Traveling Salesman SA.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Traveling Salesman Problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"TSP_image-Copy1.png\" width=\"450\" height=\"300\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\hspace{13cm}$ Image: Thomas Nield"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The problem is defined as follows. Given a number of cities scattered in space, find the shortest possible route such that a salesman visits each city once and then returns to the city he started with. This seemingly easy task has a problem that the number of possible solutions increases as N! where N is the number of cities. Moreover, the distance function that needs to be optimized is known to be highly non-linear. It is, therefore, quite difficult to get to the global minimum which is nothing but our shortest route. We use here the method of Simulated Annealing that uses a Stochastic process to get to the global minimum."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "from random import choice, sample, random\n",
    "from IPython.display import clear_output\n",
    "import copy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    '''Function definition for the purpose of SA. \n",
    "    This is an alternative to the originally proposed\n",
    "    Bolztmann distribution function in the Metropolis-Hastings\n",
    "    algo.'''\n",
    "    return 1/(1+ np.exp(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def distance(coords):\n",
    "    '''Takes in an array of the co-ordinates of the cities and \n",
    "    returns the Euclidean distance of the path for the given permutation.'''\n",
    "    dist=0\n",
    "    for i in range(len(coords)-1):\n",
    "        dist+= np.sqrt(np.sum(np.square(coords[i,]- coords[i+1,])))\n",
    "#         print(i)\n",
    "    dist+= np.sqrt(np.sum(np.square(coords[0,]- coords[-1,])))\n",
    "    return dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def distance_abs(coords):\n",
    "    '''Takes in an array of the co-ordinates of the cities and \n",
    "    returns the Manhattan distance of the path for the given permutation.'''\n",
    "    dist=0\n",
    "    for i in range(len(coords)-1):\n",
    "        dist+= np.sum(np.abs(coords[i,]- coords[i+1,]))\n",
    "#         print(i)\n",
    "    dist+= np.sum(np.abs(coords[0,]- coords[-1,]))\n",
    "    return dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_sample(cities, undo_index= None, undo= False):\n",
    "    '''Takes in two random sets of co-ordinates and swaps them to generate\n",
    "    a new solution. The indices are kept track of to undo a change.'''\n",
    "    index=[]\n",
    "    if not undo:\n",
    "        index= sample(range(0, len(cities)), 2)\n",
    "        cities[[index[0], index[1]]]= cities[[index[1], index[0]]]\n",
    "    else:\n",
    "        cities[[undo_index[0], undo_index[1]]]= cities[[undo_index[1], undo_index[0]]]\n",
    "    return cities, index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_sample_rev(cities, undo_index= None, undo= False):\n",
