TSP Dantzig–Fulkerson–Johnson (DFJ) formulation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3ce2420e",
   "metadata": {},
   "source": [
    "## TSP Dantzig–Fulkerson–Johnson (DFJ) formulation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffd96bd5",
   "metadata": {},
   "source": [
    "##### Keywords:  TSP, DFJ, Dantzig–Fulkerson–Johnson, Subtours, Linear Programming, Cplex, Python, Networkx, Docplex"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61bc44ba",
   "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}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1a74e91",
   "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",
    "& & \\sum_{i \\in Q} \\sum_{j\\neq i, j \\in Q,} x_{ij} \\leq |Q| - 1, \\quad \\forall Q \\subset{1,...,n},|Q| \\ge 2 \\\\\n",
    "&\n",
    "& & x_{ij} \\in \\{0,1\\}, \\quad i,j = 1,\\ldots,n, \\, i\\neq j, \\\\\n",
    "\\end{aligned}\n",
    "\\end{equation*}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ece0ac6",
   "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('DFJ')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ece8069",
   "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": "7135a2ff",
   "metadata": {},
   "source": [
    "#### Create the Matrix of Distances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b6db83f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Create a Random Matrix\n",
    "C = np.random.randint(1, 100, size=(50, 50))\n",
    "# A_i,i = 0\n",
    "np.fill_diagonal(C, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46da9c19",
   "metadata": {},
   "source": [
    "#### Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c91a8114",
   "metadata": {},
   "outputs": [],
   "source": [
    "Nodes=len(C)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ebf253d",
   "metadata": {},
   "source": [
    "#### Sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0d76d9b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "N=[i+1 for i in range(Nodes)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9024532",
   "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}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b128766",
   "metadata": {},
   "source": [
    "#### Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "36faf360",
   "metadata": {},
   "outputs": [],
   "source": [
    "x=mdl.binary_var_dict(Ind, name='x')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fbfcf5f",
   "metadata": {},
   "source": [
    "#### Mathematical Model of Traveling Salesman Problem DFJ (TSP DJF)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba726630",
   "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": "b05e7330",
   "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": "677fe055",
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_subtours(sol):\n",
    "    \"\"\"\n",
    "    Function to find subtours in a solution of the Traveling Salesman Problem (TSP).\n",
    "\n",
    "    Parameters:\n",
    "        sol (dict): Solution dictionary representing the TSP solution. The keys are tuples (i, j) representing edges,\n",
    "                    and the values are binary variables indicating if the edge is selected in the solution.\n",
    "    Returns:\n",
    "        subtours (list): List of subtours found in the solution.\n",
    "    \"\"\"\n",
    "\n",
    "    subtours = []  # List to store subtours\n",
    "    remaining_nodes = list(range(1, len(sol) + 1))  # List of remaining nodes to be visited\n",
    "\n",
    "    while len(remaining_nodes) > 0:\n",
    "        subtour = []  # List to store a subtour\n",
    "        subtours.append(subtour)  # Add the subtour to the list of subtours\n",
    "\n",
