EDL_4_2_PSO.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "EDL_4_2_PSO.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyOTG9Dyabkbn3kO1+PlVpSZ",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/cxbxmxcx/EvolutionaryDeepLearning/blob/main/EDL_4_2_PSO.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZWk8QVItlplD"
      },
      "source": [
        "Original Source: https://github.com/DEAP/deap/blob/master/examples/ga/onemax_numpy.py\n",
        "\n",
        "DEAP is free software: you can redistribute it and/or modify\n",
        "   it under the terms of the GNU Lesser General Public License as\n",
        "   published by the Free Software Foundation, either version 3 of\n",
        "   the License, or (at your option) any later version.\n",
        "\n",
        "   DEAP is distributed in the hope that it will be useful,\n",
        "   but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n",
        "   GNU Lesser General Public License for more details.\n",
        "   You should have received a copy of the GNU Lesser General Public\n",
        "   License along with DEAP. If not, see <http://www.gnu.org/licenses/>."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ct-pwA_aHMMa",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c48a6bb0-e8b9-42eb-8f24-9c24784879e6"
      },
      "source": [
        "#@title Install DEAP\n",
        "!pip install deap --quiet"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[?25l\r\u001b[K     |██                              | 10 kB 17.6 MB/s eta 0:00:01\r\u001b[K     |████                            | 20 kB 21.9 MB/s eta 0:00:01\r\u001b[K     |██████                          | 30 kB 23.8 MB/s eta 0:00:01\r\u001b[K     |████████▏                       | 40 kB 18.0 MB/s eta 0:00:01\r\u001b[K     |██████████▏                     | 51 kB 18.2 MB/s eta 0:00:01\r\u001b[K     |████████████▏                   | 61 kB 17.2 MB/s eta 0:00:01\r\u001b[K     |██████████████▎                 | 71 kB 17.5 MB/s eta 0:00:01\r\u001b[K     |████████████████▎               | 81 kB 18.2 MB/s eta 0:00:01\r\u001b[K     |██████████████████▎             | 92 kB 13.7 MB/s eta 0:00:01\r\u001b[K     |████████████████████▍           | 102 kB 13.9 MB/s eta 0:00:01\r\u001b[K     |██████████████████████▍         | 112 kB 13.9 MB/s eta 0:00:01\r\u001b[K     |████████████████████████▍       | 122 kB 13.9 MB/s eta 0:00:01\r\u001b[K     |██████████████████████████▌     | 133 kB 13.9 MB/s eta 0:00:01\r\u001b[K     |████████████████████████████▌   | 143 kB 13.9 MB/s eta 0:00:01\r\u001b[K     |██████████████████████████████▌ | 153 kB 13.9 MB/s eta 0:00:01\r\u001b[K     |████████████████████████████████| 160 kB 13.9 MB/s \n",
            "\u001b[?25h"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "epVL5qPDHCPW"
      },
      "source": [
        "#@title Imports\n",
        "import operator\n",
        "import random\n",
        "import math\n",
        "import time\n",
        "\n",
        "import numpy as np\n",
        "\n",
        "from deap import base\n",
        "from deap import benchmarks\n",
        "from deap import creator\n",
        "from deap import tools\n",
        "from IPython.display import clear_output"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "s3r8TiOjHYyy"
      },
      "source": [
        "#@title Setup Fitness Criteria\n",
        "creator.create(\"FitnessMax\", base.Fitness, weights=(1.0,))\n",
        "creator.create(\"Particle\", np.ndarray, fitness=creator.FitnessMax, speed=list, \n",
        "    smin=None, smax=None, best=None)"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "brtFWiHfhGHl"
      },
      "source": [
        "#@title PSO Functions\n",
        "def generate(size, pmin, pmax, smin, smax):\n",
        "  part = creator.Particle(np.random.uniform(pmin, pmax, size)) \n",
        "  part.speed = np.random.uniform(smin, smax, size)\n",
        "  part.smin = smin\n",
        "  part.smax = smax\n",
        "  return part\n",
        "\n",
        "def updateParticle(part, best, phi1, phi2):\n",
        "  u1 = np.random.uniform(0, phi1, len(part))\n",
        "  u2 = np.random.uniform(0, phi2, len(part))\n",
