ORMaterials/TSP.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TSP in Gurobi\n",
    "\n",
    "> Python 3.9.16\n",
    ">\n",
    "> MacBook Pro M2 Apple Silicon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 一、基础的TSP模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import gurobipy as grb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 计算欧氏距离\n",
    "def Eculid_dist(a, b):\n",
    "    return math.sqrt((a[0] - b[0]) * (a[0] - b[0]) + (a[1] - b[1])*(a[1] - b[1]))\n",
    "\n",
    "#  随机数生成函数\n",
    "def rndPoints(N, lb, ub, nodeID = None, rndSeed = 10):\n",
    "    \"\"\"_summary_\n",
    "\n",
    "    Args:\n",
    "        N (_type_): 节点的数字\n",
    "        lb (_type_): 坐标的下限\n",
    "        ub (_type_): 坐标的上限\n",
    "        nodeID (_type_): 节点的ID\n",
    "        rndSeed (_type_): 随机数种子\n",
    "    \"\"\"\n",
    "    \n",
    "    nodes_pos = []\n",
    "    \n",
    "    np.random.seed(rndSeed)\n",
    "    \n",
    "    poly_x = np.random.uniform(lb, ub, N)\n",
    "    poly_y = np.random.uniform(lb, ub, N)\n",
    "    \n",
    "    for i in range(N):\n",
    "        nodes_pos.append((round(poly_x[i], 2), round(poly_y[i], 2)))\n",
    "    \n",
    "    if nodeID == None or not isinstance(nodeID, list):\n",
    "        nodeID = [str(i) for i in range(N)]\n",
    "    else:\n",
    "        if len(nodeID) != N:\n",
    "            raise Exception(\"检查nodeID 长度和 N 是否相等\")\n",
    "\n",
    "    return nodes_pos, nodeID\n",
    "\n",
    "\n",
    "# TODO: 加入nodeID, 补充一点工程化的内容\n",
    "\n",
    "\n",
    "def visualize(nodes_pos, lb, ub, edges = None, save_path = '../image/result.png'):\n",
    "    \"\"\"_summary_\n",
    "\n",
    "    Args:\n",
    "        nodes_pos (_type_): 节点的坐标 list( tuple(coord_x, coord_y))\n",
    "        lb (_type_): 坐标的下界\n",
    "        ub (_type_): 坐标的上界\n",
    "        edges (_type_, optional): 边数据 list( list (org_id, dst_id))\n",
    "        save_path (str, optional): _description_. Defaults to './test_pic1.png'.\n",
    "\n",
    "    Raises:\n",
    "        Exception: _description_\n",
    "    \n",
    "    \"\"\"\n",
    "    plt.style.use('_mpl-gallery')\n",
    "    # colors = \n",
    "    fig, ax = plt.subplots(figsize = (6,6))\n",
    "    \n",
    "    ax.scatter(\n",
    "        x = [node[0] for node in nodes_pos], \n",
    "        y = [node[1] for node in nodes_pos], \n",
    "        s = [6 for _ in range(len(nodes_pos))],\n",
    "        c = [\"r\" for _ in range(len(nodes_pos))],\n",
    "        # vmin = lb,\n",
    "        # vmax = ub\n",
    "    )\n",
    "    \n",
    "    ax.set(\n",
    "        xlim = (lb - max(lb*0.1, 10), ub + 10),\n",
    "        ylim = (lb - max(lb*0.1, 10), ub + 10)\n",
    "    )\n",
    "    \n",
    "    if edges == None:\n",
    "        pass\n",
    "    else:\n",
    "        for e in edges:\n",
    "            ax.plot([nodes_pos[e[0]][0], nodes_pos[e[1]][0]],[nodes_pos[e[0]][1], nodes_pos[e[1]][1]] , \"lightgreen\", linewidth = 2)\n",
    "    ax.grid(False)\n",
    "    fig.tight_layout()\n",
    "    \n",
    "    try:\n",
    "        plt.savefig(save_path, dpi = 400)\n",
    "        print(f\"保存成功，路径{save_path}\")\n",
    "\n",
    "    except Exception:\n",
    "        raise Exception(f\"图片保存失败，路径 {save_path}，检查路径。\")\n",
    "\n",
    "    return "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-11\n",
      "Set parameter LazyConstraints to value 1\n",
      "Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[rosetta2])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 60 rows, 870 columns and 1740 nonzeros\n",
      "Model fingerprint: 0x443136fb\n",
      "Variable types: 0 continuous, 870 integer (870 binary)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [3e+00, 1e+02]\n",
      "  Bounds range     [1e+00, 1e+00]\n",
      "  RHS range        [1e+00, 1e+00]\n",
      "The length is 2\n",
      "Presolve time: 0.01s\n",
      "Presolved: 60 rows, 870 columns, 1740 nonzeros\n",
      "Variable types: 0 continuous, 870 integer (870 binary)\n",
      "The length is 14\n",
      "The length is 15\n",
      "\n",
      "Root relaxation: objective 3.978723e+02, 84 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  397.87228    0   14          -  397.87228      -     -    0s\n",