    "    '''A more complex and better strategy to generate a new solution. The function takes\n",
    "    in a section of cities and reverses the direction in which they are arranged(travelled).'''\n",
    "    index=[]\n",
    "    if not undo:\n",
    "        index= sample(range(0, len(cities)), 2)\n",
    "        cities[min(index):max(index),]=cities[min(index):max(index),][::-1]\n",
    "    else:\n",
    "        cities[min(undo_index):max(undo_index),]=cities[min(undo_index):max(undo_index),][::-1]\n",
    "    return cities, index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_circle(N_cities, r= 0.5):\n",
    "    '''Creates a random arrangement of a given number of points on a circle of a given radius.'''\n",
    "    X=[]\n",
    "    Y=[]\n",
    "    for i in range(N_cities):\n",
    "        theta= 2*np.pi*np.random.rand()\n",
    "        x= r*np.cos(theta)\n",
    "        y= r*np.sin(theta)\n",
    "        X.append(x)\n",
    "        Y.append(y)\n",
    "    X=np.array(X).reshape((N_cities,1))\n",
    "    Y=np.array(Y).reshape((N_cities,1))\n",
    "    cities= np.concatenate((X,Y), axis=1)\n",
    "    return cities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_temperature(cities, scale= 2):\n",
    "    '''Function to set up the initial temperature of the system. The maximum distance \n",
    "    found in a few random solutions is scaled by a given factor.'''\n",
    "    delta_E=[]\n",
    "    for i in range(150):\n",
    "        distance= distance_abs(cities)\n",
    "        citi, ind= get_sample_rev(cities)\n",
    "        diff= distance_abs(citi)- distance\n",
    "        delta_E.append(np.abs(diff))\n",
    "    return scale*max(delta_E)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def traveling_salesman_greedy(cities, lim=300):\n",
    "    '''A greedy algorithm that only accepts the good solutions as they are\n",
    "    generated. A bad solution is not accepted and the changes made are undone.\n",
    "    Plotting is done in real time to get an intuition. The other strategy can be\n",
    "    commented out for comparison. Additionally, the plotting portion can be commented\n",
    "    to look at just the final result.'''\n",
    "    dist= distance_abs(cities)\n",
    "    dist_new=[]\n",
    "    i=0\n",
    "    while True:\n",
    "        new_cities, ind= get_sample_rev(cities)  #Generating the sample solutions. \n",
    "#         new_cities, ind= get_sample(cities)    #Alternate strategy\n",
    "        if distance_abs(new_cities)< dist:\n",
    "            dist= distance_abs(new_cities)\n",
    "            dist_new.append(dist)\n",
    "            #plotting\n",
    "            clear_output(wait=True) #clear the previous plot to show the new solution.\n",
    "            plt.figure(figsize=(12,6))\n",
    "            plt.plot(new_cities[:,0], new_cities[:,1], marker= 'o',mfc= 'pink',mew=1.5,c='black', label=f'dist :{dist}')\n",
    "            plt.plot(new_cities[[0,-1]][:,0], new_cities[[0,-1]][:,1], marker= 'o',mfc= 'pink',mew=1.5,c='black')\n",
