Dangerous Leak at Chemical Factory - Emergency Response with Autonomous Assessment Bot.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<H1>Dangerous Leak at Chemical Factory - Emergency Response with Autonomous Assessment Bot</H1>\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Machine learning is assumed to be either supervised or unsupervised but a more recent approach is breaking the status-quo - reinforcement learning (RL). Supervised and unsupervised approaches require data to model, not reinforcement learning. RL is capable to explore space with a handful of instructions, analyze its surroundings one step at a time, and build its historical data as it learns.\n",
    "\n",
    "In this walk-through, we’ll use Q-learning to find the shortest path between two areas. It has the ability to embark on a journey with no knowledge of what to do next. This approach requires constant trial and error as it collects data about its surroundings and figures out how to accomplish its goal. This opens up interesting possibilities, what about recording additional information, like environmental details along the way that it may not fully understand until after it reaches its goal? And once reached, could it review that additional data to determine if any of it would have helped it reach its goal faster?\n",
    "\n",
    "Python code in this notebook based on Mic's great post: http://firsttimeprogrammer.blogspot.com/2016/09/getting-ai-smarter-with-q-learning.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q-learning**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to Wikipedia, \"Q-learning is a model-free reinforcement learning technique. Specifically, Q-learning can be used to find an optimal action-selection policy for any given (finite) Markov decision process (MDP).\" (https://en.wikipedia.org/wiki/Q-learning)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**installing networkx on Python 3.x**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 417,
   "metadata": {},
   "outputs": [],
   "source": [
    "# installing networkx on Python 3.x \n",
    "# download and unzip networkx at https://pypi.python.org/pypi/networkx/#downloads\n",
    "# cd\n",
    "# !python setup.py install"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<H2>Part 1: RL - Q-Learning Bot - Mapping Factory Floor for Dangerous Leak<BR></H2>\n",
    "<B>Goal:</B> Find shortest path to leak for evaluation and response team<BR><BR>\n",
    "    \n",
    "Let's create a factory floor using the network mapping library <a href='https://networkx.github.io/' target='_blank'>networkz</a>. This can easily be done by creating a list of points representing each direction our bot can take to go from one end of the map to the other. Using this format allows us to easily create complex graphs but also easily visualize everything with networkx graphs. <BR><BR>\n",
    "The map represents the chemical factory floor. The entrance is room is <b>0</b> and the room with the leak is <b>18</b>.<BR><BR>\n",
    "Our bot will use Q-Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 468,
   "metadata": {},
   "outputs": [
    {
     "data": {
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ymwT8JCYGevWKiP36RERERCT4+eIZOwl3CQlNvpSGM//2LTh6T7uGEhN9l8nf6uzXR3n5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aRM7CQ1JOexS4VwKKYklZQLqEiSpAoTO0kqKRdQkSRJFSZ2klRSEydOdC87SZIEmNhJUmk5FFOS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\nnImdJEmSJJWciZ0kSZIkldz/A4ys5RCqFRzcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a756b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pylab as plt\n",
    "import networkx as nx\n",
    "\n",
    "# map cell to cell, add circular cell to goal point\n",
    "point_list = [(0,1), (1,2), (2,3), (1,4), (4,5), (1,6), \n",
    "               (6,7), (7,8), (6,9), (9,10), (6,11), (11,12), \n",
    "               (12,13), (11,14), (14,15), (11,16), (16,17), (17,18),\n",
    "               (16,19), (19,20), (16,21), (21,22), (22,23), (21,24), \n",
    "               (24,25), (21,26), (26,27), (27,28), (26,29), (29, 30)]\n",
    "\n",
    "# goal point is where we have a leak\n",
    "fig, ax1 = plt.subplots(nrows=1, ncols=1, figsize=(15, 9))\n",
    "\n",
    "goal = 18\n",
    "G=nx.Graph()\n",
    "G.add_edges_from(point_list)\n",
    "pos = nx.spring_layout(G)\n",
    "nx.draw_networkx_nodes(G,pos)\n",
    "nx.draw_networkx_edges(G,pos)\n",
    "nx.draw_networkx_labels(G,pos)\n",
    "\n",
    "# highlight starting point\n",
    "nx.draw_networkx_nodes(G, pos,\n",
    "                       nodelist=[0],\n",
    "                       node_color='lightblue',\n",
    "                       node_size=500,\n",
    "                       alpha=0.8)\n",
    "\n",
    "# highlight end point\n",
    "nx.draw_networkx_nodes(G, pos,\n",
    "                       nodelist=[18],\n",
    "                       node_color='yellow',\n",
