16.04. ЦЛП. Задача коммивояжера.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/NikolaiZolotykh/ScientificPython/blob/master/16.04.%20%D0%A6%D0%9B%D0%9F.%20%D0%97%D0%B0%D0%B4%D0%B0%D1%87%D0%B0%20%D0%BA%D0%BE%D0%BC%D0%BC%D0%B8%D0%B2%D0%BE%D1%8F%D0%B6%D0%B5%D1%80%D0%B0.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4O5Qmcr1fzvz"
      },
      "source": [
        "# Задача коммивояжера\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yV2hpaaEfzv2"
      },
      "outputs": [],
      "source": [
        "import pulp\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ABY9XS74fzv4"
      },
      "outputs": [],
      "source": [
        "n = 50 # n=200 около 10 мин\n",
        "np.random.seed(42)\n",
        "x = 1.5*np.random.rand(n)\n",
        "y = np.random.rand(n)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "o7mL2k80fzv4",
        "outputId": "62ccdb03-27e5-4c74-ad40-6869bb9751bd"
      },
      "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": [
        "plt.plot(x, y, '*', markerfacecolor = 'red', markeredgecolor = 'red')\n",
        "plt.axis('equal')\n",
        "pass"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ee-8nFAAfzv6"
      },
      "outputs": [],
      "source": [
        "xi, xj = np.meshgrid(x, x)\n",
        "yi, yj = np.meshgrid(y, y)\n",
        "dist = np.hypot(xi - xj, yi - yj)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eHxi-1wsfzv6"
      },
      "source": [
        "## Формулируем ЗЦЛП\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lfTEFdPyfzv6"
      },
      "outputs": [],
      "source": [
        "prob = pulp.LpProblem(\"Traveling Salesman Problem\", pulp.LpMinimize)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "q5VAKja8fzv6"
      },
      "outputs": [],
      "source": [
        "roads = pulp.LpVariable.dicts(\"Road\", (range(n), range(n)), 0, 1, pulp.LpInteger)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "aneZ5RGqfzv7",
        "outputId": "febaf9e4-ca1a-40bd-d138-c3bffe9db8f1"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Road_3_1"
            ]
          },
          "execution_count": 7,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "roads[3][1]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N3ACNJI8fzv7"
      },
      "source": [
        "В каждый город въезжаем ровно $1$ раз; из каждого города выезжаем ровно $1$ раз:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "q-5aPaHofzv7"
      },
      "outputs": [],
      "source": [
        "for i in range(n):\n",
        "    prob += pulp.lpSum([roads[i][j] for j in range(n)]) == 1\n",
        "for j in range(n):\n",
        "    prob += pulp.lpSum([roads[i][j] for i in range(n)]) == 1"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XafshSfufzv8"
      },
      "source": [
        "Из города в тот же город ехать нельзя:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "MBRjyacrfzv8"
      },
      "outputs": [],
      "source": [
        "for i in range(n):\n",
        "    prob += roads[i][i] == 0"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "OhTymp8Mfzv8"
      },
      "outputs": [],
      "source": [
        "prob += pulp.lpSum([dist[i][j]*roads[i][j] for i in range(n) for j in range(n)]), \"Objective Function\" "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zT_lt_g9fzv8"
      },
      "source": [
        "## Решаем задачу"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ttXwT8G1fzv9",
        "outputId": "9897448d-8605-4f57-e09f-943c55feabb3"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Status: Optimal\n"
          ]
        }
      ],
      "source": [
        "prob.solve()\n",
        "print(\"Status:\", pulp.LpStatus[prob.status])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "26qJ-kiofzv9"
      },
      "outputs": [],
      "source": [
        "def findPath(roads):\n",
        "    path = [0]*n\n",
        "    for i in range(n):\n",
        "        for j in range(n):\n",
        "            if pulp.value(roads[i][j]) == 1:\n",
        "                path[i] = j\n",
        "    return path            "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "IXuhou53fzv9",
        "outputId": "53dae67e-d5be-42a7-e3ea-a20706c1b079"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[19, 43, 38, 30, 31, 26, 29, 33, 48, 35, 32, 34, 25, 14, 13, 46, 22, 20, 27, 5, 17, 49, 16, 0, 41, 12, 44, 18, 45, 6, 3, 4, 10, 7, 11, 9, 23, 42, 2, 47, 21, 24, 37, 1, 36, 28, 15, 39, 8, 40]\n"
          ]
        }
      ],
      "source": [
        "path = findPath(roads)\n",
        "print(path)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "JotYaauffzv9",
        "outputId": "5ab55f70-11c7-41f2-c00f-4ec86620aa8f"
      },
      "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": [
        "plt.plot(x, y, '*', markerfacecolor = 'red', markeredgecolor = 'red')\n",
        "plt.axis('equal')\n",
        "for i in range(n):\n",
        "    plt.plot((x[i], x[path[i]]), (y[i], y[path[i]]), '--b')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WWxWFXVDfzv-"
      },
      "source": [
        "## Динамическое исключение контуров"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "24wh5zZvfzv-"
      },
      "outputs": [],
      "source": [
        "def findTours(path):\n",
        "    ipath = [True]*len(path)\n",
        "    tours = []\n",
        "    while True in ipath:\n",
        "        i0 = ipath.index(True)\n",
        "        ipath[i0] = False\n",
        "        tour = [i0]\n",
        "        i = path[i0]\n",
        "        while i != i0:\n",
        "            tour.append(i)\n",
        "            ipath[i] = False\n",
        "            i = path[i]\n",
        "        tours.append(tour)\n",