    "        start = remaining_nodes[0]  # Start the subtour from the first remaining node\n",
    "\n",
    "        while True:\n",
    "            subtour.append(start)  # Add the current node to the subtour\n",
    "\n",
    "            if start in remaining_nodes:\n",
    "                remaining_nodes.remove(start)  # Remove the visited node from the remaining nodes\n",
    "\n",
    "            next_node = next((j for (i, j), value in sol.items() if i == start and value > 0.5), None)\n",
    "\n",
    "            # Find the next node in the solution that is connected to the current node and has not been visited yet\n",
    "            # The value 0.5 is used as a threshold to consider an edge selected in the solution\n",
    "\n",
    "            if next_node is None or next_node not in remaining_nodes:\n",
    "                break  # If there is no next node or the next node has already been visited, end the subtour\n",
    "\n",
    "            start = next_node  # Move to the next node in the subtour\n",
    "\n",
    "    return subtours"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a8a4c3a",
   "metadata": {},
   "source": [
    "#### Solve the Treveling Salesman Problem DFJ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "fb989c70",
   "metadata": {
    "scrolled": true
   },
   "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",
      "Found incumbent of value 2501.000000 after 0.00 sec. (0.18 ticks)\n",
      "Found incumbent of value 319.000000 after 0.00 sec. (0.25 ticks)\n",
      "Tried aggregator 1 time.\n",
      "Reduced MIP has 100 rows, 2450 columns, and 4900 nonzeros.\n",
      "Reduced MIP has 2450 binaries, 0 generals, 0 SOSs, and 0 indicators.\n",
      "Presolve time = 0.02 sec. (3.13 ticks)\n",
      "Tried aggregator 1 time.\n",
      "Detecting symmetries...\n",
      "Reduced MIP has 100 rows, 2450 columns, and 4900 nonzeros.\n",
      "Reduced MIP has 2450 binaries, 0 generals, 0 SOSs, and 0 indicators.\n",
      "Presolve time = 0.00 sec. (3.61 ticks)\n",
      "Probing time = 0.00 sec. (2.93 ticks)\n",
      "Clique table members: 100.\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 = 0.00 sec. (1.36 ticks)\n",
      "\n",
      "        Nodes                                         Cuts/\n",
      "   Node  Left     Objective  IInf  Best Integer    Best Bound    ItCnt     Gap\n",
      "\n",
      "*     0+    0                          319.0000        0.0000           100.00%\n",
      "*     0+    0                          304.0000        0.0000           100.00%\n",
      "*     0+    0                          251.0000        0.0000           100.00%\n",
      "*     0     0      integral     0      156.0000      156.0000       37    0.00%\n",
      "Elapsed time = 0.08 sec. (14.80 ticks, tree = 0.00 MB, solutions = 4)\n",
      "\n",
      "Root node processing (before b&c):\n",
      "  Real time             =    0.09 sec. (14.94 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) =    0.09 sec. (14.94 ticks)\n",
      "The subtours are: [[1, 28, 23, 21, 47, 33, 24, 14, 4, 2, 37, 3, 25, 49, 19, 8, 50, 15, 27, 41, 20, 48, 10, 42, 32, 7, 31, 46, 45, 12, 17, 30, 44, 36, 39, 16, 26, 38, 11, 34, 29, 40, 18, 22, 43, 13, 5], [6, 9, 35]]\n",
      "Version identifier: 12.10.0.0 | 2019-11-26 | 843d4de2ae\n",
      "CPXPARAM_Read_DataCheck                          1\n",
      "CPXPARAM_RandomSeed                              201903125\n",
      "4 of 5 MIP starts provided solutions.\n",
      "MIP start 'm3' defined initial solution with objective 251.0000.\n",
      "Retaining values of one MIP start for possible repair.\n",
      "Tried aggregator 1 time.\n",
