problem. The response contains a number of rows. Each row represents the optimization result of a single shot, including the binary decision variables $[x_T,\\cdots,x_{T+n-1}]$, and corresponding energy which is the negative value of objective function, i.e. $H$. Below we show how to submit a QUBO problem to D-Wave and provide a sample response. Here, the key figure of merit is listed in the column labelled with energy, representing the value for the objective function . We can then easily read off the best bit string found.\n", @@ -741,7 +757,7 @@ { "cell_type": "code", "execution_count": 15, - "id": "f690c6d6", + "id": "b762f1e9", "metadata": { "scrolled": true }, @@ -964,7 +980,7 @@ }, { "cell_type": "markdown", - "id": "a1b9ddd8", + "id": "ec86a64d", "metadata": {}, "source": [ "## 3.1 Evaluate the results" @@ -972,7 +988,7 @@ }, { "cell_type": "markdown", - "id": "2ba24b89", + "id": "0fb4bbfb", "metadata": {}, "source": [ "With the response, we can decode the binary array results into the optimal price results" @@ -981,7 +997,7 @@ { "cell_type": "code", "execution_count": 16, - "id": "a582d6a2", + "id": "43d94f12", "metadata": {}, "outputs": [ { @@ -1016,7 +1032,7 @@ }, { "cell_type": "markdown", - "id": "cb96c9b2", + "id": "43a86a5e", "metadata": {}, "source": [ "The optimized price path and corresponding demand curve are plotted below, respectively. The optimal price level is higher than the past 7 days, which results in the demand decreasing." @@ -1025,7 +1041,7 @@ { "cell_type": "code", "execution_count": 17, - "id": "5f7e78da", + "id": "efa123fb", "metadata": {}, "outputs": [ { @@ -1052,7 +1068,7 @@ }, { "cell_type": "markdown", - "id": "b06dd1df", + "id": "6342fa6d", "metadata": {}, "source": [ "Let's also calculate the total revenue, and plot the demand of each day." @@ -1061,7 +1077,7 @@ { "cell_type": "code", "execution_count": 18, - "id": "4d922b80", + "id": "ce8ec494", "metadata": {}, "outputs": [ { @@ -1091,7 +1107,7 @@ { "cell_type": "code", "execution_count": 19, - "id": "77b88f14", + "id": "0e621ea0", "metadata": {}, "outputs": [ { @@ -1118,7 +1134,7 @@ }, { "cell_type": "markdown", - "id": "f2cf2845", + "id": "fa79da19", "metadata": {}, "source": [ "Finally, let's get the overall uncertainty of the demand predictions. Here we simply use the estimated demand variance to indicate the uncertainty." @@ -1127,7 +1143,7 @@ { "cell_type": "code", "execution_count": 20, - "id": "4a24740c", + "id": "169d083b", "metadata": {}, "outputs": [ { @@ -1149,7 +1165,7 @@ }, { "cell_type": "markdown", - "id": "8d12e6a0", + "id": "0fb60623", "metadata": {}, "source": [ "__We can also derive the standard deviation of the revenue based on the variance of demand__\n", @@ -1159,7 +1175,7 @@ }, { "cell_type": "markdown", - "id": "90443622", + "id": "ea9d6a49", "metadata": {}, "source": [ "where $cov(\\hat{d}_{t_1} \\hat{d}_{t_2}) = \\sigma^2(1+\\vec{p}_{t_1}'(\\vec{X}'\\vec{X})^{-1}\\vec{p}_{t_2})$" @@ -1168,7 +1184,7 @@ { "cell_type": "code", "execution_count": 21, - "id": "64009d9d", + "id": "b916ae54", "metadata": {}, "outputs": [ { @@ -1224,7 +1240,7 @@ }, { "cell_type": "markdown", - "id": "a4539fa6", + "id": "c2340e8b", "metadata": {}, "source": [ "We can investigate the value of the penality terms to see if any equality constraints are violated. The penalty is close to zero showing that all the constraints are satisfied. This small but non-zero value is due to floating point precision." @@ -1233,7 +1249,7 @@ { "cell_type": "code", "execution_count": 22, - "id": "aeccb8b2", + "id": "8cc64429", "metadata": {}, "outputs": [ { @@ -1255,7 +1271,7 @@ }, { "cell_type": "markdown", - "id": "b200d0ae", + "id": "f8ca8c97", "metadata": {}, "source": [ "For comparison, to assess the quality of this optimized result, we also iterate (by brute-force search) through all the $7^7=823,543$ possible price solutions to obtain the energy for each one, which takes more than 5 minutes to run on a standard ml.m5.2xlarge AWS instance. We plot the distribution of the energies of all the 823,543 possible solutions as shown below, where the red line represents our optimized result obtained from the quantum annealer. We can see that although the optimized result from the quantum annealer is not the global optimum with minimum cost, it is close-to-optimal and of good quality. " @@ -1264,7 +1280,7 @@ { "cell_type": "code", "execution_count": 23, - "id": "c64a44d0", + "id": "0bed907a", "metadata": { "scrolled": true }, @@ -2127,7 +2143,7 @@ { "cell_type": "code", "execution_count": 24, - "id": "cc17d5f9", + "id": "c218c92f", "metadata": {}, "outputs": [ { @@ -2155,7 +2171,7 @@ }, { "cell_type": "markdown", - "id": "70ae441a", + "id": "f5089d50", "metadata": {}, "source": [ "# 4. Trade-off between expected revenue and prediction uncertainty." @@ -2163,7 +2179,7 @@ }, { "cell_type": "markdown", - "id": "1b0ae4ba", + "id": "85862da0", "metadata": {}, "source": [ "Let's first wrap the above price optimization into a single optimize function for convenience." @@ -2172,7 +2188,7 @@ { "cell_type": "code", "execution_count": 25, - "id": "258c0f2d", + "id": "36b838f3", "metadata": {}, "outputs": [ { @@ -2219,7 +2235,7 @@ }, { "cell_type": "markdown", - "id": "28a35d53", + "id": "5b8efe22", "metadata": {}, "source": [ "In order to investigate the trade-off between the expected revenue and prediction uncertainties, we vary the hyperparameter $\\beta$ within a large range of $[1e2,1e9]$ and run multiple experiments on D-Wave with different $\\beta$ values. The scatter plot is shown below, where each dot represents the optimized result of an experiment with x-axis representing its expected revenue and y-axis representing the estimated standard deviation of revenue $std(R)$." @@ -2227,7 +2243,7 @@ }, { "cell_type": "markdown", - "id": "9bd6ff2d", + "id": "1e11af8f", "metadata": {}, "source": [ "
\n", @@ -2238,7 +2254,7 @@ { "cell_type": "code", "execution_count": 26, - "id": "24be7ba5", + "id": "a047a433", "metadata": { "scrolled": true }, @@ -2715,7 +2731,7 @@ }, { "cell_type": "markdown", - "id": "8f3a95a0", + "id": "d853f336", "metadata": {}, "source": [ "We can see from the plot below that there is a Pareto front [11] where the expected revenue cannot be increased without increasing the standard deviation (i.e. uncertainties), and the other way around.\n", @@ -2726,7 +2742,7 @@ { "cell_type": "code", "execution_count": 27, - "id": "d8bd786d", + "id": "b6db5e4c", "metadata": {}, "outputs": [], "source": [ @@ -2746,7 +2762,7 @@ { "cell_type": "code", "execution_count": 28, - "id": "fb3ad095", + "id": "719f9fce", "metadata": {}, "outputs": [ { @@ -2773,7 +2789,7 @@ }, { "cell_type": "markdown", - "id": "ebbad1ef", + "id": "f2667f41", "metadata": {}, "source": [ "# 5. Conclusion" @@ -2781,7 +2797,7 @@ }, { "cell_type": "markdown", - "id": "a977be27", + "id": "febb3839", "metadata": {}, "source": [ "In this notebook, we demonstrate how to leverage a quantum annealer on Amazon Braket to solve a price optimization use case. We showed how to mathematically formulate the problem within the (quantum-ready) QUBO framework, and then subsequently solve the optimization problem on a D-Wave quantum annealer. Our results are promising in terms of both close-to-optimal quality and computational efficiency. Since the QUBO formalism is a generalized framework that can embrace a variety of combinatorial optimization use cases (e.g. scheduling/planning, routing, portfolio management), the proposed solution can be arguably adapted and recycled by customers across other multiple industries. Already today our customers can get quantum-ready, and easily leverage Amazon Braket to help solve