      "The length is 10\n",
      "The length is 5\n",
      "The length is 2\n",
      "The length is 1\n",
      "H    0     0                     564.0669649  397.87228  29.5%     -    0s\n",
      "The length is 3\n",
      "The length is 1\n",
      "H    0     0                     547.0960909  397.87228  27.3%     -    0s\n",
      "The length is 5\n",
      "     0     0  439.92816    0    -  547.09609  439.92816  19.6%     -    0s\n",
      "The length is 1\n",
      "*    0     0               0     443.6816846  443.68168  0.00%     -    0s\n",
      "\n",
      "Cutting planes:\n",
      "  Lazy constraints: 54\n",
      "\n",
      "Explored 1 nodes (145 simplex iterations) in 0.04 seconds (0.01 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 3: 443.682 547.096 564.067 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 4.436816846342e+02, best bound 4.436816846342e+02, gap 0.0000%\n",
      "\n",
      "User-callback calls 131, time in user-callback 0.01 sec\n",
      "443.68168463423405\n",
      "保存成功，路径../image/result.png\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def TSPwithLazyCuts(nodes_pos):\n",
    "\n",
    "    adj_matrix = [\n",
    "        [0 for _ in range(len(nodes_pos))] for _ in range(len(nodes_pos))\n",
    "    ]\n",
    "\n",
    "    # adjacent matrice\n",
    "\n",
    "    N = len(nodes_pos)\n",
    "\n",
    "    # number of nodes\n",
    "\n",
    "    TSP = grb.Model('TSP')\n",
    "\n",
    "    # Decision Variables ======================== \n",
    "\n",
    "    x = {}\n",
    "\n",
    "    for i in range(N):\n",
    "        for j in range(N):\n",
    "            if i != j:\n",
    "                x[i, j] = TSP.addVar(\n",
    "                    vtype = grb.GRB.BINARY,\n",
    "                    obj = Eculid_dist(nodes_pos[i], nodes_pos[j]),\n",
    "                    name = f\"x_{i}_{j}\"\n",
    "                )\n",
    "                adj_matrix[i][j] = Eculid_dist(nodes_pos[i], nodes_pos[j])\n",
    "\n",
    "    TSP.modelSense = grb.GRB.MINIMIZE\n",
    "    TSP.Params.lazyConstraints = 1\n",
    "    TSP.update()\n",
    "\n",
    "    # Decision Variables ======================== \n",
    "            \n",
    "    # Constraints ==========\n",
    "\n",
    "    # Degree constraints ======================================================\n",
    "    for i in range(N):\n",
    "        TSP.addConstr(grb.quicksum(x[i, j] for j in range(N) if i != j) == 1, name = 'leave_%s' % str(i))\n",
    "        TSP.addConstr(grb.quicksum(x[j, i] for j in range(N) if i != j) == 1, name = 'enter_%s' % str(i))\n",
    "        \n",
    "    TSP._x = x\n",
    "\n",
    "    # 在模型求解中声明的自己的变量？\n",
    "\n",
    "    def subtourelim(model, where):\n",
    "        if (where == grb.GRB.Callback.MIPSOL):\n",
    "            x_sol = model.cbGetSolution(model._x)\n",
    "            # 从新的 MIP 解决方案中检索值。\n",
    "            G = nx.Graph()\n",
    "            for (i, j) in x.keys():\n",
    "                if (x_sol[i, j] > 0.9):\n",
    "                    G.add_edge(i, j, weight = adj_matrix[i][j])\n",
    "            components = [list(c) for c in nx.connected_components(G)]\n",
    "            print(\"The length is \" + str(len(components)))\n",
    "            for component in components:\n",
    "                if (len(component) < N):\n",
    "                    model.cbLazy(grb.quicksum(x[i,j] for i in component for j in component if i != j) <= len(component) - 1)\n",
    "                    \n",
    "                    # 这里相当于在原来的有环的情况上加了一个约束进去\n",
    "\n",
    "    # TSP with callback =======================================================\n",
    "    \n",
    "    TSP.optimize(subtourelim)\n",
    "    # TSP.write(\"models.lp\")\n",
    "\n",
    "    ofv = None\n",
    "    seq = []\n",
    "    arcs = []\n",
    "    solType = None\n",
    "    gap = None\n",
    "    lb = None\n",
    "    ub = None\n",
    "    runtime = None\n",
    "    if (TSP.status == grb.GRB.status.OPTIMAL):\n",
    "        solType = 'IP_Optimal'\n",
    "        ofv = TSP.getObjective().getValue()\n",
    "        print(ofv)\n",
    "        for i, j in x:\n",
    "            if (x[i, j].x > 0.5):\n",
