TSP Miller–Tucker–Zemlin (MTZ) formulation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a8e032e4",
   "metadata": {},
   "source": [
    "##  TSP Miller–Tucker–Zemlin (MTZ) formulation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cb7c75e",
   "metadata": {},
   "source": [
    "##### Keywords:  TSP, MTZ, Miller–Tucker–Zemlin, Subtours, Linear Programming, Cplex, Python, Networkx, Docplex"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "336e950c",
   "metadata": {},
   "source": [
    "$ \\text{Variables} $\n",
    "\n",
    "$x_{ij}={\\begin{cases}1&{\\text{the path goes from city }}i{\\text{ to city }}j\\\\0&{\\text{otherwise}}\\end{cases}}$\n",
    "\n",
    "$u_{i}=\\text{keeps track of the order in which the cities are visited, counting from city 1 the interpretation is that $u_{i}$ < $u_{j}$ implies city i}\\\\ \\quad ~~~~\\text{is visited before city j}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e73bfe6",
   "metadata": {},
   "source": [
    "\\begin{equation*}\n",
    "\\begin{aligned}\n",
    "& \\underset{}{\\text{Minimize}}\n",
    "& & \\sum_{i=1}^{n} \\sum_{j=1, j\\neq i}^{n} c_{ij} x_{ij} \\\\\n",
    "& \\text{Subject to}\n",
    "& & \\sum_{j=1, j\\neq i}^{n} x_{ij} = 1, \\quad i = 1,\\ldots,n, \\\\\n",
    "& \n",
    "& & \\sum_{i=1, i\\neq j}^{n} x_{ij} = 1, \\quad j = 1,\\ldots,n, \\\\\n",
    "& \n",
    "& & u_{i} - u_{j} + n x_{ij} \\leq n - 1, \\quad 2 \\leq i \\neq j \\leq n.\\\\\n",
    "&\n",
    "& & x_{ij} \\in \\{0,1\\}, \\quad i,j = 1,\\ldots,n, \\, i\\neq j, \\\\\n",
    "&\n",
    "& & u_{i} \\in \\mathbf {Z}, \\quad i=2,\\ldots ,n.\n",
    "\\end{aligned}\n",
    "\\end{equation*}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e18fd45",
   "metadata": {},
   "source": [
    "#### Import Library and Model Enviroment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "be618bc2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from docplex.mp.model import Model\n",
    "import networkx as nx   \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "mdl=Model('MTZ')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6388020",
   "metadata": {},
   "source": [
    "#### Function to Visualize the Traveling Salesman Problem (TSP) Graphically"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8f526ad6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def graphic(x, d, N):\n",
    "    \"\"\"\n",
    "    Function to visualize the Traveling Salesman Problem (TSP) graphically.\n",
    "\n",
    "    Parameters:\n",
    "        x (numpy.ndarray): Distance matrix representing the pairwise distances between cities.\n",
    "        d (list): List of cities with their corresponding distances.\n",
    "        N (range): Range object representing the number of cities.\n",
    "\n",
    "    Returns:\n",
    "        None\n",
    "    \"\"\"\n",
    "\n",
    "    edges = []\n",
    "    for i in N:\n",
    "        for j in N:\n",
    "            if i != j and x[i, j] > 0.5:  # This is a tolerance value, it can be adjusted as needed\n",
    "                edges.append((i, j, d[i - 1][j - 1]))\n",
    "\n",
    "    G = nx.Graph()\n",
    "    for edge in edges:\n",
    "        G.add_edge(edge[0], edge[1], weight=edge[2])\n",
    "\n",
    "    plt.figure(figsize=(10, 10))\n",
    "    pos = nx.spring_layout(G)\n",
    "    nx.draw(G, pos, with_labels=True)\n",
    "    labels = nx.get_edge_attributes(G, 'weight')\n",
    "    nx.draw_networkx_edge_labels(G, pos, edge_labels=labels)\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a83a6ec2",
   "metadata": {},
   "source": [
    "#### Create the Matrix of Distances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b6db83f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "C = np.random.randint(1, 100, size=(50, 50))\n",
    "# A_i,i = 0\n",
    "np.fill_diagonal(C, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8595a1ea",
   "metadata": {},
   "source": [
    "#### Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c91a8114",
   "metadata": {},
   "outputs": [],
   "source": [
    "n=len(C)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa09c3e8",
   "metadata": {},
   "source": [
    "#### Sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0d76d9b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "N=[i+1 for i in range(n)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "105f7366",
   "metadata": {},
   "source": [
    "#### Index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0502fcb2",
   "metadata": {},
   "outputs": [],
   "source": [
    "Ind={(i,j) for i in N for j in N if i!=j}\n",
    "Ind2={(i) for i in N if i!=1}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d1c5b4d",
   "metadata": {},
   "source": [
    "#### Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "36faf360",
   "metadata": {},
   "outputs": [],
   "source": [
    "x=mdl.binary_var_dict(Ind, name='x')\n",
    "u=mdl.integer_var_dict(Ind2, name='u')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d3567ae",
   "metadata": {},
   "source": [
    "#### Mathematical Model of Travelling Salesman Problem MTZ (TSP MTZ)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00c83dfd",