their daily combinatorial optimization challenges, and make better business and operation decisions." @@ -2789,7 +2805,7 @@ }, { "cell_type": "markdown", - "id": "f0a4ded6", + "id": "9c00a940", "metadata": {}, "source": [ "# 6. References:\n", @@ -2809,7 +2825,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bcd8e68c", + "id": "5a26a9dc", "metadata": {}, "outputs": [], "source": [] From d80fe970c770402ec9e85fdef24f7ae0f2da3193 Mon Sep 17 00:00:00 2001 From: Jordan Sullivan Date: Thu, 3 Mar 2022 15:02:36 -0800 Subject: [PATCH 12/13] Removed references to `s3_folder` since this is assumed by default now --- .../price_optimization/qubo_dynamic_pricing.py | 7 +++---- 1 file changed, 3 insertions(+), 4 deletions(-) diff --git a/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py b/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py index d6bc51498..aa7871a79 100644 --- a/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py +++ b/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py @@ -168,7 +168,6 @@ def optimize( sigma, beta, vol_bound, - s3_folder, dwave=True ): """ @@ -199,7 +198,7 @@ def optimize( ) # qubo solver - response = dwave_solver(obj,s3_folder) if dwave else qubo_solver(obj) + response = dwave_solver(obj) if dwave else qubo_solver(obj) # get optimal prices opt_prices, _, energy = decoder_price_response(response, len(a), price_levels) opt_demand, max_revenue = get_demands_rev(a, b, selected_hist_prices, opt_prices) @@ -218,11 +217,11 @@ def qubo_solver(obj): return response -def dwave_solver(obj,s3_folder): +def dwave_solver(obj): model = (-obj).compile().to_bqm() num_shots = 10000 - sampler = BraketDWaveSampler(s3_folder, + sampler = BraketDWaveSampler(device_arn= 'arn:aws:braket:::device/qpu/d-wave/Advantage_system4') sampler = EmbeddingComposite(sampler) response = sampler.sample(model, num_reads=num_shots) From 5380e8d7237541efb6b8b4d573645706998187ef Mon Sep 17 00:00:00 2001 From: Jordan Sullivan Date: Thu, 3 Mar 2022 15:26:23 -0800 Subject: [PATCH 13/13] make backwards compatible with previous version of notebook --- .../price_optimization/qubo_dynamic_pricing.py | 16 +++++++++++----- 1 file changed, 11 insertions(+), 5 deletions(-) diff --git a/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py b/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py index aa7871a79..fffbc2137 100644 --- a/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py +++ b/examples/quantum_annealing/price_optimization/qubo_dynamic_pricing.py @@ -1,7 +1,7 @@ from pyqubo import Binary import numpy as np import dimod -from braket.ocean_plugin import BraketSampler, BraketDWaveSampler +from braket.ocean_plugin import BraketDWaveSampler from dwave.system.composites import EmbeddingComposite from itertools import combinations @@ -168,6 +168,7 @@ def optimize( sigma, beta, vol_bound, + s3_folder=None, dwave=True ): """ @@ -198,7 +199,8 @@ def optimize( ) # qubo solver - response = dwave_solver(obj) if dwave else qubo_solver(obj) + response = dwave_solver(obj, s3_folder) if dwave else qubo_solver(obj) + # get optimal prices opt_prices, _, energy = decoder_price_response(response, len(a), price_levels) opt_demand, max_revenue = get_demands_rev(a, b, selected_hist_prices, opt_prices) @@ -217,12 +219,16 @@ def qubo_solver(obj): return response -def dwave_solver(obj): +def dwave_solver(obj, s3_folder): model = (-obj).compile().to_bqm() num_shots = 10000 - sampler = BraketDWaveSampler(device_arn= - 'arn:aws:braket:::device/qpu/d-wave/Advantage_system4') + device_arn = 'arn:aws:braket:::device/qpu/d-wave/Advantage_system4' + if s3_folder: + sampler = BraketDWaveSampler(s3_folder, device_arn=device_arn) + else: + sampler = BraketDWaveSampler(device_arn=device_arn) + sampler = EmbeddingComposite(sampler) response = sampler.sample(model, num_reads=num_shots) return response