    "                arcs.append([i, j])\n",
    "        # assert len(arcs) == len(nodes_pos) - 1\n",
    "        # currentNode = nodeIDs[0]\n",
    "        # seq.append(currentNode)\n",
    "        # while (len(arcs) > 0):\n",
    "        #     for i in range(len(arcs)):\n",
    "        #         if (arcs[i][0] == currentNode):\n",
    "        #             currentNode = arcs[i][1]\n",
    "        #             seq.append(currentNode)\n",
    "        #             arcs.pop(i)\n",
    "        #             break\n",
    "        gap = 0\n",
    "        lb = ofv\n",
    "        ub = ofv\n",
    "        runtime = TSP.Runtime\n",
    "    elif (TSP.status == grb.GRB.status.TIME_LIMIT):\n",
    "        solType = 'IP_TimeLimit'\n",
    "        ofv = None\n",
    "        seq = []\n",
    "        gap = TSP.MIPGap\n",
    "        lb = TSP.ObjBoundC\n",
    "        ub = TSP.ObjVal\n",
    "        runtime = TSP.Runtime\n",
    "    \n",
    "    return {\n",
    "        \"TotalCost\": ofv,\n",
    "        \"runtime\": runtime,\n",
    "        \"arcs\": arcs\n",
    "    }\n",
    "\n",
    "# print({\n",
    "#         'ofv': ofv,\n",
    "#         'seq': seq,\n",
    "#         'gap': gap,\n",
    "#         'solType': solType,\n",
    "#         'lowerBound': lb,\n",
    "#         'upperBound': ub,\n",
    "#         'runtime': runtime\n",
    "# })\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    nodes, nodeID = rndPoints(30, 0, 100)\n",
    "    arcs = TSPwithLazyCuts(nodes)[\"arcs\"]\n",
    "    visualize(nodes, 0, 100, arcs)\n",
    "    \n",
    "    # nodes, nodeID = rndPoints(30, 0, 100, 2912) \n",
    "    # 测试\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "cbLazy 是什么？\n",
    "\n",
    "- [参考链接](https://www.gurobi.com/documentation/10.0/refman/py_model_cblazy.html):从回调函数中向 MIP 模型添加新的惰性约束。当 MIP 模型的完整约束集太大而无法显式表示时，通常使用延迟约束。通过仅包括在分支和切割搜索期间找到的解决方案实际违反的约束，有时可以找到经过验证的最佳解决方案，同时只添加整套约束的一小部分。\n",
    "- LazyConstraint 参数一定要设置\n",
    "\n",
    "\n",
    "- nx.connected_components: 怎么理解？\n",
    "> 获取网络中的联通子图，按照子图大小从大到小输出\n",
    "\n",
    "\n",
    "怎么理解Gurobi中的Callback函数？\n",
    "\n",
    "> 回调是由 Gurobi 优化器定期调用的用户函数，以允许用户查询或修改优化的状态。更准确地说，如果将两个参数（ model 和 where ）作为参数的函数传递给 Model.optimize 或 Model.computeIIS，则在优化期间将调用您的函数。[链接](https://www.gurobi.com/documentation/current/refman/py_cb_s.html#pythonclass:Callback). Gurobi 回调类提供一组在用户回调函数中使用的常量。此类中的第一组常量列出了用户回调函数的 where 参数选项。该 where 参数指示从优化过程中调用用户回调的位置。选项列于本文档的回调代码部分. [参考链接](https://support.gurobi.com/hc/en-us/articles/14126389733777-Tutorial-Customization-Through-Callbacks)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------\n",
    "\n",
    "\n",
    "解释一下`nx.connected_components`. 这里用到了经典的图网络分析的包 networkx。\n",
    "\n",
    "在图中，这个方法可以搜索并按照从大到小输出所有的联通分量。下面我们的图中有3个联通分量，分别是10-11-12-13-14相连接、4-5-9相互连接以及0-1-2-3相互连接。用这个方法可以把这三个联通分量全部输出出来。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{10, 11, 12, 13, 14}, {0, 1, 2, 3}, {9, 4, 5}]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# TO explain nx.connected_components\n",
    "\n",
    "G = nx.path_graph(4)\n",
    "nx.add_path(G, [4, 5 ,9])\n",
    "nx.add_path(G, [10,11,12,13,14])\n",
    "\n",
    "a = [c for c in sorted(nx.connected_components(G), key=len, reverse=True)]\n",
    "nx.draw(G, node_size = 20, with_labels = True, font_size = 8)\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MTZ implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[rosetta2])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 1640 rows, 1600 columns and 7644 nonzeros\n",
      "Model fingerprint: 0x3ccd7621\n",
      "Variable types: 40 continuous, 1560 integer (1560 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 4e+01]\n",
      "  Objective range  [2e+00, 1e+02]\n",
      "  Bounds range     [1e+00, 1e+00]\n",
      "  RHS range        [1e+00, 4e+01]\n",
      "Presolve removed 78 rows and 1 columns\n",
      "Presolve time: 0.01s\n",
      "Presolved: 1562 rows, 1599 columns, 7566 nonzeros\n",
      "Variable types: 39 continuous, 1560 integer (1560 binary)\n",
      "Found heuristic solution: objective 2011.9634110\n",
      "Found heuristic solution: objective 1988.6219153\n",
      "\n",