    "                       node_size=500,\n",
    "                       alpha=0.8)\n",
    " \n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The map shows that point 0 is where our bot will start its search and point 18 is the leak, the goal point. The extra added points and false paths are obstacles the bot will have to contend with. \n",
    "<BR>\n",
    "We then create the rewards graph - this is the matrix version of our list of points map. We initialize the matrix to be the height and width of our points list (31 in this example) and initialize all values to -1. We then change the values to be 0 if it is a viable path and 100 if it is a goal path (for more on this topic, see Mnemosyne_studio’s great tutorial: <a href='http://mnemstudio.org/path-finding-q-learning-tutorial.htm' target='_blank'>Deep Q Learning for Video Games - The Math of Intelligence #9</a>)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 441,
   "metadata": {},
   "outputs": [],
   "source": [
    "# how many points in graph? x points\n",
    "MATRIX_SIZE = 31\n",
    "\n",
    "# create matrix x*y\n",
    "R = np.matrix(np.ones(shape=(MATRIX_SIZE, MATRIX_SIZE)))\n",
    "R *= -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 442,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1.  0. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[ 0. -1.  0. -1.  0. -1.  0. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1.  0. -1.  0. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1.  0. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1.  0. -1. -1. -1.  0. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1.  0. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1.  0. -1. -1. -1. -1. -1.  0. -1.  0. -1.  0. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1.  0. -1.  0. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1.  0. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1.  0. -1. -1. -1.  0. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1.  0. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1.  0. -1. -1. -1. -1. -1.  0. -1.  0. -1.  0. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.  0. -1.  0. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.  0. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.  0. -1. -1. -1.  0. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.  0. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.  0. -1. -1. -1. -1. -1.  0.\n",
      "  -1.  0. -1.  0. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[  -1.   -1.   -1.   -1.   -1.   -1.   -1.   -1.   -1.   -1.   -1.   -1.\n",
      "    -1.   -1.   -1.   -1.    0.   -1.  100.   -1.   -1.   -1.   -1.   -1.\n",
      "    -1.   -1.   -1.   -1.   -1.   -1.   -1.]]\n",
      "[[  -1.   -1.   -1.   -1.   -1.   -1.   -1.   -1.   -1.   -1.   -1.   -1.\n",
      "    -1.   -1.   -1.   -1.   -1.    0.  100.   -1.   -1.   -1.   -1.   -1.\n",
      "    -1.   -1.   -1.   -1.   -1.   -1.   -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.  0. -1.\n",
      "  -1. -1.  0. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1.  0. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.  0. -1.\n",
      "  -1. -1. -1. -1.  0. -1.  0. -1.  0. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1.  0. -1.  0. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1.  0. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1.  0. -1. -1. -1.  0. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1.  0. -1. -1. -1. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1.  0. -1. -1. -1. -1. -1.  0. -1.  0. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1.  0. -1.  0. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1.  0. -1. -1. -1.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1.  0. -1. -1. -1.  0.]]\n",
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      "  -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.  0. -1.]]\n"
     ]
    }
   ],
   "source": [
    "# assign zeros to paths and 100 to goal-reaching point\n",
    "for point in point_list:\n",
    "    if point[1] == goal:\n",
    "        R[point] = 100\n",
    "    else:\n",
    "        R[point] = 0\n",
    "\n",
    "    if point[0] == goal:\n",
    "        R[point[::-1]] = 100\n",
    "    else:\n",
    "        # reverse of point\n",
    "        R[point[::-1]]= 0\n",
    "\n",
    "# add goal point round trip\n",
    "R[goal,goal]= 100\n",
    "\n",
    " \n",
    "R.shape\n",
    "\n",
    "for r in R:\n",
    "    print(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Build a function to test the current best path with the actual best path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 443,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_best_path(Q, solution_path):\n",
    "    current_state = 0\n",
    "    steps = [current_state]\n",
    "    while current_state != 18:\n",
