AEM3 — candidates.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.spatial import distance_matrix\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "import itertools\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load instance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "instance_number = 1  # 0 - \"kroA200.tsp\"    1 - \"kroB200.tsp\"\n",
    "instances_names = [\"kroA200.tsp\",\"kroB200.tsp\"]\n",
    "data = np.genfromtxt(f'instances/{instances_names[instance_number]}', skip_header=6, skip_footer=1, dtype='int64')[:,1:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculating distance matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_distance_matrix(data):\n",
    "    dist_matrix = distance_matrix(data, data)\n",
    "    dist_matrix = np.around(dist_matrix, decimals=0)\n",
    "    dist_matrix = dist_matrix.astype(int)\n",
    "    return dist_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   0, 2607,  549, ..., 1240, 1232, 3117],\n",
       "       [2607,    0, 3154, ..., 3442, 1644,  933],\n",
       "       [ 549, 3154,    0, ..., 1097, 1713, 3658],\n",
       "       ...,\n",
       "       [1240, 3442, 1097, ...,    0, 2398, 3680],\n",
       "       [1232, 1644, 1713, ..., 2398,    0, 2406],\n",
       "       [3117,  933, 3658, ..., 3680, 2406,    0]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance_matrix = calc_distance_matrix(data)\n",
    "distance_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# GREEDY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def random_path(length, dataset_size):\n",
    "    points = np.arange(dataset_size)\n",
    "    np.random.shuffle(points)\n",
    "    path, outside = points[:length], points[length:]\n",
    "    return path, outside"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def knn(k, x, out, distance_matrix):\n",
    "    tab = []\n",
    "    pomx = x.tolist()\n",
    "    for i in range(len(x)):\n",
    "        sort_neigh = np.argsort(distance_matrix[x[i]])[1:]\n",
    "        sort_neigh = sort_neigh[~np.in1d(sort_neigh, out)]\n",
    "        for elem in sort_neigh[:5]:\n",
    "            j = pomx.index(elem)\n",
    "            neigh = [i, j]\n",
    "            neigh.sort()\n",
    "            if 1 < neigh[1] - neigh[0] < len(x) - 1:\n",
    "                tab.append(neigh)\n",
    "    tab = np.array(tab)\n",
    "    tab = np.unique(tab,axis=0)\n",
    "    return tab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def path_length(path):\n",
    "\tlength = 0\n",
    "\tfor i in range(len(path)-1):\n",
    "\t\tlength += distance_matrix[path[i], path[i+1]]\n",
    "\n",
    "\tlength += distance_matrix[path[-1], path[0]]\n",
    "\treturn length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def delta_change_outside(size, x, out, index, distance_matrix):\n",
    "    i = index[0]\n",
    "    j = index[1]\n",
    "    \n",
    "    old = distance_matrix[x[(i-1)%size], x[i]] + distance_matrix[x[i], x[(i+1)%size]]\n",
    "    new = distance_matrix[x[(i-1)%size], out[j]] + distance_matrix[out[j], x[(i+1)%size]]\n",
    "       \n",
    "    return old - new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def delta_change_inside_edges(size, x, index, distance_matrix):\n",
    "    i = index[0]\n",
    "    j = index[1]\n",
    "    \n",
    "    old = distance_matrix[x[(i-1)%size], x[i]] + distance_matrix[x[j], x[(j+1)%size]]\n",
    "    new = distance_matrix[x[(i-1)%size], x[j]] + distance_matrix[x[i], x[(j+1)%size]]\n",
    "    \n",
    "    return old - new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def swap_vertices_outside(x):\n",
    "    idx = []\n",
    "    for i in range(len(x)):\n",
    "        for j in range(len(x)):\n",
    "            idx.append([i, j])\n",
    "        \n",
    "    idx = np.array(idx)\n",
    "    return idx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def steepest_edge_candidate(size, start, out):\n",
    "    x = start\n",
    "    \n",
    "    # wyznaczenie sąsiedztwa\n",
    "    N_in = knn(5, x, out, distance_matrix)  \n",
    "    N_out = swap_vertices_outside(x)\n",
    "    \n",
    "    while True:\n",
    "        # wybór najlepszego ruchu zamiany dwóch wierzchołków \n",
    "        max_diff_o = 0\n",
    "        idx_o = 0\n",
    "        for id in range(len(N_out)):\n",
    "            idx = N_out[id]\n",
