TSP-MTZ-Gurobi.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "toc_visible": true
    },
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "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": "3.8.10"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zuOBhCFx9xbo"
      },
      "source": [
        "### 1. Importing packages"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rf1m6DHrzm1k"
      },
      "source": [
        "!pip install gurobipy"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "id": "zoBbiCaJ9PvV"
      },
      "source": [
        "import pandas as pd\n",
        "from scipy.spatial.distance import squareform, pdist\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZDfkAOEA974v"
      },
      "source": [
        "import gurobipy as gp\n",
        "from gurobipy import GRB"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S4O_7v0j-DYi"
      },
      "source": [
        "### 2. Loading dataset"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wZT-hDE6-AUm"
      },
      "source": [
        "# reading data and creating distance matrix\n",
        "def prepare_tsp_data(filename):\n",
        "    df = pd.read_csv(filename)\n",
        "    D = squareform(pdist(df))\n",
        "    return df, D"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "id": "P1kmxAk-9PvX"
      },
      "source": [
        "# plotting cities and tour\n",
        "def plot_tsp(df, tour=None, open_tour=False):\n",
        "    plt.figure(figsize=(10,10))\n",
        "    plt.scatter(df.x, df.y)\n",
        "    if tour:\n",
        "        for i, j in tour:\n",
        "            x1 = df.loc[i]['x']\n",
        "            x2 = df.loc[j]['x']\n",
        "            y1 = df.loc[i]['y']\n",
        "            y2 = df.loc[j]['y']\n",
        "            plt.text(df.loc[i]['x'], df.loc[i]['y'], df.loc[i]['id'])\n",
        "            plt.text(df.loc[j]['x'], df.loc[j]['y'], df.loc[j]['id'])\n",
        "            x = [x1, x2]\n",
        "            y = [y1, y2]\n",
        "            if j == 0:\n",
        "                if not open_tour:\n",
        "                    plt.plot(x, y, 'r')\n",
        "            else:\n",
        "                plt.plot(x, y, 'b')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NMMLLhWE9PvX"
      },
      "source": [
        "df, D = prepare_tsp_data('usa35.csv')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plot_tsp(df)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 592
        },
        "id": "AXloinTtBUGj",
        "outputId": "cff10170-2c44-46f0-c8e6-5f26b60b667f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gxaWvzhu-R1A"
      },
      "source": [
        "### 3. MTZ formulation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "N9sz9yDi9PvZ"
      },
      "source": [
        "# solving tsp\n",
        "def solve_tsp(df, D):\n",
        "    try:\n",
        "        N = df.shape[0]\n",
        "\n",
        "        # model\n",
        "        tsp_model = gp.Model('tsp')\n",
        "\n",
        "        # variables\n",
        "        x, u = {}, {}\n",
        "        for i in range(N):\n",
        "            u[i] = tsp_model.addVar(lb=0, ub=N-1, vtype=GRB.CONTINUOUS, name=f'u{i}')\n",
        "            for j in range(N):\n",
        "                x[i,j] = tsp_model.addVar(vtype=GRB.BINARY, name=f'x{i,j}')\n",
        "        \n",
        "        # objective\n",
        "        obj = gp.quicksum(x[i,j] * D[i,j] for j in range(N) for i in range(N))\n",
        "        tsp_model.setObjective(obj, GRB.MINIMIZE)\n",
        "        \n",
        "        # constraints\n",
        "        # no self-connection\n",
        "        for i in range(N):\n",
        "            tsp_model.addConstr(x[i,i] == 0)\n",
        "\n",
        "        # unique incoming edge\n",
        "        for j in range(N):\n",
        "            tsp_model.addConstr(gp.quicksum(x[i,j] for i in range(N)) == 1)\n",
        "\n",
        "        # unique outgoing edge\n",
        "        for i in range(N):\n",
        "            tsp_model.addConstr(gp.quicksum(x[i,j] for j in range(N)) == 1)\n",
        "\n",
        "        # preventing sub-tours\n",
        "        for i in range(N):\n",
        "            for j in range(N):\n",
        "                if j != 0:\n",
        "                    tsp_model.addConstr(u[j] >= u[i] + 1 - (2 * N) * (1 - x[i,j]))\n",
        "        \n",
        "        # optimizing model\n",
        "        tsp_model.optimize()\n",
        "\n",
        "        print('-----------------------------')\n",
        "        print(f'Min. Dist = {tsp_model.objVal}')\n",
        "        tour = [(i,j) for i in range(N) for j in range(N) if x[i,j].x == 1]\n",
        "        plot_tsp(df, tour)\n",
        "    except gp.GurobiError as e:\n",
        "        print(f'Error code {e.errno} : {e}')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3KvmZmNl-iw8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "ce344cf1-6547-4c8c-eaf6-f85f47f1d9fa"
      },
      "source": [
        "solve_tsp(df, D)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Restricted license - for non-production use only - expires 2023-10-25\n",
            "Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)\n",
            "Thread count: 1 physical cores, 2 logical processors, using up to 2 threads\n",
            "Optimize a model with 1295 rows, 1260 columns and 5987 nonzeros\n",