    "        next_step_index = np.where(Q[current_state,] == np.max(Q[current_state,]))[1]\n",
    "        if next_step_index.shape[0] > 1:\n",
    "            next_step_index = int(np.random.choice(next_step_index, size = 1))\n",
    "        else:\n",
    "            next_step_index = int(next_step_index)\n",
    "        steps.append(next_step_index)\n",
    "        current_state = next_step_index\n",
    "    if steps == solution_path:\n",
    "        return steps, True\n",
    "    else:\n",
    "        return steps, False\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The matrix is too big to show in this notebook but the y-axis is the state or where your bot is currently located, and the x-axis is your possible next actions. We then build our Q-learning matrix which will hold all the lessons learned from our bot. The Q-learning model uses a transitional rule formula and gamma is the learning parameter (see <a href='http://mnemstudio.org/path-finding-q-learning-tutorial.htm' target='_blank'>Deep Q Learning for Video Games - The Math of Intelligence #9</a> for more details). The rest of this example is mostly copied from Mic’s blog post <a href='http://firsttimeprogrammer.blogspot.com/2016/09/getting-ai-smarter-with-q-learning.html' target='_blank'>Getting AI smarter with Q-learning: a simple first step in Python</a>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 444,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 444,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q = np.matrix(np.zeros([MATRIX_SIZE,MATRIX_SIZE]))\n",
    "\n",
    "# rewards discout\n",
    "gamma = 0.8\n",
    "\n",
    "initial_state = 1\n",
    "\n",
    "def available_actions(state):\n",
    "    current_state_row = R[state,]\n",
    "    av_act = np.where(current_state_row >= 0)[1]\n",
    "    return av_act\n",
    "\n",
    "available_act = available_actions(initial_state) \n",
    "\n",
    "def sample_next_action(available_actions_range):\n",
    "    next_action = int(np.random.choice(available_act,1))\n",
    "    return next_action\n",
    "\n",
    "action = sample_next_action(available_act)\n",
    "\n",
    "def update(current_state, action, gamma):\n",
    "    \n",
    "  max_index = np.where(Q[action,] == np.max(Q[action,]))[1]\n",
    "  \n",
    "  if max_index.shape[0] > 1:\n",
    "      max_index = int(np.random.choice(max_index, size = 1))\n",
    "  else:\n",
    "      max_index = int(max_index)\n",
    "  max_value = Q[action, max_index]\n",
    "  \n",
    "  Q[current_state, action] = R[current_state, action] + gamma * max_value\n",
    "\n",
    "  if (np.max(Q) > 0):\n",
    "    return(np.sum(Q/np.max(Q)*100))\n",
    "  else:\n",
    "    return (0)\n",
    "    \n",
    "update(initial_state, action, gamma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# We keep following Mic’s blog and run the training and testing functions that will run the update function 1000 times allowing the Q-learning model to figure out the most efficient path:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 445,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "660 True\n",
      "671 True\n",
      "672 True\n",
      "673 True\n",
      "674 True\n",
      "675 True\n",
      "Found most efficient path:\n",
      "[0, 1, 6, 11, 16, 17, 18]\n"
     ]
    },
    {
     "data": {
      "image/png": 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6ctcOtqxeQEtLc9i6udveoZS+TL/i18kKzyRYLM1ZG4C3RGQWUN1aqKq/TVRQ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d2e5860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Training\n",
    "scores = []\n",
    "wins_found = 0\n",
    "for i in range(1000):\n",
    "    current_state = np.random.randint(0, int(Q.shape[0]))\n",
    "    available_act = available_actions(current_state)\n",
    "    action = sample_next_action(available_act)\n",
    "    score = update(current_state,action,gamma)\n",
    "    steps, win = test_best_path(Q, [0, 1, 6, 11, 16, 17, 18])\n",
    "    if (win):\n",
    "        wins_found += 1\n",
    "        print(i, win)\n",
    "        if wins_found > 5:\n",
    "            break;\n",
    "    scores.append(score)\n",
    "\n",
    "# Testing\n",
    "current_state = 0\n",
    "steps = [current_state]\n",
    "\n",
    "# Testing\n",
    "steps, win = test_best_path(Q, [0, 1, 6, 11, 16, 17, 18])\n",
    "if win:\n",
    "    print('Found most efficient path:')\n",
    "else:\n",
    "    print(\"Could not find most efficient path:\")\n",
    "print(steps)\n",
    "\n",
    "plt.plot(scores)\n",
    "plt.plot(scores)\n",
    "plt.suptitle('QL-Learning Search Scoring with Early Stop\\nStop Once Ideal Path Confirmed')\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('Reward Score')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, as we would have guessed, it found the correct path to go from the entrance to the leak:\n",