      "Root relaxation: objective 4.158563e+02, 154 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  415.85630    0   82 1988.62192  415.85630  79.1%     -    0s\n",
      "     0     0  479.87785    0   68 1988.62192  479.87785  75.9%     -    0s\n",
      "H    0     0                     771.0726897  479.87785  37.8%     -    0s\n",
      "H    0     0                     761.2277103  479.87785  37.0%     -    0s\n",
      "H    0     0                     734.4942418  479.87785  34.7%     -    0s\n",
      "H    0     0                     683.4074569  479.87785  29.8%     -    0s\n",
      "     0     0  489.59503    0   68  683.40746  489.59503  28.4%     -    0s\n",
      "     0     0  489.59503    0   82  683.40746  489.59503  28.4%     -    0s\n",
      "     0     0  489.59503    0   52  683.40746  489.59503  28.4%     -    0s\n",
      "     0     0  489.59503    0   52  683.40746  489.59503  28.4%     -    0s\n",
      "H    0     0                     664.4093558  489.59503  26.3%     -    0s\n",
      "     0     0  489.59503    0   52  664.40936  489.59503  26.3%     -    0s\n",
      "     0     0  489.59503    0   52  664.40936  489.59503  26.3%     -    0s\n",
      "     0     0  489.69345    0   59  664.40936  489.69345  26.3%     -    0s\n",
      "H    0     0                     644.1938021  489.69345  24.0%     -    0s\n",
      "     0     0  489.74396    0   88  644.19380  489.74396  24.0%     -    0s\n",
      "     0     0  489.74396    0   88  644.19380  489.74396  24.0%     -    0s\n",
      "     0     0  489.75029    0   88  644.19380  489.75029  24.0%     -    0s\n",
      "     0     0  489.75029    0   88  644.19380  489.75029  24.0%     -    0s\n",
      "H    0     0                     632.4877377  489.75029  22.6%     -    0s\n",
      "     0     2  491.33437    0   88  632.48774  491.33437  22.3%     -    0s\n",
      "H   31    36                     627.7423097  494.75627  21.2%  12.1    0s\n",
      "H   33    36                     627.5118576  494.75627  21.2%  12.0    0s\n",
      "H   37    36                     624.4711927  494.75627  20.8%  11.8    0s\n",
      "H  584   439                     560.9384550  495.02787  11.8%   7.9    0s\n",
      "H  688   474                     530.5485337  495.06943  6.69%   8.0    0s\n",
      "* 3287  1161              35     526.7822610  504.80634  4.17%  10.7    2s\n",
      "* 3742  1037              38     525.8212212  507.71458  3.44%  11.4    2s\n",
      "\n",
      "Cutting planes:\n",
      "  Learned: 18\n",
      "  Gomory: 30\n",
      "  Implied bound: 11\n",
      "  Projected implied bound: 7\n",
      "  MIR: 15\n",
      "  Flow cover: 125\n",
      "  Inf proof: 8\n",
      "  Zero half: 13\n",
      "  RLT: 13\n",
      "  Relax-and-lift: 5\n",
      "\n",
      "Explored 5389 nodes (69738 simplex iterations) in 2.85 seconds (3.72 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 10: 525.821 526.782 530.549 ... 664.409\n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 5.258212212469e+02, best bound 5.258212212469e+02, gap 0.0000%\n",
      "保存成功，路径../image/result40v.png\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# def _ipTSPGurobiMTZ(nodeIDs, tau, outputFlag, timeLimit, gapTolerance):\n",
    "def TSP_Guribi_MTZ(nodeIDs, nodes_pos):\n",
    "    \n",
    "    # Initialize\n",
    "    \n",
    "    N = len(nodeIDs)\n",
    "    TSP = grb.Model('TSP')\n",
    "    \n",
    "    # if (outputFlag == False):\n",
    "    #     TSP.setParam('OutputFlag', 0)\n",
    "    # if (timeLimit != None):\n",
    "    #     TSP.setParam(grb.GRB.Param.TimeLimit, timeLimit)\n",
    "    # if (gapTolerance != None):\n",
    "    #     TSP.setParam(grb.GRB.Param.MIPGap, gapTolerance)\n",
    "\n",
    "    # Decision variables ======================================================\n",
    "    # x = {}\n",
    "    # for i in range(n):\n",
    "    #     for j in range(n):\n",
    "    #         if i != j:\n",
    "    #             x[i, j] = TSP.addVar(\n",
    "    #                 vtype = grb.GRB.BINARY, \n",
    "    #                 obj = tau[nodeIDs[i], nodeIDs[j]], \n",
    "    #                 name = 'x_%s_%s' % (i, j))\n",
    "    \n",
    "    x = dict()\n",
    "    \n",
    "    adj_matrix = [\n",