            "Model fingerprint: 0x2da8c234\n",
            "Variable types: 35 continuous, 1225 integer (1225 binary)\n",
            "Coefficient statistics:\n",
            "  Matrix range     [1e+00, 7e+01]\n",
            "  Objective range  [2e+02, 8e+03]\n",
            "  Bounds range     [1e+00, 3e+01]\n",
            "  RHS range        [1e+00, 7e+01]\n",
            "Presolve removed 69 rows and 36 columns\n",
            "Presolve time: 0.02s\n",
            "Presolved: 1226 rows, 1224 columns, 5814 nonzeros\n",
            "Variable types: 34 continuous, 1190 integer (1190 binary)\n",
            "Found heuristic solution: objective 94573.641349\n",
            "\n",
            "Root relaxation: objective 2.383162e+04, 111 iterations, 0.00 seconds (0.00 work units)\n",
            "\n",
            "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
            " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
            "\n",
            "     0     0 23831.6235    0   60 94573.6413 23831.6235  74.8%     -    0s\n",
            "H    0     0                    31552.791686 23831.6235  24.5%     -    0s\n",
            "     0     0 26114.1949    0   65 31552.7917 26114.1949  17.2%     -    0s\n",
            "     0     0 26114.1949    0   63 31552.7917 26114.1949  17.2%     -    0s\n",
            "     0     0 26384.6919    0   67 31552.7917 26384.6919  16.4%     -    0s\n",
            "     0     0 26384.6919    0   67 31552.7917 26384.6919  16.4%     -    0s\n",
            "     0     0 26384.6919    0   67 31552.7917 26384.6919  16.4%     -    0s\n",
            "H    0     0                    30368.409260 26384.6919  13.1%     -    0s\n",
            "     0     0 26384.6919    0   67 30368.4093 26384.6919  13.1%     -    0s\n",
            "     0     0 26384.6919    0   44 30368.4093 26384.6919  13.1%     -    0s\n",
            "     0     0 26384.6919    0   44 30368.4093 26384.6919  13.1%     -    0s\n",
            "     0     0 26384.6919    0   44 30368.4093 26384.6919  13.1%     -    0s\n",
            "H    0     0                    29540.359361 26496.1198  10.3%     -    0s\n",
            "     0     0 26496.1198    0   60 29540.3594 26496.1198  10.3%     -    0s\n",
            "     0     0 26496.1198    0   58 29540.3594 26496.1198  10.3%     -    0s\n",
            "     0     0 26496.1198    0   58 29540.3594 26496.1198  10.3%     -    0s\n",
            "     0     0 26496.1198    0   60 29540.3594 26496.1198  10.3%     -    0s\n",
            "     0     0 26496.1198    0   60 29540.3594 26496.1198  10.3%     -    0s\n",
            "     0     0 26496.1198    0   64 29540.3594 26496.1198  10.3%     -    0s\n",
            "     0     0 26496.1198    0   64 29540.3594 26496.1198  10.3%     -    0s\n",
            "     0     0 26496.1198    0   58 29540.3594 26496.1198  10.3%     -    0s\n",
            "     0     0 26496.1198    0   58 29540.3594 26496.1198  10.3%     -    0s\n",
            "H    0     0                    27973.311604 26580.5306  4.98%     -    0s\n",
            "     0     0 26580.5306    0   60 27973.3116 26580.5306  4.98%     -    0s\n",
            "     0     0 26580.5306    0   64 27973.3116 26580.5306  4.98%     -    0s\n",
            "     0     0 26580.5306    0   64 27973.3116 26580.5306  4.98%     -    0s\n",
            "     0     0 26580.5306    0   44 27973.3116 26580.5306  4.98%     -    0s\n",
            "     0     0 26580.5306    0   64 27973.3116 26580.5306  4.98%     -    0s\n",
            "     0     0 26580.5306    0   68 27973.3116 26580.5306  4.98%     -    0s\n",
            "     0     0 26629.7781    0   66 27973.3116 26629.7781  4.80%     -    0s\n",
            "     0     0 26651.7932    0   64 27973.3116 26651.7932  4.72%     -    0s\n",
            "     0     0 26651.7932    0   64 27973.3116 26651.7932  4.72%     -    0s\n",
            "     0     0 26651.7932    0   64 27973.3116 26651.7932  4.72%     -    0s\n",
            "     0     0 26651.7932    0   64 27973.3116 26651.7932  4.72%     -    0s\n",
            "     0     0 26651.7932    0   40 27973.3116 26651.7932  4.72%     -    0s\n",
            "     0     2 26712.4949    0   40 27973.3116 26712.4949  4.51%     -    0s\n",
            "H  104    63                    27840.241732 26728.7975  3.99%  10.7    1s\n",
            "*  159    86              16    27812.055428 26740.8793  3.85%  10.3    1s\n",
            "H  789   208                    27567.635723 26901.0323  2.42%  11.2    1s\n",
            "\n",
            "Cutting planes:\n",
            "  Learned: 24\n",
            "  Gomory: 12\n",
            "  Cover: 12\n",
            "  Implied bound: 85\n",
            "  MIR: 40\n",
            "  Inf proof: 23\n",
            "  RLT: 9\n",
            "  Relax-and-lift: 52\n",
            "\n",
            "Explored 2199 nodes (28529 simplex iterations) in 2.73 seconds (1.41 work units)\n",
            "Thread count was 2 (of 2 available processors)\n",
            "\n",
            "Solution count 8: 27567.6 27812.1 27840.2 ... 94573.6\n",
            "\n",
            "Optimal solution found (tolerance 1.00e-04)\n",
            "Best objective 2.756763572320e+04, best bound 2.756587925356e+04, gap 0.0064%\n",
            "-----------------------------\n",
            "Min. Dist = 27567.635723197694\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "Z2jPRpRm6uGC"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}