      "Reduced MIP has 102 rows, 2450 columns, and 7068 nonzeros.\n",
      "Reduced MIP has 2450 binaries, 0 generals, 0 SOSs, and 0 indicators.\n",
      "Presolve time = 0.02 sec. (4.60 ticks)\n",
      "Tried aggregator 1 time.\n",
      "Detecting symmetries...\n",
      "Reduced MIP has 102 rows, 2450 columns, and 7068 nonzeros.\n",
      "Reduced MIP has 2450 binaries, 0 generals, 0 SOSs, and 0 indicators.\n",
      "Presolve time = 0.00 sec. (5.20 ticks)\n",
      "Probing time = 0.00 sec. (2.86 ticks)\n",
      "Clique table members: 100.\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 = 0.00 sec. (1.51 ticks)\n",
      "\n",
      "        Nodes                                         Cuts/\n",
      "   Node  Left     Objective  IInf  Best Integer    Best Bound    ItCnt     Gap\n",
      "\n",
      "*     0+    0                          251.0000        0.0000           100.00%\n",
      "*     0+    0                          248.0000        0.0000           100.00%\n",
      "*     0+    0                          241.0000        0.0000           100.00%\n",
      "*     0     0      integral     0      156.0000      156.0000       38    0.00%\n",
      "Elapsed time = 0.06 sec. (19.73 ticks, tree = 0.00 MB, solutions = 7)\n",
      "\n",
      "Root node processing (before b&c):\n",
      "  Real time             =    0.06 sec. (19.92 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) =    0.06 sec. (19.92 ticks)\n",
      "The subtours are: [[1, 28, 23, 4, 2, 37, 42, 32, 7], [3, 25, 49, 19, 8, 50, 15, 35, 6, 9, 14, 31, 46, 45, 12, 17, 30, 44, 24, 21, 47, 33, 27, 41, 20, 48, 10, 36, 39, 16, 26, 38, 11, 34, 29, 40, 18, 22, 43, 13, 5]]\n",
      "Version identifier: 12.10.0.0 | 2019-11-26 | 843d4de2ae\n",
      "CPXPARAM_Read_DataCheck                          1\n",
      "CPXPARAM_RandomSeed                              201903125\n",
      "5 of 7 MIP starts provided solutions.\n",
      "MIP start 'm6' defined initial solution with objective 241.0000.\n",
      "Retaining values of one MIP start for possible repair.\n",
      "Tried aggregator 1 time.\n",
      "Reduced MIP has 104 rows, 2450 columns, and 8780 nonzeros.\n",
      "Reduced MIP has 2450 binaries, 0 generals, 0 SOSs, and 0 indicators.\n",
      "Presolve time = 0.02 sec. (5.20 ticks)\n",
      "Tried aggregator 1 time.\n",
      "Detecting symmetries...\n",
      "Reduced MIP has 104 rows, 2450 columns, and 8780 nonzeros.\n",
      "Reduced MIP has 2450 binaries, 0 generals, 0 SOSs, and 0 indicators.\n",
      "Presolve time = 0.00 sec. (5.89 ticks)\n",
      "Probing time = 0.00 sec. (2.86 ticks)\n",
      "Clique table members: 100.\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. (1.70 ticks)\n",
      "\n",
      "        Nodes                                         Cuts/\n",
      "   Node  Left     Objective  IInf  Best Integer    Best Bound    ItCnt     Gap\n",
      "\n",
      "*     0+    0                          241.0000        0.0000           100.00%\n",
      "*     0+    0                          235.0000        0.0000           100.00%\n",
      "*     0+    0                          231.0000        0.0000           100.00%\n",
      "      0     0      156.0000    14      231.0000      156.0000       37   32.47%\n",
      "*     0+    0                          157.0000      156.0000             0.64%\n",
      "*     0+    0                          156.0000      156.0000             0.00%\n",
      "      0     0        cutoff            156.0000      156.0000       38    0.00%\n",
      "Elapsed time = 0.06 sec. (26.09 ticks, tree = 0.01 MB, solutions = 9)\n",
      "\n",
      "Root node processing (before b&c):\n",