    "        [0 for _ in range(len(nodes_pos))] for _ in range(len(nodes_pos))\n",
    "    ]\n",
    "    \n",
    "    for i in range(N):\n",
    "        for j in range(N):\n",
    "            if i != j:\n",
    "                adj_matrix[i][j] = Eculid_dist(nodes_pos[i], nodes_pos[j])\n",
    "                x[i, j] = TSP.addVar(\n",
    "                    vtype = grb.GRB.BINARY,\n",
    "                    obj = adj_matrix[i][j],\n",
    "                    name = f\"x_{i}_{j}\"\n",
    "                )\n",
    "                \n",
    "\n",
    "    u = dict()\n",
    "    for i in range(N):\n",
    "        u[i] = TSP.addVar(\n",
    "            vtype = grb.GRB.CONTINUOUS,\n",
    "            name = 'u_%s' % (i))\n",
    "\n",
    "    # TSP objective function ==================================================\n",
    "    TSP.modelSense = grb.GRB.MINIMIZE\n",
    "    TSP.update()\n",
    "\n",
    "    # Degree constraints ======================================================\n",
    "    for i in range(N):\n",
    "        TSP.addConstr(grb.quicksum(x[i, j] for j in range(N) if i != j) == 1, name = 'leave_%s' % str(i))\n",
    "        TSP.addConstr(grb.quicksum(x[j, i] for j in range(N) if i != j) == 1, name = 'enter_%s' % str(i))\n",
    "\n",
    "    # Sequence constraints ====================================================\n",
    "    for i in range(1, N):\n",
    "        for j in range(1, N):\n",
    "            if (i != j):\n",
    "                TSP.addConstr(u[i] - u[j] + (N - 1) * x[i, j] <= N - 2, name = 'seq_%s_%s' % (i, j))\n",
    "    for i in range(1, N):\n",
    "        TSP.addConstr(1 <= u[i])\n",
    "        TSP.addConstr(u[i] <= N - 1)\n",
    "\n",
    "    # TSP =====================================================================\n",
    "    TSP.optimize()\n",
    "\n",
    "    # Reconstruct solution ====================================================\n",
    "    ofv = None\n",
    "    gap = None\n",
    "    seq = []\n",
    "    arcs = []\n",
    "    solType = None\n",
    "    gap = None\n",
    "    lb = None\n",
    "    ub = None\n",
    "    runtime = None\n",
    "    if (TSP.status == grb.GRB.status.OPTIMAL):\n",
    "        solType = 'IP_Optimal'\n",
    "        ofv = TSP.getObjective().getValue()\n",
    "        gap = TSP.Params.MIPGapAbs\n",
    "        for i, j in x:\n",
    "            if (x[i, j].x > 0.5):\n",
    "                arcs.append([i, j])\n",
    "        \n",
    "        # currentNode = 0\n",
    "        # seq.append(nodeIDs[currentNode])\n",
    "        # while (len(arcs) > 0):\n",
    "        #     for i in range(len(arcs)):\n",
    "        #         if (arcs[i][0] == currentNode):\n",
    "        #             currentNode = arcs[i][1]\n",
    "        #             seq.append(nodeIDs[currentNode])\n",
    "        #             arcs.pop(i)\n",
    "        #             break\n",
    "        \n",
    "        gap = 0\n",
    "        lb = ofv\n",
    "        ub = ofv\n",
    "        runtime = TSP.Runtime\n",
    "    elif (TSP.status == grb.GRB.status.TIME_LIMIT):\n",
    "        solType = 'IP_TimeLimit'\n",
    "        ofv = None\n",
    "        seq = []\n",
    "        gap = TSP.MIPGap\n",
    "        lb = TSP.ObjBoundC\n",
    "        ub = TSP.ObjVal\n",
    "        runtime = TSP.Runtime\n",
    "\n",
    "    return {\n",
    "        'ofv': ofv,\n",
    "        'seq': seq,\n",
    "        'gap': gap,\n",
    "        'solType': solType,\n",
    "        'lowerBound': lb,\n",
    "        'upperBound': ub,\n",
    "        'runtime': runtime,\n",
    "        \"arcs\": arcs\n",
    "    }\n",
    "    \n",
    "if __name__ == \"__main__\":\n",
    "    \n",
    "    nodes, nodeID = rndPoints(40, 0, 100)\n",
    "    arcs = TSP_Guribi_MTZ(nodeID, nodes)[\"arcs\"]\n",
    "    visualize(nodes, 0, 100, arcs, save_path = \"../image/result40v.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---------\n",
    "\n",
    "# TSP in ortools\n",
    "\n",
    "\n",
    "> ortools才学所以直接用了官网的代码\n",
    ">\n",
    "> [参考链接](https://developers.google.cn/optimization/routing/tsp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Objective: 2790\n",
      "Route:\n",