    "[0, 1, 6, 11, 16, 17, 18]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the model did correctly find the most efficient path from the starting node 0 to the goal node 18 and took around 600 iterations to converge to a solution. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<H2>Part 2: Analysis of Environmental Data</H2>\n",
    "<B>Goal:</B> Model historic data and find correlations to emergency\n",
    "\n",
    "Now, imagine that our bot was recording environmental data as it was scurrying through each rooms building its internal maps. For example, what if it recorded the temperature of each room on its journey. \n",
    "\n",
    "<TABLE>\n",
    "    <TR><TD>6, 12, 14, 19, 24, 26, 22)</TD><TD>1 degree higher</TD></TR>\n",
    "    <TR><TD>11,16,21</TD><TD>2 degrees higher</TD></TR>\n",
    "    <TR><TD>17</TD><TD>5 degress higher</TD></TR>\n",
    "    <TR><TD>18</TD><TD>10 degress higher</TD></TR>\n",
    "</TABLE>\n",
    "\n",
    "For example, using linear regression, we model the distance to leak from start using environment data and discover relationship between leak and temperature reading, the higher the reading get, the closer to the leak. The <b>blue</b> color represents a 2 degree higher temperature and the <b>red</b>, 4 degrees higher."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 458,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TLkeJnYhIEz0wyd0PMe2RDwO1QAzUJ8BLeWZaJjBhwgTy8vK44oorSE5ONre/955Z55Oa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HnSLfNj4Fwgzxizxl1ObeX7ShKx1jJx4kRGjhzJJZdc4nU4EgVqsROJA/n5B5K7pnpFGHMgqcvP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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e137390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "G=nx.Graph()\n",
    "fig, ax1 = plt.subplots(nrows=1, ncols=1, figsize=(15, 9))\n",
    "\n",
    "G.add_edges_from(point_list)\n",
    "pos = nx.spring_layout(G)\n",
    "nx.draw_networkx_nodes(G,pos)\n",
    "nx.draw_networkx_edges(G,pos)\n",
    "nx.draw_networkx_labels(G,pos)\n",
    "\n",
    "# highlight starting point\n",
    "nx.draw_networkx_nodes(G, pos,\n",
    "                       nodelist=[0],\n",
    "                       node_color='lightblue',\n",
    "                       node_size=500,\n",
    "                       alpha=0.8)\n",
    "\n",
    "# highlight end point\n",
    "nx.draw_networkx_nodes(G, pos,\n",
    "                       nodelist=[18],\n",
    "                       node_color='yellow',\n",
    "                       node_size=500,\n",
    "                       alpha=0.8)\n",
    "\n",
    "nx.draw_networkx_edges(G, pos,\n",
    "                       edgelist=[(6,11),(11,12),(11,14),(16,19),(21,24),(21,26),(21,22)],\n",
    "                       width=8, alpha=0.5, edge_color='orange')\n",
    "\n",
    "nx.draw_networkx_edges(G, pos,\n",
    "                       edgelist=[(16,17),(17,18)],\n",
    "                       width=8, alpha=0.5, edge_color='red')\n",
    "\n",
    "nx.draw_networkx_edges(G, pos,\n",
    "                       edgelist=[(11,16),(16,21)],\n",
    "                       width=8, alpha=0.5, edge_color='blue')\n",
    " \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create a temperature difference list and add the temperature differential at each point. We set all points to <b>0</b>, some to <b>+2</b> and the point leading the goal to <b>+5</b> and the goal to <b>+10</b> degrees. And the way we are going to suggest to the Q-Learning model to favorize paths with a rising temperature is to drop a certain amount of 'next actions' that are decreasing in temperature (not all as we want to handle certain noisy situations). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 447,
   "metadata": {},
   "outputs": [],
   "source": [
    "# let's add our temparature readings\n",
    "temperature_differential_readings = [0] * 31\n",
    "temperature_differential_readings[6] = 1\n",
    "temperature_differential_readings[12] = 1\n",
    "temperature_differential_readings[14] = 1\n",
    "temperature_differential_readings[19] = 1\n",
    "temperature_differential_readings[24] = 1\n",
    "temperature_differential_readings[26] = 1\n",
    "temperature_differential_readings[22] = 1\n",
    "temperature_differential_readings[11] = 2\n",
    "temperature_differential_readings[16] = 2\n",
    "temperature_differential_readings[21] = 2\n",
    "temperature_differential_readings[17] = 5\n",
    "temperature_differential_readings[18] = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<H2>Part 3: Factory with Dangerous Leak - Using Enhanced Q-Learning with Case-based reasoning (CBR)</H2>\n",
    "<B>Goal:</B> Find shortest path to leak for evaluation and response team\n",
    "\n",
    "\n",
    "**Case-based reasoning (CBR)**\n",
    "\n",
    "\"Case-based reasoning (CBR), broadly construed, is the process of solving new problems based on the solutions of similar past problems.\" (https://en.wikipedia.org/wiki/Case-based_reasoning)\n",