      "  Real time             =    0.08 sec. (26.31 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) =    0.08 sec. (26.31 ticks)\n",
      "The subtours are: [[1, 28, 23, 11, 34, 29, 40, 18, 22, 43, 13, 5], [2, 37, 3, 25, 49, 19, 8, 50, 15, 35, 6, 9, 14, 4], [7, 31, 46, 45, 12, 17, 30, 44, 24, 21, 47, 33, 27, 41, 20, 48, 10, 42, 32], [16, 26, 38, 36, 39]]\n",
      "Version identifier: 12.10.0.0 | 2019-11-26 | 843d4de2ae\n",
      "CPXPARAM_Read_DataCheck                          1\n",
      "CPXPARAM_RandomSeed                              201903125\n",
      "7 of 9 MIP starts provided solutions.\n",
      "MIP start 'm8' defined initial solution with objective 157.0000.\n",
      "Retaining values of one MIP start for possible repair.\n",
      "Tried aggregator 1 time.\n",
      "Reduced MIP has 108 rows, 2450 columns, and 9456 nonzeros.\n",
      "Reduced MIP has 2450 binaries, 0 generals, 0 SOSs, and 0 indicators.\n",
      "Presolve time = 0.02 sec. (5.17 ticks)\n",
      "Tried aggregator 1 time.\n",
      "Detecting symmetries...\n",
      "Reduced MIP has 108 rows, 2450 columns, and 9456 nonzeros.\n",
      "Reduced MIP has 2450 binaries, 0 generals, 0 SOSs, and 0 indicators.\n",
      "Presolve time = 0.00 sec. (5.88 ticks)\n",
      "Probing time = 0.00 sec. (2.87 ticks)\n",
      "Clique table members: 100.\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. (2.34 ticks)\n",
      "\n",
      "        Nodes                                         Cuts/\n",
      "   Node  Left     Objective  IInf  Best Integer    Best Bound    ItCnt     Gap\n",
      "\n",
      "*     0+    0                          157.0000        0.0000           100.00%\n",
      "      0     0      156.6000    29      157.0000      156.6000       52    0.25%\n",
      "      0     0        cutoff            157.0000      156.6000       52    0.25%\n",
      "Elapsed time = 0.06 sec. (24.74 ticks, tree = 0.01 MB, solutions = 7)\n",
      "\n",
      "Root node processing (before b&c):\n",
      "  Real time             =    0.06 sec. (24.93 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) =    0.06 sec. (24.93 ticks)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The subtours are: [[1, 28, 23, 4, 2, 50, 15, 35, 6, 9, 14, 31, 46, 45, 12, 17, 30, 44, 24, 21, 47, 33, 27, 41, 20, 48, 10, 36, 39, 16, 26, 38, 11, 34, 29, 40, 18, 22, 43, 13, 5, 3, 25, 49, 19, 8, 37, 42, 32, 7]]\n",
      "solution for: modelo\n",
      "objective: 157\n",
      "x_25_49=1\n",
      "x_24_21=1\n",
      "x_28_23=1\n",
      "x_37_42=1\n",
      "x_17_30=1\n",
      "x_45_12=1\n",
      "x_6_9=1\n",
      "x_43_13=1\n",
      "x_13_5=1\n",
      "x_41_20=1\n",
      "x_39_16=1\n",
      "x_47_33=1\n",
      "x_32_7=1\n",
      "x_5_3=1\n",
      "x_14_31=1\n",
      "x_12_17=1\n",
      "x_19_8=1\n",
      "x_15_35=1\n",
      "x_49_19=1\n",
      "x_33_27=1\n",
      "x_3_25=1\n",
      "x_40_18=1\n",
      "x_9_14=1\n",
      "x_26_38=1\n",
      "x_7_1=1\n",
      "x_4_2=1\n",
      "x_23_4=1\n",
      "x_27_41=1\n",
      "x_35_6=1\n",
      "x_1_28=1\n",
      "x_10_36=1\n",
      "x_18_22=1\n",
      "x_31_46=1\n",
      "x_20_48=1\n",
      "x_36_39=1\n",
      "x_29_40=1\n",
      "x_16_26=1\n",
      "x_2_50=1\n",
      "x_50_15=1\n",
      "x_38_11=1\n",
      "x_46_45=1\n",
      "x_42_32=1\n",
      "x_48_10=1\n",
      "x_11_34=1\n",
      "x_8_37=1\n",
      "x_44_24=1\n",
      "x_21_47=1\n",
      "x_34_29=1\n",
      "x_22_43=1\n",
      "x_30_44=1\n",
      "\n",
      "Version identifier: 12.10.0.0 | 2019-11-26 | 843d4de2ae\n",
      "CPXPARAM_Read_DataCheck                          1\n",
      "CPXPARAM_RandomSeed                              201903125\n",
      "7 of 7 MIP starts provided solutions.\n",