      " 0 -> 1 -> 279 -> 2 -> 278 -> 277 -> 248 -> 247 -> 243 -> 242 -> 241 -> 240 -> 239 -> 238 -> 245 -> 244 -> 246 -> 249 -> 250 -> 229 -> 228 -> 231 -> 230 -> 237 -> 236 -> 235 -> 234 -> 233 -> 232 -> 227 -> 226 -> 225 -> 224 -> 223 -> 222 -> 218 -> 221 -> 220 -> 219 -> 202 -> 203 -> 204 -> 205 -> 207 -> 206 -> 211 -> 212 -> 215 -> 216 -> 217 -> 214 -> 213 -> 210 -> 209 -> 208 -> 251 -> 254 -> 255 -> 257 -> 256 -> 253 -> 252 -> 139 -> 140 -> 141 -> 142 -> 143 -> 199 -> 201 -> 200 -> 195 -> 194 -> 193 -> 191 -> 190 -> 189 -> 188 -> 187 -> 163 -> 164 -> 165 -> 166 -> 167 -> 168 -> 169 -> 171 -> 170 -> 172 -> 105 -> 106 -> 104 -> 103 -> 107 -> 109 -> 110 -> 113 -> 114 -> 116 -> 117 -> 61 -> 62 -> 63 -> 65 -> 64 -> 84 -> 85 -> 115 -> 112 -> 86 -> 83 -> 82 -> 87 -> 111 -> 108 -> 89 -> 90 -> 91 -> 102 -> 101 -> 100 -> 99 -> 98 -> 97 -> 96 -> 95 -> 94 -> 93 -> 92 -> 79 -> 88 -> 81 -> 80 -> 78 -> 77 -> 76 -> 74 -> 75 -> 73 -> 72 -> 71 -> 70 -> 69 -> 66 -> 68 -> 67 -> 57 -> 56 -> 55 -> 54 -> 53 -> 52 -> 51 -> 50 -> 49 -> 48 -> 47 -> 46 -> 45 -> 44 -> 43 -> 58 -> 60 -> 59 -> 42 -> 41 -> 40 -> 39 -> 38 -> 37 -> 36 -> 35 -> 34 -> 33 -> 32 -> 31 -> 30 -> 29 -> 124 -> 123 -> 122 -> 121 -> 120 -> 119 -> 118 -> 156 -> 157 -> 158 -> 173 -> 162 -> 161 -> 160 -> 174 -> 159 -> 150 -> 151 -> 155 -> 152 -> 154 -> 153 -> 128 -> 129 -> 130 -> 131 -> 18 -> 19 -> 20 -> 127 -> 126 -> 125 -> 28 -> 27 -> 26 -> 25 -> 21 -> 24 -> 22 -> 23 -> 13 -> 12 -> 14 -> 11 -> 10 -> 9 -> 7 -> 8 -> 6 -> 5 -> 275 -> 274 -> 273 -> 272 -> 271 -> 270 -> 15 -> 16 -> 17 -> 132 -> 149 -> 177 -> 176 -> 175 -> 178 -> 179 -> 180 -> 181 -> 182 -> 183 -> 184 -> 186 -> 185 -> 192 -> 196 -> 197 -> 198 -> 144 -> 145 -> 146 -> 147 -> 148 -> 138 -> 137 -> 136 -> 135 -> 134 -> 133 -> 269 -> 268 -> 267 -> 266 -> 265 -> 264 -> 263 -> 262 -> 261 -> 260 -> 258 -> 259 -> 276 -> 3 -> 4 -> 0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "\"\"\"Simple Travelling Salesperson Problem (TSP) on a circuit board.\"\"\"\n",
    "\n",
    "import math\n",
    "from ortools.constraint_solver import routing_enums_pb2\n",
    "from ortools.constraint_solver import pywrapcp\n",
    "\n",
    "\n",
    "def create_data_model():\n",
    "    \"\"\"Stores the data for the problem.\"\"\"\n",
    "    data = {}\n",
    "    # Locations in block units\n",
    "    data[\"locations\"] = [\n",
    "        # fmt: off\n",
    "      (288, 149), (288, 129), (270, 133), (256, 141), (256, 157), (246, 157),\n",
    "      (236, 169), (228, 169), (228, 161), (220, 169), (212, 169), (204, 169),\n",
    "      (196, 169), (188, 169), (196, 161), (188, 145), (172, 145), (164, 145),\n",
    "      (156, 145), (148, 145), (140, 145), (148, 169), (164, 169), (172, 169),\n",
    "      (156, 169), (140, 169), (132, 169), (124, 169), (116, 161), (104, 153),\n",
    "      (104, 161), (104, 169), (90, 165), (80, 157), (64, 157), (64, 165),\n",
    "      (56, 169), (56, 161), (56, 153), (56, 145), (56, 137), (56, 129),\n",
    "      (56, 121), (40, 121), (40, 129), (40, 137), (40, 145), (40, 153),\n",
    "      (40, 161), (40, 169), (32, 169), (32, 161), (32, 153), (32, 145),\n",
    "      (32, 137), (32, 129), (32, 121), (32, 113), (40, 113), (56, 113),\n",
    "      (56, 105), (48, 99), (40, 99), (32, 97), (32, 89), (24, 89),\n",
    "      (16, 97), (16, 109), (8, 109), (8, 97), (8, 89), (8, 81),\n",
    "      (8, 73), (8, 65), (8, 57), (16, 57), (8, 49), (8, 41),\n",
    "      (24, 45), (32, 41), (32, 49), (32, 57), (32, 65), (32, 73),\n",
    "      (32, 81), (40, 83), (40, 73), (40, 63), (40, 51), (44, 43),\n",
    "      (44, 35), (44, 27), (32, 25), (24, 25), (16, 25), (16, 17),\n",
    "      (24, 17), (32, 17), (44, 11), (56, 9), (56, 17), (56, 25),\n",
    "      (56, 33), (56, 41), (64, 41), (72, 41), (72, 49), (56, 49),\n",
    "      (48, 51), (56, 57), (56, 65), (48, 63), (48, 73), (56, 73),\n",
    "      (56, 81), (48, 83), (56, 89), (56, 97), (104, 97), (104, 105),\n",
    "      (104, 113), (104, 121), (104, 129), (104, 137), (104, 145), (116, 145),\n",
    "      (124, 145), (132, 145), (132, 137), (140, 137), (148, 137), (156, 137),\n",
    "      (164, 137), (172, 125), (172, 117), (172, 109), (172, 101), (172, 93),\n",
    "      (172, 85), (180, 85), (180, 77), (180, 69), (180, 61), (180, 53),\n",