    "            plt.legend()\n",
    "            plt.show()\n",
    "        else:                            #To undo the unsuccessful change made earlier\n",
    "            dist_new.append(dist)\n",
    "            get_sample_rev(cities,undo_index= ind, undo= True)\n",
    "#             get_sample(cities,undo_index= ind, undo= True)\n",
    "        if dist_new[-lim:].count(dist)== lim: #The loop is stopped when the solution does not improve for 'lim' no. of iterations.\n",
    "            print('Exit loop :',i)\n",
    "            break\n",
    "        i+=1\n",
    "    return dist, new_cities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def traveling_salesman_SA(cities, alpha=0.9, N_out=100, N_in=50, lim=300):\n",
    "    '''The Simulated annealing method.\n",
    "    The system starts at a high temperature and accepts solutions based on the Metropolis\n",
    "    alogorithm. The temperature is cooled down at a rate alpha. The function returns the\n",
    "    optimal distance obtained, the corresponding arrangement of cities, the specfic heat\n",
    "    variation and the temperature variation with the iterations.\n",
    "    \n",
    "    N_out is the number of iterations through which the temperature is reduced. N_in is\n",
    "    the number of iterations for which the annealing occurs at a particular temperature.\n",
    "    alpha, N_out, N_in and the initial temperature constiture the annealing schedule.\n",
    "    lim decides the when the loops break. A sudden change in the specific heat is indicative\n",
    "    of a phase tansition which can be used to stop/slow down the cooling.'''\n",
    "    dist_new=[]\n",
    "    cv=[]\n",
    "    cv_list= []\n",
    "    exit= False\n",
    "    temp=[]\n",
    "    dist= distance_abs(cities)\n",
    "    T= get_temperature(cities, scale= 1)   #To determine the initial temperature.\n",
    "    for i in range(N_out):\n",
    "        for j in range(N_in):\n",
    "            new_cities, ind= get_sample_rev(cities)\n",
    "            del_E= distance_abs(new_cities)- dist\n",
    "            if del_E<0:\n",
    "                #Update\n",
    "                dist= distance_abs(new_cities)\n",
    "                dist_new.append(dist)\n",
    "                cv_list.append(dist)\n",
    "            #plotting\n",
    "                clear_output(wait=True)  #clear the previous plot to show the new solution.\n",
    "                plt.figure(figsize=(12,6))\n",
    "                plt.plot(new_cities[:,0], new_cities[:,1], marker= 'o',mfc= 'pink',mew=1.5,c='black', label=f'dist :{\"{:.2f}\".format(dist)}')\n",
    "                plt.plot(new_cities[[0,-1]][:,0], new_cities[[0,-1]][:,1], marker= 'o',mfc= 'pink',mew=1.5,c='black', label=f'Temp:{\"{:.2f}\".format(T)}')\n",
    "                plt.legend()\n",
    "                plt.show()\n",
    "            else:\n",
    "                P= np.exp(-del_E/T)\n",
    "                rand= np.random.uniform()\n",
    "                if rand<= P:\n",