        "  v_u1 = u1 * (part.best - part)\n",
        "  v_u2 = u2 * (best - part)\n",
        "  part.speed += v_u1 + v_u2\n",
        "  for i, speed in enumerate(part.speed):\n",
        "    if abs(speed) < part.smin:\n",
        "      part.speed[i] = math.copysign(part.smin, speed)\n",
        "    elif abs(speed) > part.smax:\n",
        "      part.speed[i] = math.copysign(part.smax, speed)\n",
        "  part += part.speed"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xVhtoopvtlr1"
      },
      "source": [
        "#@title Evaluation Function\n",
        "distance = 575 #@param {type:\"slider\", min:10, max:1000, step:5}\n",
        "def evaluate(individual):\n",
        "  v = individual[0] if individual[0] > 0 else 0  #velocity\n",
        "  a = individual[1] * math.pi / 180  #angle to radians\n",
        "  return ((2*v**2 * math.sin(a) * math.cos(a))/9.8 - distance)**2,"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DP0BRxxAH1uh"
      },
      "source": [
        "#@title Add Functions to Toolbox\n",
        "toolbox = base.Toolbox()\n",
        "toolbox.register(\"particle\", \n",
        "                 generate, size=2, pmin=-6, pmax=6, smin=-3, smax=3)\n",
        "toolbox.register(\"population\", \n",
        "                 tools.initRepeat, list, toolbox.particle)\n",
        "toolbox.register(\"update\", \n",
        "                 updateParticle, phi1=200, phi2=200)\n",
        "toolbox.register(\"evaluate\", evaluate)"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UM87TusHv8ab"
      },
      "source": [
        "#@title Code to Plot the Expression Tree\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def plot_population(pop):  \n",
        "  xs = [x for x,_ in pop]\n",
        "  ys = [y for _,y in pop]    \n",
        "  plt.scatter(xs,ys)  \n",
        "  plt.show()"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "id": "FC0-B2wAID9Z",
        "outputId": "ece6d7cf-9918-431c-b105-5eb4c7a68c19"
      },
      "source": [
        "#@title Run the Evolution\n",
        "random.seed(64)\n",
        "    \n",
        "pop = toolbox.population(n=500)\n",
        "stats = tools.Statistics(lambda ind: ind.fitness.values)\n",
        "stats.register(\"avg\", np.mean)\n",
        "stats.register(\"std\", np.std)\n",
        "stats.register(\"min\", np.min)\n",
        "stats.register(\"max\", np.max)\n",
        "\n",
        "logbook = tools.Logbook()\n",
        "logbook.header = [\"gen\", \"evals\"] + stats.fields\n",
        "\n",
        "GEN = 100\n",
        "best = None\n",
        "\n",
        "for g in range(GEN):          \n",
        "  for part in pop:\n",
        "    part.fitness.values = tuple(np.subtract((0,), toolbox.evaluate(part)))        \n",
        "    if part.best is None or part.best.fitness < part.fitness:\n",
        "      part.best = creator.Particle(part)\n",
        "      part.best.fitness.values = part.fitness.values\n",
        "    if best is None or best.fitness < part.fitness:\n",
        "      best = creator.Particle(part)\n",
        "      best.fitness.values = part.fitness.values\n",
        "  for part in pop:\n",
        "    toolbox.update(part, best)\n",
        "  \n",
        "  if (g+1) % 10 == 0:\n",
        "    logbook.record(gen=g, evals=len(pop), **stats.compile(pop))      \n",
        "    clear_output()\n",
        "    print(best)\n",
        "    plot_population(pop) \n",
        "    print(logbook.stream)\n",
        "    time.sleep(1)\n",
        "\n"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[75.06912074 44.85161278]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "99 \t500  \t-670.749\t519.582\t-4399.59\t-2.82224  \n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TW5XQ3S4QnYA",
        "outputId": "5b708913-80a4-429e-d5f6-cdb83f7b63e8"
      },
      "source": [
        "v, a = best\n",
        "a = a * math.pi / 180  #angle to radians\n",
        "distance = (2*v**2 * math.sin(a) * math.cos(a))/9.8\n",
        "print(distance)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "575.0303359637201\n"
          ]
        }
      ]
    }
  ]
}