    "\n",
    "We create the same factory map with the same story, suffering from same chemical leak (where temperature relationship applies). We fire off the bot using an enhanced Q-Learning algorithm with CBR, to attempt to favorize steps with increasing temperatures versus steps with decreasing ones or non-changing ones. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 450,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 450,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# re-initialize the matrices for new run\n",
    "Q = np.matrix(np.zeros([MATRIX_SIZE,MATRIX_SIZE]))\n",
    "\n",
    "# learning parameter\n",
    "gamma = 0.8\n",
    "\n",
    "\n",
    "\n",
    "initial_state = 1\n",
    "\n",
    "def available_actions(state):\n",
    "    current_state_row = R[state,]\n",
    "    av_act = np.where(current_state_row >= 0)[1]\n",
    "    return av_act\n",
    "\n",
    "available_act = available_actions(initial_state) \n",
    "\n",
    "# we add past action to know where we're coming from\n",
    "def sample_next_action(available_actions_range, past_action):\n",
    "    # see if we can go up in temperature\n",
    "    found_rising_temp_path = False\n",
    "    for act in available_act:\n",
    "        if temperature_differential_readings[past_action] < temperature_differential_readings[int(act)]:\n",
    "            next_action = int(act)\n",
    "            found_rising_temp_path = True\n",
    "            break;\n",
    "    \n",
    "    if found_rising_temp_path == False:\n",
    "        next_action = int(np.random.choice(available_act,1))\n",
    "   \n",
    "    return next_action\n",
    "\n",
    "action = sample_next_action(available_act, 0)\n",
    "\n",
    "def update(current_state, action, gamma):\n",
    "    \n",
    "  max_index = np.where(Q[action,] == np.max(Q[action,]))[1]\n",
    "  \n",
    "  if max_index.shape[0] > 1:\n",
    "      max_index = int(np.random.choice(max_index, size = 1))\n",
    "  else:\n",
    "      max_index = int(max_index)\n",
    "  max_value = Q[action, max_index]\n",
    "  \n",
    "  Q[current_state, action] = R[current_state, action] + gamma * max_value\n",
    "  # print('max_value', R[current_state, action] + gamma * max_value)\n",
    "  \n",
    "  if (np.max(Q) > 0):\n",
    "    return(np.sum(Q/np.max(Q)*100))\n",
    "  else:\n",
    "    return (0)\n",
    "    \n",
    "update(initial_state, action, gamma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 451,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "383 True\n",
      "384 True\n",
      "385 True\n",
      "386 True\n",
      "387 True\n",
      "388 True\n",
      "Found most efficient path:\n",
      "[0, 1, 6, 11, 16, 17, 18]\n"
     ]
    },
    {
     "data": {
      "image/png": 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DkiY0GXwOcFp+fhNwHyl5nANMi4gAHpE0WNKoPO3dEbEKQNLdwJnALeXEYGbd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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d42f3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# re-initialize the matrices for new run\n",
    "Q = np.matrix(np.zeros([MATRIX_SIZE,MATRIX_SIZE]))\n",
    "\n",
    "\n",
    "scores = []\n",
    "wins_found = 0\n",
    "for i in range(1000):\n",
    "    current_state = np.random.randint(0, int(Q.shape[0]))\n",
    "    available_act = available_actions(current_state)\n",
    "    action = sample_next_action(available_act, action)\n",
    "    score = update(current_state,action,gamma)\n",
    "    steps, win = test_best_path(Q, [0, 1, 6, 11, 16, 17, 18])\n",
    "    if (win):\n",
    "        wins_found += 1\n",
    "        print(i, win)\n",
    "        if wins_found > 5:\n",
    "            break;\n",
    "    scores.append(score)\n",
    "    \n",
    "# Testing\n",
    "steps, win = test_best_path(Q, [0, 1, 6, 11, 16, 17, 18])\n",
    "if win:\n",
    "    print('Found most efficient path:')\n",
    "else:\n",
    "    print(\"Could not find most efficient path:\")\n",
    "\n",
    "print(steps)\n",
    "\n",
    "plt.plot(scores)\n",
    "plt.suptitle('CBR & QL Search Scoring with Early Stop\\nStop Once Ideal Path Confirmed')\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('Reward Score')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You may need to run both examples a couple of times in order to see patterns emerge. Overall, it only takes our CBR enhanced model a half to two-thirds the time to reach the leak than the original approach. This is a toy problem but the ramifications of using RL to map areas along with the ability of recording additional data of which the immediate use may not be apparent opens up interesting possibilites. This is a bit like unsupervised learning where we don't quite know what we are going to learn but at times can be very profitable. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}