    "                    dist= distance_abs(new_cities)\n",
    "                    dist_new.append(dist)\n",
    "                    cv_list.append(dist)\n",
    "                else:                            #To undo the unsuccessful change made earlier\n",
    "                    dist_new.append(dist)\n",
    "                    get_sample_rev(cities,undo_index= ind, undo= True)\n",
    "#                     get_sample(cities,undo_index= ind, undo= True)\n",
    "            #Larger number of cities need a larger threshold.\n",
    "            if dist_new[-lim:].count(dist)== lim:\n",
    "                exit= True\n",
    "                print('Exit loop: ',(i,j))\n",
    "                break\n",
    "        if exit:\n",
    "            break\n",
    "        cv.append(np.var(cv_list)/(T**2))\n",
    "        cv_list=[]\n",
    "        temp.append(T)\n",
    "        T= alpha*T\n",
    "#     plt.plot(temp, cv)\n",
    "#     plt.show()\n",
    "    return dist, new_cities, cv, temp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#To determine alpha by trial and error.\n",
    "# T= get_temperature(cities,50)\n",
    "T=2\n",
    "a=[T]\n",
    "for i in range(50):\n",
    "    T= 0.75*T\n",
    "    a.append(T)\n",
    "plt.plot(a, label='alpha: 0.9')\n",
    "plt.title(\"T= alpha*T\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"Iterations\")\n",
    "plt.ylabel(\"Temperature\")\n",
    "# plt.savefig(\"temp_1\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# cities= np.random.random((20,2))  #To get a random arrangement of cities.\n",
    "cities= create_circle(20)           #To generate a circular/oval arrangement of cities."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The annealing schedule is highly crucial for a good result in SA. Notice how the distance ocassionally increases. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exit loop:  (23, 30)\n"
     ]
    }
   ],
   "source": [
    "test_cities= copy.deepcopy(cities) #To maintain a copy of the initial arrangement for the greedy algorithm.\n",
    "length, citi, CV, temp= traveling_salesman_SA(cities,0.80,50,50, 100) \n",
    "\n",
    "# If only the result is needed:\n",
    "# plt.figure(figsize=(12,6))\n",
    "# plt.plot(citi[:,0], citi[:,1], marker= 'o',mfc= 'pink',mew=1.5, c='black', label=f'dist :{\"{:.2f}\".format(length)}')\n",
    "# plt.plot(citi[[0,-1]][:,0], citi[[0,-1]][:,1], marker= 'o',mfc= 'pink',mew=1.5, c='black')\n",
    "# plt.legend()\n",
    "# plt.savefig(\"Filename\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Temperature')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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exxERKRCvjxG0MbPvzOwzM4vObSEz629mK8xsxe7du4syn1/MjIceeog1a9awcOFCr+OIiBSIl0WwCqjrnGsG/Av4JLcFnXPjnHMxzrmYatWqFVW+AunTpw/nnXeeTiUVkRLHsyJwziU751J8t2cB4WZW1as8Z+ucc86hf//+fPLJJyQmJnodR0TEb54VgZnVMDPz3Y71ZdnrVZ7CMGDAAMyM119/3esoIiJ+C+Tpo5OApcBlZpZkZneZ2b1mdq9vkV7AejP7DhgN9HYl/Ehr7dq16dWrF2+++SYpKSlexxER8YuVtL+9MTExrjiP7bN06VLatm3L66+/zv333+91HBERAMxspXMuJqfn/NoiMLO6Znal