        "    return tours   "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xKjx76IPfzv-",
        "outputId": "582eeee0-25ba-4068-d0f0-9614a8bcab35"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[[0, 19, 5, 26, 44, 36, 23],\n",
              " [1, 43],\n",
              " [2, 38],\n",
              " [3, 30],\n",
              " [4, 31],\n",
              " [6, 29],\n",
              " [7, 33],\n",
              " [8, 48],\n",
              " [9, 35],\n",
              " [10, 32],\n",
              " [11, 34],\n",
              " [12, 25],\n",
              " [13, 14],\n",
              " [15, 46],\n",
              " [16, 22],\n",
              " [17, 20],\n",
              " [18, 27],\n",
              " [21, 49, 40],\n",
              " [24, 41],\n",
              " [28, 45],\n",
              " [37, 42],\n",
              " [39, 47]]"
            ]
          },
          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "findTours(path)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zcwFonxQfzv_",
        "outputId": "e47a73b5-52ff-40fe-d76f-cf88012fc925"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Iteration No 1  Number of tours =  22\n",
            "Iteration No 2  Number of tours =  7\n",
            "Iteration No 3  Number of tours =  5\n",
            "Iteration No 4  Number of tours =  7\n",
            "Iteration No 5  Number of tours =  4\n",
            "Iteration No 6  Number of tours =  3\n",
            "Iteration No 7  Number of tours =  2\n",
            "Iteration No 8  Number of tours =  2\n",
            "Iteration No 9  Number of tours =  1\n"
          ]
        }
      ],
      "source": [
        "itCount = 0\n",
        "while True:\n",
        "    itCount += 1\n",
        "    print('Iteration No', itCount, end = '')\n",
        "    result = prob.solve()\n",
        "    if result != 1:\n",
        "        print('\\nSomething Wrong!')\n",
        "        break\n",
        "    path = findPath(roads) \n",
        "    tours = findTours(path)\n",
        "    print('  Number of tours = ', len(tours))\n",
        "    if len(tours) == 1:\n",
        "        break\n",
        "    for tour in tours:\n",
        "        prob += pulp.lpSum([roads[i][j] for i in tour for j in tour]) <= len(tour) - 1    "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PvFPZyCpfzv_",
        "outputId": "74aa71eb-8bc4-4d77-e3a7-beb5128222f1"
      },
      "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": [
        "plt.plot(x, y, '*', markerfacecolor = 'red', markeredgecolor = 'red')\n",
        "plt.axis('equal')\n",
        "for i in range(n):\n",
        "    plt.plot((x[i], x[path[i]]), (y[i], y[path[i]]), '--b')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XOQ9GXgMfzv_",
        "outputId": "d57a304f-ff1b-46e2-c207-5cd327179791"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Total Distanse =  7.287766432262201\n"
          ]
        }
      ],
      "source": [
        "print(\"Total Distanse = \", pulp.value(prob.objective))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eC0FWS6Mfzv_"
      },
      "source": [
        "## Условия Таккера\n",
        "\n",
        "Вместо динамического исключения контуров\n",
        "\n",
        "Работает медленно (при `n=40` около 15 минут)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "id": "hw0IL0CqfzwA"
      },
      "outputs": [],
      "source": [
        "beats = pulp.LpVariable.dicts(\"Beat\", range(1, n))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KCO3MwzgfzwA"
      },
      "outputs": [],
      "source": [
        "for i in range(1, n):\n",
        "    for j in range(1, n):\n",
        "        if i != j:\n",
        "            prob += beats[i] - beats[j] + n*roads[i][j] <= n - 1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "id": "_J_zMEhffzwA"
      },
      "outputs": [],
      "source": [
        "prob.writeLP(\"TSP.lp\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0pYPyfOsfzwA",
        "outputId": "fb06bd3d-2097-4cde-fbe5-07f0d44cadf1"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "execution_count": 20,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "prob.solve()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "UNo3YQJufzwB",
        "outputId": "309bf6ae-895f-4c64-a292-cb301e85c41a"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Status: Optimal\n"
          ]
        }
      ],
      "source": [
        "print(\"Status:\", pulp.LpStatus[prob.status])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xUsZpp9GfzwB",
        "outputId": "82333038-016b-41fe-dbd6-211da5e9b12c"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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JyWEZiTOAk4F9zVidjsfMeWU6EJ7BXR2HcOWsTVi0khhMjQuHgRabxavXv3O5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\neXF3zrkE8uLunHMJ9P9fl/Lj9h6fxgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0xb8b0e10>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(x, y, '*', markerfacecolor = 'red', markeredgecolor = 'red')\n",
        "plt.axis('equal')\n",
        "for i in range(n):\n",
        "    for j in range(n):\n",
        "        if pulp.value(roads[i][j]) == 1:\n",
        "            plt.plot((x[i], x[j]), (y[i], y[j]), '--b')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "St7gxCfTfzwB",
        "outputId": "e9bc659d-4dbf-4d0d-97ae-393832e392a2"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Total Distanse =  6.36682378831\n"
          ]
        }
      ],
      "source": [
        "print(\"Total Distanse = \", pulp.value(prob.objective))"
      ]
    }
  ],
  "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": "3.7.3"
    },
    "colab": {
      "provenance": [],
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}