    "      (172, 53), (172, 61), (172, 69), (172, 77), (164, 81), (148, 85),\n",
    "      (124, 85), (124, 93), (124, 109), (124, 125), (124, 117), (124, 101),\n",
    "      (104, 89), (104, 81), (104, 73), (104, 65), (104, 49), (104, 41),\n",
    "      (104, 33), (104, 25), (104, 17), (92, 9), (80, 9), (72, 9),\n",
    "      (64, 21), (72, 25), (80, 25), (80, 25), (80, 41), (88, 49),\n",
    "      (104, 57), (124, 69), (124, 77), (132, 81), (140, 65), (132, 61),\n",
    "      (124, 61), (124, 53), (124, 45), (124, 37), (124, 29), (132, 21),\n",
    "      (124, 21), (120, 9), (128, 9), (136, 9), (148, 9), (162, 9),\n",
    "      (156, 25), (172, 21), (180, 21), (180, 29), (172, 29), (172, 37),\n",
    "      (172, 45), (180, 45), (180, 37), (188, 41), (196, 49), (204, 57),\n",
    "      (212, 65), (220, 73), (228, 69), (228, 77), (236, 77), (236, 69),\n",
    "      (236, 61), (228, 61), (228, 53), (236, 53), (236, 45), (228, 45),\n",
    "      (228, 37), (236, 37), (236, 29), (228, 29), (228, 21), (236, 21),\n",
    "      (252, 21), (260, 29), (260, 37), (260, 45), (260, 53), (260, 61),\n",
    "      (260, 69), (260, 77), (276, 77), (276, 69), (276, 61), (276, 53),\n",
    "      (284, 53), (284, 61), (284, 69), (284, 77), (284, 85), (284, 93),\n",
    "      (284, 101), (288, 109), (280, 109), (276, 101), (276, 93), (276, 85),\n",
    "      (268, 97), (260, 109), (252, 101), (260, 93), (260, 85), (236, 85),\n",
    "      (228, 85), (228, 93), (236, 93), (236, 101), (228, 101), (228, 109),\n",
    "      (228, 117), (228, 125), (220, 125), (212, 117), (204, 109), (196, 101),\n",
    "      (188, 93), (180, 93), (180, 101), (180, 109), (180, 117), (180, 125),\n",
    "      (196, 145), (204, 145), (212, 145), (220, 145), (228, 145), (236, 145),\n",
    "      (246, 141), (252, 125), (260, 129), (280, 133)\n",
    "        # fmt: on\n",
    "    ]\n",
    "    data[\"num_vehicles\"] = 1\n",
    "    data[\"depot\"] = 0\n",
    "    return data\n",
    "\n",
    "\n",
    "def compute_euclidean_distance_matrix(locations):\n",
    "    \"\"\"Creates callback to return distance between points.\"\"\"\n",
    "    distances = {}\n",
    "    for from_counter, from_node in enumerate(locations):\n",
    "        distances[from_counter] = {}\n",
    "        for to_counter, to_node in enumerate(locations):\n",
    "            if from_counter == to_counter:\n",
    "                distances[from_counter][to_counter] = 0\n",
    "            else:\n",
    "                # Euclidean distance\n",
    "                distances[from_counter][to_counter] = int(\n",
    "                    math.hypot((from_node[0] - to_node[0]), (from_node[1] - to_node[1]))\n",
    "                )\n",
    "                # 第一次知道欧氏距离可以这样算..\n",
    "    return distances\n",
    "\n",
    "\n",
    "def print_solution(manager, routing, solution):\n",
    "    \"\"\"Prints solution on console.\"\"\"\n",
    "    print(f\"Objective: {solution.ObjectiveValue()}\")\n",
    "    index = routing.Start(0)\n",
    "    plan_output = \"Route:\\n\"\n",
    "    route_distance = 0\n",
    "    while not routing.IsEnd(index):\n",
    "        plan_output += f\" {manager.IndexToNode(index)} ->\"\n",
    "        previous_index = index\n",
    "        index = solution.Value(routing.NextVar(index))\n",
    "        route_distance += routing.GetArcCostForVehicle(previous_index, index, 0)\n",
    "    plan_output += f\" {manager.IndexToNode(index)}\\n\"\n",
    "    print(plan_output)\n",
    "    plan_output += f\"Objective: {route_distance}m\\n\"\n",
    "\n",
    "\n",
    "def TSP_ortools():\n",
    "    \"\"\"Entry point of the program.\"\"\"\n",
    "    # Instantiate the data problem.\n",
    "    data = create_data_model()\n",
    "\n",
    "    # Create the routing index manager.\n",
    "    manager = pywrapcp.RoutingIndexManager(\n",
    "        len(data[\"locations\"]), data[\"num_vehicles\"], data[\"depot\"]\n",
    "    )\n",
    "\n",
    "    # Create Routing Model.\n",
    "    routing = pywrapcp.RoutingModel(manager)\n",
    "\n",
    "    distance_matrix = compute_euclidean_distance_matrix(data[\"locations\"])\n",
    "\n",
    "    def distance_callback(from_index, to_index):\n",