73akmVUozIClSVxcHK1bt2b06NGkp6d7HUdEJF/5FoGZ/QX4CHjD91Bt8jjDJ9iZGQMHDmTz5s3MmTPH6zgiIvnyZ4tgANAOSAZwzv0AVA9kqJLu5ptv5oILLuDVV1/1OoqISL78KYKjzrljmXfMLAwoWQcWiliZMmV4+OGH+eKLL5g/f77XcURE8uRPEcw3syeBSDO7CpgCfBrYWCXfAw88QO3atXn00Uc17ISIFGv+FMFjwG5gHXAPMAt4KpChSoPIyEiGDx/O8uXL+eijj7yOIyKSqzxPHzWzEGCtc65x0UXKW3E/fTS7EydO0KJFC44cOUJCQgLh4eFeRxKRIHXGp48659KB78ysTkCSlXKhoaGMHDmSLVu2MG7cOK/jiIjkKN8vlJnZV0BrYDlwKPNx51yPwEbLWUnaIgBwztG5c2c2bNjA1q1bqVBBX8EQkaKX1xZBmB+vf6aQ8wQVM+Mf//gHsbGxvPzyyzzzjN5OESleNMREEbn11luZOXMmW7ZsoUaNGl7HEZEgc1ZDTJjZQTNL9l1SzeyEmSUXfszS7fnnn+fo0aPaIhCRYiffInDOVXDOVfRdIoCbgDGBj1a6XHLJJdxzzz28+eabbN682es4IiJZCjwMtXPuE6Bz4Ucp/YYOHUpkZCRPPvmk11FERLLke7DYzG7MdjcEiEFDTJyR6tWrM2TIEP7+97/zzTffEBcX53UkERG/Th/9T7a7aUAi8KZzblcAc+WqpB4szpSSksIll1zCpZdeyvz58/FN0iYiElBnOx/BW865fr7LX5xzzwMNCjdi8ChfvjzDhg1j4cKFzJgxw+s4IiJ+bRGscs61zO+xolLStwgAjh8/TuPGjQkLC+O7774jLMyfr3OIiJy5M9oiMLM2ZvZXoJqZPZLtMgwIDVDWoBAeHs6IESNISEhgwoQJXscRkSCX166hMkB5Mg4oV8h2SSZj4nk5CzfccANt2rRh6NChHD582Os4IhLEct0n4ZybT8ZcBO84534qwkxBIXPoiQ4dOvDaa6/xxBNPeB1JRIKUPweLD5vZS2Y2y8y+yrwEPFkQaN++PT169GDkyJHs2bPH6zgiEqT8KYKJwCagPhkD0CUC3wYwU1AZMWIEKSkpPP/8815HEZEg5U8RVHHOjQeOO+fmO+fuBPRNqELSqFEj+vXrx+uvv862bdu8jiMiQcifIjjuu95hZt3NrAVQO4CZgs4zzzxDWFgYTz2lGUBFpOj5UwTPmdm5wF+BwcBbwMMBTRVkatWqxaBBg3j//fdZtWqV13FEJMjkWQRmFgo0cM4dcM6td851cs61cs5NL6J8QeOxxx6jSpUqPPbYY15HEZEgk9+cxScAT6akDDbnnnsuTz31FHPnzmXOnDlexxGRIOLPEBPPA+cCkzl5zmJP9mGUhiEmcnP06FGioqIoU6YMq1evJjIy0utIIlJKnO2gc22BaOBZ4BXf5eXCiyeZypYty7hx49i8eTN/+9vfvI4jIkEi39HOnHOdiiKIZLjyyiu5//77GTVqFNdffz2XX36515FEpJTzZ87i881svJl95rvfyMzuCny04PXiiy9y0UUX0bdvX1JSUryOIyKlnD+7ht4BZgM1ffe/BwYFKI+QMWfBO++8Q2JiIkOGDPE6joiUcv4UQVXn3IdAOoBzLg04EdBUQvv27XnkkUcYO3Yss2fP9jqOiJRi/hTBITOrgm+eYjOLAw4ENJUA8NxzzxEVFcVdd93F/v37vY4jIqWUP0XwCDAduNjMFgPvAg8GNJUAEBERwYQJE/jtt98YNGiQ13FEpJTKtwh83xe4gozTSO8Bop1za/N7nZm9bWa7zGx9Ls+bmY02sy1mttbMPJn6srhr3bo1Tz75JBMmTGDatGlexxGRUsifs4YigIeA4WQMQz3A91h+3gGuyeP5bkAD36U/8G8/1hmUnnrqKZo3b07//v01b4GIFDp/dg29S8YXyv4FjAEaAe/l9yLn3ALg9zwW6Qm86zJ8A1Qyswv8yBN0ypQpw4QJE9i3bx8DBgzwOo6IlDL+FMFlzrm7nHNf+y79gUsL4WfXAn7Jdj/J95jkoGnTpjzzzDN8+OGHTJ482es4IlKK+FMEq31nCgFgZn8CFhfCz7YcHstx4CMz629mK8xsxe7duwvhR5dMQ4YMITY2lvvvv5/ffvvN6zgiUkr4UwR/ApaYWaKZJQJLgSvMbJ2Z5XvQOA9JwIXZ7tcGfs1pQefcOOdcjHMuplq1amfxI0u2sLAwJkyYwOHDh/nLX/5CfgMGioj4w58iuIaM+Yqv8F3qA9cCfwauO4ufPR24w3f2UBxwwDm34yzWFxQaNmzIiBEjmDFjBhMmTPA6joiUAvkOQw1gZpXJ+N971iB1+Q1DbWaTgI5AVWAn8Hcg3PfasWZmZBx8vgY4DPRzzuU7vnRpHobaX+np6XTu3JnVq1ezbt066tSp43UkESnm8hqG2p/5CIYDfYGt/LEP3znnOhdmSH+pCDL8+OOPNG3alDZt2jBnzhwyelVEJGdnOx/BLcDFzrmOvqkqO3lVAvKHiy66iFdeeYW5c+cyduxYr+OISAnmTxGsByoFOIecgf79+3P11VczePBgtm7d6nUcESmh/CmCEWScQjrbzKZnXgIdTPJnZowfP57w8HD69u3LiRMaFFZECs6fIpgAvAiM5I+pKl8JZCjxX+3atRk9ejSLFi1ixIgRXscRkRIo36kqgT3OudEBTyJn7Pbbb2f27Nk8/fTTNGzYkF69enkdSURKEH+KYKWZjSDjvP+jmQ/md/qoFJ3MXUTbtm3j9ttvp27durRu3drrWCJSQvhz+ujXOTys00eLoV27dvGnP/2J1NRUli1bpu8XiEiWvE4fzXeLwDnXqfAjSSBUr16dGTNm0LZtW6677joWLVpEhQoVvI4lIsWcP/MRnG9m483sM9/9RmZ2V+CjyZmIjo5mypQpbNiwgfj4eJ1JJCL58uesoXeA2UBN3/3vgUEByiOF4Oqrr+Zf//oXM2fOZPDgwV7HEZFiLtciMLPM3UZVnXMfAukAzrk0QP/NLObuu+8+Bg4cyKhRo/TNYxHJU15