   "metadata": {},
   "source": [
    "#### Objective Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c08114b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "mdl.minimize(mdl.sum(x[i,j]*C[i-1][j-1] for i in N for j in N if i!=j))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e1dca60",
   "metadata": {},
   "source": [
    "#### Subject to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ae1417c2",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "for i in N:\n",
    "    mdl.add_constraint(mdl.sum(x[i,j] for j in N if i!=j)==1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f9cd0a5b",
   "metadata": {},
   "outputs": [],
   "source": [
    "for j in N:\n",
    "    mdl.add_constraint(mdl.sum(x[i,j] for i in N if i!=j)==1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "deed687d",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(2,n+1):\n",
    "    for j in range(2,n+1):\n",
    "        if i!=j:\n",
    "            if i!=1:\n",
    "                mdl.add_constraint(u[i]-u[j]+(n-1)*x[i,j]<=(n-2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7c27ccc",
   "metadata": {},
   "source": [
    "#### Solve the Traveling Salesman Problem MTZ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "fb989c70",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Version identifier: 12.10.0.0 | 2019-11-26 | 843d4de2ae\n",
      "CPXPARAM_Read_DataCheck                          1\n",
      "CPXPARAM_RandomSeed                              201903125\n",
      "Tried aggregator 1 time.\n",
      "Reduced MIP has 2452 rows, 2499 columns, and 11956 nonzeros.\n",
      "Reduced MIP has 2450 binaries, 49 generals, 0 SOSs, and 0 indicators.\n",
      "Presolve time = 0.00 sec. (5.66 ticks)\n",
      "Probing time = 0.00 sec. (3.29 ticks)\n",
      "Tried aggregator 1 time.\n",
      "Detecting symmetries...\n",
      "Reduced MIP has 2452 rows, 2499 columns, and 11956 nonzeros.\n",
      "Reduced MIP has 2450 binaries, 49 generals, 0 SOSs, and 0 indicators.\n",
      "Presolve time = 0.02 sec. (7.76 ticks)\n",
      "Probing time = 0.02 sec. (3.29 ticks)\n",
      "Clique table members: 1219.\n",
      "MIP emphasis: balance optimality and feasibility.\n",
      "MIP search method: dynamic search.\n",
      "Parallel mode: deterministic, using up to 8 threads.\n",
      "Root relaxation solution time = 0.02 sec. (8.38 ticks)\n",
      "\n",
      "        Nodes                                         Cuts/\n",
      "   Node  Left     Objective  IInf  Best Integer    Best Bound    ItCnt     Gap\n",
      "\n",
      "      0     0      157.1429    32                    157.1429      165         \n",
      "      0     0      158.0306    32                    Cuts: 22      209         \n",
      "      0     0      158.6667    32                    Cuts: 12      229         \n",
      "      0     0      158.6667    32                    Cuts: 23      250         \n",
      "      0     0      158.6667    32                     Cuts: 4      255         \n",
      "      0     0      159.0000    32                 ZeroHalf: 2      289         \n",
      "Detecting symmetries...\n",
      "*     0+    0                          160.0000      159.0000             0.62%\n",
      "      0     0        cutoff            160.0000      160.0000      334    0.00%\n",
      "Elapsed time = 0.41 sec. (208.34 ticks, tree = 0.01 MB, solutions = 1)\n",
      "\n",
      "Implied bound cuts applied:  13\n",
      "Mixed integer rounding cuts applied:  8\n",
      "Zero-half cuts applied:  8\n",
      "Multi commodity flow cuts applied:  6\n",
      "Gomory fractional cuts applied:  2\n",
      "\n",
      "Root node processing (before b&c):\n",
      "  Real time             =    0.41 sec. (208.47 ticks)\n",
      "Parallel b&c, 8 threads:\n",
      "  Real time             =    0.00 sec. (0.00 ticks)\n",
      "  Sync time (average)   =    0.00 sec.\n",
      "  Wait time (average)   =    0.00 sec.\n",
      "                          ------------\n",
      "Total (root+branch&cut) =    0.41 sec. (208.47 ticks)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Objective Value: 160\n"
     ]
    }
   ],
   "source": [
    "solution = mdl.solve(log_output=True) # Solve the TSP problem\n",
    "#print(mdl.export_to_string()) # Export the model to String\n",
    "valor_objetivo = mdl.solution.get_objective_value() # Get the objective value of the final solution\n",
    "x=solution.get_value_dict(x, keep_zeros=True, precision=1) # Update the 'x' dictionary with zero-valued variables\n",
    "graphic(x,C,N) # Visualize the final solution\n",
    "print(\"Objective Value:\",valor_objetivo) # Print the objective value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c421691e",
   "metadata": {},
   "source": [
    "#### Literature \n",
    "C. E. Miller, A. W. Tucker, and R. A. Zemlin. 1960. Integer Programming Formulation of Traveling Salesman Problems. J. ACM 7, 4 (Oct. 1960), 326–329. https://doi.org/10.1145/321043.321046\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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