    "            diff = delta_change_outside(size, x, out, idx, distance_matrix)\n",
    "            if diff > max_diff_o:\n",
    "                max_diff_o = diff\n",
    "                idx_o = idx\n",
    "                \n",
    "        #wybór najlepszego ruchu zamiany dówch krawędzi \n",
    "        max_diff_i = 0\n",
    "        idx_i = 0\n",
    "        for id in range(len(N_in)):\n",
    "            idx = [N_in[id][0], (N_in[id][1]-1)%size]\n",
    "            diff = delta_change_inside_edges(size, x, idx, distance_matrix)\n",
    "            if diff > max_diff_i:\n",
    "                max_diff_i = diff\n",
    "                idx_i = idx\n",
    "                \n",
    "            idx = [(N_in[id][0]+1)%size, N_in[id][1]]\n",
    "            diff = delta_change_inside_edges(size, x, idx, distance_matrix)\n",
    "            if diff > max_diff_i:\n",
    "                max_diff_i = diff\n",
    "                idx_i = idx\n",
    "            \n",
    "                \n",
    "        if (max_diff_i > 0) or (max_diff_o > 0):        \n",
    "            # ruch zmieniający zbiór wierzchołków \n",
    "            if max_diff_o > max_diff_i:\n",
    "                ver1 = x[idx_o[0]]\n",
    "                ver2 = out[idx_o[1]]\n",
    "                x[idx_o[0]] = ver2\n",
    "                out[idx_o[1]] = ver1  \n",
    "                N_in = knn(5, x, out, distance_matrix) \n",
    "                N_out = swap_vertices_outside(x)\n",
    "\n",
    "            #ruch wewnątrztrasowy zamiana krawędzi\n",
    "            else:\n",
    "                a = x[idx_i[0]:idx_i[1]+1]\n",
    "                a = np.flip(a)\n",
    "                x[idx_i[0]:idx_i[1]+1] = a\n",
    "                N_in = knn(5, x, out, distance_matrix) \n",
    "                N_out = swap_vertices_outside(x)\n",
    "        else:\n",
    "            break\n",
    "            \n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "MIN = 1000000\n",
    "MAX = 0\n",
    "SUM = 0\n",
    "T_MIN = 1000000\n",
    "T_MAX = 0\n",
    "T_SUM = 0\n",
    "\n",
    "for i in range(100):\n",
    "    if i%5 == 0:\n",
    "        print(i)\n",
    "    x, out = random_path(100, 200)\n",
    "    start = time.time()\n",
    "    x = steepest_edge_candidate(100, x, out)\n",
    "    t = time.time() - start\n",
    "    len_x = path_length(x)\n",
    "    \n",
    "    if len_x > MAX:\n",
    "        MAX = len_x\n",
    "    if len_x < MIN:\n",
    "        MIN = len_x\n",
    "        T = x\n",
    "    SUM += len_x\n",
    "    \n",
    "    if t > T_MAX:\n",
    "        T_MAX = t\n",
    "    if t < T_MIN:\n",
    "        T_MIN = t\n",
    "    T_SUM += t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15528\n",
      "18793\n",
      "17204.21\n"
     ]
    }
   ],
   "source": [
    "print(MIN)\n",
    "print(MAX)\n",
    "print(SUM/100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.065017461776733\n",
      "16.93482518196106\n",
      "14.191400835514068\n"
     ]
    }
   ],
   "source": [
    "#time\n",
    "print(T_MIN)\n",
    "print(T_MAX)\n",
    "print(T_SUM/100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_plot(data, points):\n",
    "    f = plt.figure()\n",
    "    plt.plot(data[:, 0], data[:, 1], \"o\", linewidth=0, alpha=0.4)\n",
    "    plt.plot(data[points, 0], data[points, 1], \"o\", color='tab:blue',  linewidth=0, alpha=0.6)\n",
    "    plt.plot(data[points, 0], data[points, 1], \"--\", color=\"tab:cyan\", linewidth=1, alpha=2)\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"y\")\n",
    "    plt.title(\"Ruchy kandydackie - kroB200\")\n",
    "    plt.grid(False)\n",
    "    \n",
    "    plt.show()\n",
    "    f.savefig('candidateB.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([157,   2,  10,  92, 121,  72,  52, 169, 148,  69,  38,  39, 189,\n",
       "       110,  48,  85, 137, 165, 151,  37,  19,  79,  29,  74, 126, 123,\n",
       "        64, 187,  78, 178,  46,  87, 170, 103, 152,  23,  17,  44,  35,\n",
       "        16, 191,  77, 186, 125,  12, 154,   1, 108,  41, 119,  13, 124,\n",
       "        15, 104,  76, 102, 182, 139, 105, 158,  49, 184,  88,  86, 113,\n",
       "       167, 198, 130, 177,  73, 164,  59, 185,   6,  83,  57,  51, 162,\n",
       "        53, 114, 168,  24,   8, 160,  11, 173,   0,  94,  97,  31, 166,\n",