bBMt914fMrAq+cYYyRwoNdDA5e6+88grdu3fngQceYM6cOV7HEZFiKq8iyBzF7BEyTh292MwWkzF15YOBDiZnLzQ0lEmTJhEdHc3NN9/Mhg0bvI4kIsVQrqePmlkS8KrvbghQloxyOAqccM69muMLA0ynjxbczz//TGxsLJGRkSxbtozq1at7HUlEitiZjj4aCpQHKgDlyDjVNBQ4x/eYlBB16tRh+vTp/Pbbb1x//fWkpqZ6HUlEipG8vkewwzn3bJElkYCKjY3lvffe4+abb+bOO+9k4sSJmsNARAD/jhFIKdGrVy+ef/55Jk2axLPPquNFJENeWwRdiiyFFJknnniC77//nmHDhnHppZcSHx/vdSQR8ViuWwTOud+LMogUDTPjjTfeoEOHDvTr148lS5Z4HUlEPObPN4ullClbtixTp07lwgsv5Prrr+eHH37wOpKIeEhFEKSqVKnCjBkzcM5x+eWXs27dOq8jiYhHVARB7LLLLmPBggWEhIRwxRVXsHz58vxfJCKljoogyEVFRbFo0SIqV65Mly5dmDdvnteRRKSIqQiE+vXrs3DhQurUqUO3bt2YOXOm15FEpAipCASAmjVrMn/+fKKjo7n++uuZPHmy15FEpIioCCRL1apV+eqrr2jTpg3x8fGMHz/e60giUgRUBHKSihUr8vnnn9O1a1fuvvtu/vnPf3odSUQCTEUgpznnnHOYNm0avXr14pFHHuGZZ54ht1FqRaTky3fyeglOZcqUYdKkSZQvX55hw4aRnJzMyy+/rIHqREohFYHkKiwsjPHjx1OxYkVeffVVkpOTGTt2LKGhoV5HE5FCpCKQPIWEhDBq1CgqVqzIc889x8GDB3n33XcpU6aM19FEpJCoCCRfZsbw4cOpWLEijz76KCkpKUyZMoXIyEivo4lIIdDBYvHbkCFDGDt2LLNmzeLaa6/l9981QK1IaaAikAK55557+L//+z8WL15MixYtWLZsmdeRROQsqQikwG677TaWLFlCSEgIHTp0YNSoUTq9VKQEUxHIGYmJiWHVqlVce+21PPzww9x0003s37/f61gicgZUBHLGKleuzNSpU3n11Vf59NNPadmyJStWrPA6logUUECLwMyuMbPNZrbFzB7P4fmOZnbAzNb4LkMDmUcKn5nx8MMPs3DhQtLS0mjXrh1jxozRriKREiRgRWBmocDrQDegERBvZo1yWHShc6657/JsoPJIYMXFxbF69WquuuoqHnzwQW699VYOHDjgdSwR8UMgtwhigS3OuR+dc8eAD4CeAfx54rEqVaowffp0XnzxRT7++GNiYmJYs2aN17FEJB+BLIJawC/Z7if5HjtVGzP7zsw+M7PonFZkZv3NbIWZrdi9e3cgskohCQkJ4dFHH2XevHkcOXKEuLg43njjDe0qEinGAlkEOY1Odupfg1VAXedcM+BfwCc5rcg5N845F+Oci6lWrVrhppSAaN++PatXr6Zjx47ce++99OnTh4MHD3odS0RyEMgiSAIuzHa/NvBr9gWcc8nOuRTf7VlAuJlVDWAmKULVqlVj1qxZPPfcc0yePJmYmBjWrl3rdSwROUUgi+BboIGZ1TezMkBvYHr2BcyshvnGNTazWF+evQHMJEUsJCSEv/3tb3z55ZckJyfTunVrhg4dypEjR7yOJiI+ASsC51wa8AAwG9gIfOic22Bm95rZvb7FegHrzew7YDTQ22lncqnUsWNH1qxZQ69evRg+fDiNGjXi008/9TqWiABW0v7uxsTEOH1pqWSbN28eAwYMICEhgeuuu47XXnuN+vXrex1LpFQzs5XOuZicntM3i6XIZW4dvPTSS3z11Vc0atSI4cOHk5qa6nU0kaCkIhBPhIeHM3jwYDZt2kSPHj0YOnQoTZo04fPPP/c6mkjQURGIp2rXrs3kyZOZM2cOISEhdOvWjZtuuomff/7Z62giQUNFIMXCVVddxdq1a3nhhRf47LPPiIqKYuTIkRw7dszraCKlnopAio2yZcvyxBNPsHHjRrp27coTTzxB06ZN+fLLL72OJlKqqQik2Klbty4ff/wxs2bNIi0tjSuvvJKbbrqJ7777zutoIqWSikCKrW7durF+/XqeffZZvvjiC5o3b06PHj00PaZIIVMRSLEWERHB008/zU8//cSzzz7L4sWLiYuL46qrrmL+/PkazE6kEKgIpESoXLlyViG89NJLrFu3jo4dO9KhQwc+++wzFYLIWVARSIlSvnx5Bg8ezLZt2xgzZgw///wz1157LTExMUydOpX09HSvI4qUOCoCKZEiIyMZMGAAW7Zs4a233uLAgQPceOONNG3alPfff5+0tDSvI4qUGCoCKdHKlCnDXXfdxaZNm5g4cSLOOfr06UNUVBTjx4/X9xBE/KAikFIhLCyM2267jXXr1vHxxx9TsWJF7r77bi688EKGDBnCpk2bvI4oUmypCKRUCQkJ4YYbbmDFihV8/vnntG3bllGjRhEVFUW7du14++23SUlJ8TqmSLGiIpBSyczo2rUrU6dOJSkpiX/84x/s3buXu+66ixo1anDXXXexZMkSnW0kguYjkCDinGPp0qWMHz+eyZMnc+jQIaKiorjzzju54447qF69utcRRQJG8xGIkLGV0LZtW8aPH8+OHTt46623qFSpEkOGDKFWrVrceOONzJw5U2ccSdDRFoEEvYSEBN5++23effdddu/eTc2aNbnlllvo2bMn7du3JywszOuIImctry0CFYGIz7Fjx5g5cyb/+c9/mDNnDkePHuW8886je/fuXH/99Vx99dWUL1/e65giZ0RFIFJAKSkpzJ49m2nTpjFjxgz27dtH2bJlufLKK+nZsyfXXXcdNWrU8DqmiN9UBCJnIS0tjYULFzJt2jSmTZtGYmIiZkZcXBw9e/akZ8+eNGzY0OuYInlSEYgUEucc69atyyqFlStXAnDppZfSs2dPrrzyStq2batdSFLsqAhEAuSXX35h+vTpTJs2ja+//pq0tDTCwsKIiYnhiiuuoGPHjrRr144KFSp4HVWCnIpApAgcPHiQJUuWMH/+fObPn8/y5ctJS0sjNDSUli1bZhVD+/btOffcc72OK0FGRSDigUOHDrF06dKsYli2bBnHjh0jJCSE5s2bZxVDhw4dqFy5stdxpZRTEYgUA0eOHOGbb75h/vz5zJs3j2+++YajR48CcMkll9CqVStatmyZda1ykMKkIhAphlJTU1m+fDmLFi1i5cqVrFy5kp9++inr+fr1659WDlWrVvUwsZRkKgKREmLv3r2sWrWKlStXZl3/+OOPWc/XqVMnqxRatGhBo0aNqFu3LiEhGi1G8qYiECnB9u3bx+rVq08qhx9++CHr+YiICC677DIaNmxIVFQUUVFRNGzYkEsvvZSIiAgPk0txoiIQKWUOHDjAunXr2LRpExs3bsy6TkxMzBpa28yoX79+VjFkL4iqVatiZh7/FlKUVAQiQeLIkSN8//33pxXE5s2bsw5MA5QrV4569epRv379k64zb1eqVElFUcrkVQQaVlGkFImMjKRZs2Y0a9bspMdPnDjBTz/9xMaNG9myZQuJiYls27aNxMREFixYQHJy8knLV6xY8bSCqFOnDjVr1qRmzZrUqFGDMmXKFOWvJgGkIhAJAqGhoVx00UVcdNFFpz3nnGP//v0nlUPm9datW5k7dy6HDh067XXVqlXLKobcLtWrV9cw3iWA/oVEgpyZUblyZSpXrkyLFi1Oe945x549e9i+fTu//vprjpc1a9awc+dO0tPTT3ptSEgIVapUoVq1alStWpVq1arle7ts2bJF9auLj4pARPJkZll/qJs3b57rcmlpaezatYsdO3ZkFcT27dvZvXt31iUhIYE9e/awd+/e00ojU4UKFahWrVpWOVWqVMmv25UqVSI8PDxA70LppiIQkUIRFhaWtUuoVatWeS574sQJ9u3bx549e04qiuz39+3bx/79+0lKSmL//v3s27fvpAPeOSlXrhwVK1akQoUKJ11OfSynZcqVK8c555xDuXLlsm4Hy3GQgBaBmV0DvAaEAm8550ae8rz5nr8WOAz0dc6tCmQmEfFeaGgoVatWpWrVqgWay+HIkSNZpZB5nf32/v37OXjwIMnJyRw8eJCDBw/y888/Z91OTk7Ot0yyCwsLy7EgMq/POeccIiMjiYiIOOk6p8eyX0dERFC2bFnKlClD2bJlsy6Z94v6jK2AFYGZhQKvA1cBScC3ZjbdOZeQbbFuQAPf5U/Av33XIiKnyfwje8EFF5zxOo4fP35SMWTePnz4MIcOHcq6zn47p8d27drF4cOHSU1NJTU1lSNHjnDkyJFcd3kVRHh4+GnlULZsWfr3788jjzxy1us/VSC3CGKBLc65HwHM7AOgJ5C9CHoC77qMLzN8Y2aVzOwC59yOAOYSkSAWHh7Oeeedx3nnnReQ9R8/fvykcjj1+siRIxw9ejTrcuzYsZPu5/Xc+eefH5DMgSyCWsAv2e4ncfr/9nNaphZwUhGYWX+gP2SMtSIiUlyFh4cTHh5eoiYjCuRIVTnt5Dr1a8z+LINzbpxzLsY5F1OtWrVCCSciIhkCWQRJwIXZ7tcGfj2DZUREJIACWQTfAg3MrL6ZlQF6A9NPWWY6cIdliAMO6PiAiEjRCtgxAudcmpk9AMwm4/TRt51zG8zsXt/zY4FZZJw6uoWM00f7BSqPiIjkLKDfI3DOzSLjj332x8Zmu+2AAYHMICIiedO0RiIiQU5FICIS5FQEIiJBrsTNUGZmu4GfzvDlVYE9hRintND7cjq9J6fTe3K6kvSe1HXO5fhFrBJXBGfDzFbkNlVbMNP7cjq9J6fTe3K60vKeaNeQiEiQUxGIiAS5YCuCcV4HKKb0vpxO78np9J6crlS8J0F1jEBERE4XbFsEIiJyChWBiEiQC5oiMLNrzGyzmW0xs8e9zlMcmFmima0zszVmtsLrPF4xs7fNbJeZrc/22Hlm9oWZ/eC7ruxlxqKWy3syzMy2+z4va8zsWi8zFiUzu9DMvjazjWa2wcwG+h4vFZ+ToCiCbPMndwMaAfFm1sjbVMVGJ+dc89JwLvRZeAe45pTHHge+dM41AL703Q8m73D6ewLwT9/npblvUMlgkQb81TkXBcQBA3x/Q0rF5yQoioBs8yc7544BmfMni+CcWwD8fsrDPYEJvtsTgOuLMpPXcnlPgpZzbodzbpXv9kFgIxnT6paKz0mwFEFucyMHOwfMMbOVvnmh5Q/nZ06S5Luu7nGe4uIBM1vr23VUIneDnC0zqwe0AJZRSj4nwVIEfs2NHITaOedakrHLbICZXe51ICnW/g1cDDQHdgCveJrGA2ZWHvgvMMg5l+x1nsISLEWguZFz4Jz71Xe9C5hKxi40ybDTzC4A8F3v8jiP55xzO51zJ5xz6cCbBNnnxczCySiBic65j30Pl4rPSbAUgT/zJwcVMytnZhUybwNXA+vzflVQmQ78P9/t/wdM8zBLsZD5B8/nBoLo82JmBowHNjrnXs32VKn4nATNN4t9p7qN4o/5k5/3NpG3zOwiMrYCIGPK0veD9T0xs0lARzKGFN4J/B34BPgQqAP8DNzsnAuag6e5vCcdydgt5IBE4J7M/eOlnZm1BxYC64B038NPknGcoMR/ToKmCEREJGfBsmtIRERyoSIQEQlyKgIRkSCnIhARCXIqAhGRIKcikKBjZim+63pmdlshr/vJU+4vKcz1iwSCikCCWT2gQEXgG8k2LycVgXOubQEziRQ5FYEEs5FAB9/Y+g+bWaiZvWRm3/oGVrsHwMw6+saif5+MLxRhZp/4BuvbkDlgn5mNBCJ965voeyxz68N8617vmwPi1mzrnmdmH5nZJjOb6PsWK2Y20swSfFleLvJ3R4JGmNcBRDz0ODDYOfdnAN8f9APOudZmVhZYbGZzfMvGAo2dc9t89+90zv1uZpHAt2b2X+fc42b2gHOueQ4/60YyvpXbjIxv635rZgt8z7UAoskY/2ox0M7MEsgYxqGhc86ZWaXC/dVF/qAtApE/XA3cYWZryBg6oArQwPfc8mwlAPCQmX0HfEPGgIYNyFt7YJJv0LadwHygdbZ1J/kGc1tDxi6rZCAVeMvMbgQOn+XvJpIrFYHIHwx4MNsMXPWdc5lbBIeyFjLrCFwJtHHONQNWAxF+rDs3R7PdPgGEOefSyNgK+S8Zk518XoDfQ6RAVAQSzA4CFbLdnw3c5xtuGDO71Dcy66nOBfY55w6bWUMypi7MdDzz9adYANzqOw5RDbgcWJ5bMN+49+f6poMcRMZuJZGA0DECCWZrgTTfLp53gNfI2C2zynfAdjc5Tz34OXCvma0FNpOxeyjTOGCtma1yzvXJ9vhUoA3wHRmjdz7qnPvNVyQ5qQBMM7MIMrYmHj6j31DEDxp9VEQkyGnXkIhIkFMRiIgEORWBiEiQUxGIiAQ5FYGISJBTEYiIBDkVgYhIkPv/bGgYRDF+1uAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(temp, label=f'Initial temperature:{\"{:.2f}\".format(temp[0])}', c='black')\n",