      "MIP start 'm1' defined initial solution with objective 157.0000.\n",
      "Tried aggregator 1 time.\n",
      "Reduced MIP has 108 rows, 2450 columns, and 9456 nonzeros.\n",
      "Reduced MIP has 2450 binaries, 0 generals, 0 SOSs, and 0 indicators.\n",
      "Presolve time = 0.02 sec. (5.17 ticks)\n",
      "Tried aggregator 1 time.\n",
      "Detecting symmetries...\n",
      "Reduced MIP has 108 rows, 2450 columns, and 9456 nonzeros.\n",
      "Reduced MIP has 2450 binaries, 0 generals, 0 SOSs, and 0 indicators.\n",
      "Presolve time = 0.00 sec. (5.88 ticks)\n",
      "Probing time = 0.00 sec. (2.87 ticks)\n",
      "Clique table members: 100.\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. (2.34 ticks)\n",
      "\n",
      "        Nodes                                         Cuts/\n",
      "   Node  Left     Objective  IInf  Best Integer    Best Bound    ItCnt     Gap\n",
      "\n",
      "*     0+    0                          157.0000        0.0000           100.00%\n",
      "      0     0      156.6000    29      157.0000      156.6000       52    0.25%\n",
      "      0     0        cutoff            157.0000      156.6000       52    0.25%\n",
      "Elapsed time = 0.06 sec. (24.11 ticks, tree = 0.01 MB, solutions = 7)\n",
      "\n",
      "Root node processing (before b&c):\n",
      "  Real time             =    0.06 sec. (24.30 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) =    0.06 sec. (24.30 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: 157\n"
     ]
    }
   ],
   "source": [
    "while True:\n",
    "    solution = mdl.solve(log_output=True)  # Solve the TSP problem\n",
    "    if solution is None:\n",
    "        print(\"No solution found\")  # Print a message if no solution is found\n",
    "        break\n",
    "    \n",
    "    sol = solution.get_value_dict(x, keep_zeros=False)  # Get the solution as a dictionary\n",
    "    subtours = find_subtours(sol)  # Find subtours in the solution\n",
    "    print(\"The subtours are:\", subtours)  # Print the subtours\n",
    "    \n",
    "    if len(subtours) > 1:  # If there are more than one subtour\n",
    "        for subtour in subtours:\n",
    "            if len(subtour) < Nodes:  # If the subtour is not the full tour\n",
    "                mdl.add_constraint(mdl.sum(x[i, j] for i in subtour for j in subtour if i != j) <= len(subtour) - 1)\n",
    "                # Add a constraint to eliminate the subtour by limiting the total number of edges within the subtour\n",
    "    else:\n",
    "        break  # Break the loop if there is only one subtour or no subtour\n",
    "    \n",
    "print(solution)  # Print the final solution\n",
    "\n",
    "solution = mdl.solve(log_output=True)  # Solve the TSP problem again with the final solution\n",
    "objective_value = 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",
    "\n",
    "graphic(x, C, N)  # Visualize the final solution\n",
    "\n",
    "print(\"Objective Value:\", objective_value)  # Print the objective value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a80f44f",
   "metadata": {},
   "source": [
    "#### Literature\n",
    "\n",
    "Dantzig, G., Fulkerson, R., & Johnson, S. (1954). Solution of a Large-Scale Traveling-Salesman Problem. Journal of the Operations Research Society of America, 2(4), 393–410. http://www.jstor.org/stable/166695"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9a2d968b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "hide_input": false,
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
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 },
 "nbformat": 4,
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}