       "       174,  58, 135,  28,   7,  98,  90, 128,  27, 157])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = np.append(T, T[0])\n",
    "T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "print_plot(data, T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zwykły steepest - dla porównania"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def swap_edges(x):\n",
    "    combinations = itertools.combinations(np.arange(len(x)), 2)\n",
    "    return np.array([[v1,v2] for v1, v2 in combinations if 1 < v2 - v1 < len(x) - 1 ], 'int')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def steepest_edge(size, start, out):\n",
    "    x = start\n",
    "    N_in = swap_edges(x)\n",
    "    N_out = swap_vertices_outside(x)\n",
    "    while True:\n",
    "        max_diff_o = 0\n",
    "        idx_o = 0\n",
    "        for id in range(len(N_out)):\n",
    "            idx = N_out[id]\n",
    "            diff = delta_change_outside(size, x, out, idx, distance_matrix)\n",
    "            if diff > max_diff_o:\n",
    "                max_diff_o = diff\n",
    "                idx_o = idx\n",
    "        max_diff_i = 0\n",
    "        idx_i = 0\n",
    "        for id in range(len(N_in)):\n",
    "            idx = N_in[id]\n",
    "            diff = delta_change_inside_edges(size, x, idx, distance_matrix)\n",
    "            if diff > max_diff_i:\n",
    "                max_diff_i = diff\n",
    "                idx_i = idx\n",
    "                \n",
    "        if (max_diff_i > 0) or (max_diff_o > 0):        \n",
    "            # ruch zmieniający zbiór wierzchołków \n",
    "            if max_diff_o > max_diff_i:\n",
    "                ver1 = x[idx_o[0]]\n",
    "                ver2 = out[idx_o[1]]\n",
    "                x[idx_o[0]] = ver2\n",
    "                out[idx_o[1]] = ver1                \n",
    "                N_in = swap_edges(x)\n",
    "                N_out = swap_vertices_outside(x)\n",
    "\n",
    "            #ruch wewnątrztrasowy zamiana krawędzi\n",
    "            else:\n",
    "                a = x[idx_i[0]:idx_i[1]+1]\n",
    "                a = np.flip(a)\n",
    "                x[idx_i[0]:idx_i[1]+1] = a\n",
    "                N_in = swap_edges(x)\n",
    "                N_out = swap_vertices_outside(x)\n",
    "        else:\n",
    "            break\n",
    "            \n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "MIN = 100000\n",
    "MAX = 0\n",
    "SUM = 0\n",
    "T_MIN = 100000\n",
    "T_MAX = 0\n",
    "T_SUM = 0\n",
    "\n",
    "for i in range(100):\n",
    "    print(i)\n",
    "    x, out = random_path(100, 200)\n",
    "    start = time.time()\n",
    "    x = steepest_edge(100, x, out)\n",
    "    t = time.time() - start\n",
    "    len_x = path_length(x)\n",
    "    \n",
    "    if len_x > MAX:\n",
    "        MAX = len_x\n",
    "    if len_x < MIN:\n",
    "        MIN = len_x\n",
    "        T = x\n",
    "    SUM += len_x\n",
    "    \n",
    "    if t > T_MAX:\n",
    "        T_MAX = t\n",
    "    if t < T_MIN:\n",
    "        T_MIN = t\n",
    "    T_SUM += t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15920\n",
      "19339\n",
      "17321.31\n",
      "14.472309350967407\n",
      "19.466919660568237\n",
      "16.652854590415956\n"
     ]
    }
   ],
   "source": [
    "print(MIN)\n",
    "print(MAX)\n",
    "print(SUM/100)\n",
    "#time\n",
    "print(T_MIN)\n",
    "print(T_MAX)\n",
    "print(T_SUM/100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_plot(data, points):\n",
    "    f = plt.figure()\n",
    "    plt.plot(data[:, 0], data[:, 1], \"o\", linewidth=0, alpha=0.4)\n",
    "    plt.plot(data[points, 0], data[points, 1], \"o\", color='tab:blue',  linewidth=0, alpha=0.6)\n",
    "    plt.plot(data[points, 0], data[points, 1], \"--\", color=\"tab:cyan\", linewidth=1, alpha=2)\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"y\")\n",
    "    plt.title(\"Steepest - kroB200\")\n",
    "    plt.grid(False)\n",
    "    \n",
    "    plt.show()\n",
    "    f.savefig('steepestB.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "T = np.append(T, T[0])\n",
    "T\n",
    "print_plot(data, T)"
   ]
  },
  {
   "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": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}