    "plt.legend()\n",
    "plt.xlabel(\"Iterations\")\n",
    "plt.ylabel(\"Temperature\")\n",
    "# plt.savefig('temp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Variance <(E-<E>)^2>')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Relationship between the energy variance and the temperature.\n",
    "#The variance is expected to tend to zero for small temperatures.\n",
    "cv, T= np.array(CV), np.array(temp)\n",
    "var= cv*(T**2)\n",
    "plt.plot(T, var)\n",
    "plt.xlabel(\"Temperature\")\n",
    "plt.ylabel(\"Variance <(E-<E>)^2>\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The specific heat, cv, is seen to spike at a certain low temperature indicating that the system has 'frozen' and a phase transition is taking place. This is an analogy from Statistical Physics. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#An optional plotting section for the purpose of presentation.\n",
    "for i in range(len(cv)):\n",
    "    clear_output(wait=True)\n",
    "    plt.subplot(1,2,1)\n",
    "    plt.subplots_adjust(right= 2)\n",
    "    plt.plot(temp[:i], cv[:i], marker='o',mfc='yellow',c='black',markersize=3)\n",
    "    plt.xticks(np.arange(0,3,0.5))             #Needs to be changes based on the particular array range.\n",
    "    plt.yticks(np.arange(0,max(cv)+3,3)) \n",
    "    plt.xlabel('Temperature')\n",
    "    plt.ylabel('Heat Capacity')\n",
    "    plt.subplot(1,2,2)\n",
    "    plt.plot(temp[:i], marker='o',mfc='red', c='black',markersize=3)\n",
    "    plt.yticks(np.arange(0,3))\n",
    "    plt.xticks(np.arange(0,35,5))             #Needs to be changes based on the particular array range.   \n",
    "    plt.xlabel('Iterations')\n",
    "    plt.ylabel('Temperature')\n",
    "    plt.pause(0.2)\n",
    "    plt.show()\n",
    "    plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Notice that distance in the greedy algorithm strictly decreases in contrast to the SA algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exit loop : 2208\n"
     ]
    }
   ],
   "source": [
    "length, citi= traveling_salesman_greedy(test_cities, 1500) \n",
    "\n",
    "# If only the result is needed:\n",
    "# plt.figure(figsize=(12,6))\n",
    "# plt.plot(citi[:,0], citi[:,1], marker= 'o',mfc= 'pink',mew=1.5, c='black', label=f'Distance :{length}')\n",
    "# plt.plot(citi[[0,-1]][:,0], citi[[0,-1]][:,1], marker= 'o',mfc= 'pink',mew=1.5, c='black')\n",
    "# plt.legend()\n",
    "# plt.savefig(\"Greedy\")"
   ]
  },
  {
   "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": "3.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}