    "        \"\"\"Returns the distance between the two nodes.\"\"\"\n",
    "        # Convert from routing variable Index to distance matrix NodeIndex.\n",
    "        from_node = manager.IndexToNode(from_index)\n",
    "        to_node = manager.IndexToNode(to_index)\n",
    "        return distance_matrix[from_node][to_node]\n",
    "\n",
    "    transit_callback_index = routing.RegisterTransitCallback(distance_callback)\n",
    "\n",
    "    # Define cost of each arc.\n",
    "    routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)\n",
    "\n",
    "    # Setting first solution heuristic.\n",
    "    search_parameters = pywrapcp.DefaultRoutingSearchParameters()\n",
    "    search_parameters.first_solution_strategy = (\n",
    "        routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC\n",
    "    )\n",
    "\n",
    "    # Solve the problem.\n",
    "    solution = routing.SolveWithParameters(search_parameters)\n",
    "\n",
    "    # Print solution on console.\n",
    "    if solution:\n",
    "        print_solution(manager, routing, solution)\n",
    "\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    TSP_ortools()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MTZ via SCIP solver\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Miller-Tucker-Zemlin's model:\n",
      "Optimal value: 330.0\n",
      "x(1,4) = 1.0\n",
      "x(2,3) = 1.0\n",
      "x(3,5) = 1.0\n",
      "x(4,2) = 1.0\n",
      "x(5,1) = 1.0\n",
      "u(5) = 4.0\n",
      "u(2) = 2.0\n",
      "u(3) = 3.0\n",
      "u(4) = 1.0\n",
      "[1, 4, 2, 3, 5]\n",
      "[1, 4, 2, 3]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "from pyscipopt import Model, quicksum, multidict\n",
    "\n",
    "def mtz(n,c):\n",
    "    \"\"\"mtz: Miller-Tucker-Zemlin's model for the (asymmetric) traveling salesman problem\n",
    "    (potential formulation)\n",
    "    Parameters:\n",
    "        - n: number of nodes\n",
    "        - c[i,j]: cost for traversing arc (i,j)\n",
    "    Returns a model, ready to be solved.\n",
    "    \"\"\"\n",
    "\n",
    "    model = Model(\"atsp - mtz\")\n",
    "\n",
    "    x,u = {},{}\n",
    "    for i in range(1,n+1):\n",
    "        u[i] = model.addVar(lb=0, ub=n-1, vtype=\"C\", name=\"u(%s)\"%i)\n",
    "        for j in range(1,n+1):\n",
    "            if i != j:\n",
    "                x[i,j] = model.addVar(vtype=\"B\", name=\"x(%s,%s)\"%(i,j))\n",
    "\n",
    "    for i in range(1,n+1):\n",
    "        model.addCons(quicksum(x[i,j] for j in range(1,n+1) if j != i) == 1, \"Out(%s)\"%i)\n",
    "        model.addCons(quicksum(x[j,i] for j in range(1,n+1) if j != i) == 1, \"In(%s)\"%i)\n",
    "\n",
    "    for i in range(1,n+1):\n",
    "        for j in range(2,n+1):\n",
    "            if i != j:\n",
    "                model.addCons(u[i] - u[j] + (n-1)*x[i,j] <= n-2, \"MTZ(%s,%s)\"%(i,j))\n",
    "\n",
    "    model.setObjective(quicksum(c[i,j]*x[i,j] for (i,j) in x), \"minimize\")\n",
    "\n",
    "    model.data = x,u\n",
    "    return model\n",
    "\n",
    "\n",
    "def sequence(arcs):\n",
    "    \"\"\"sequence: make a list of cities to visit, from set of arcs\"\"\"\n",
    "    succ = {}\n",
    "    for (i,j) in arcs:\n",
    "        succ[i] = j\n",
    "    curr = 1    # first node being visited\n",
    "    sol = [curr]\n",
    "    for i in range(len(arcs)-2):\n",
    "        curr = succ[curr]\n",
    "        sol.append(curr)\n",
    "    return sol\n",
    "\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    n = 5\n",
    "    c = { (1,1):0,  (1,2):1989,  (1,3):102, (1,4):102, (1,5):103,\n",
    "          (2,1):104, (2,2):0,  (2,3):11,  (2,4):104, (2,5):108,\n",
    "          (3,1):107, (3,2):108, (3,3):0,  (3,4):19,  (3,5):102,\n",
    "          (4,1):109, (4,2):102, (4,3):107, (4,4):0,  (4,5):15,\n",
    "          (5,1):13,  (5,2):103, (5,3):104, (5,4):101, (5,5):0,\n",
    "         }\n",
    "\n",
    "    model = mtz(n,c)\n",
    "    model.hideOutput() # silent mode\n",
    "    model.optimize()\n",
    "    cost = model.getObjVal()\n",
    "    print()\n",
    "    print(\"Miller-Tucker-Zemlin's model:\")\n",
    "    print(\"Optimal value:\", cost)\n",
    "    #model.printAttr(\"X\")\n",
    "    for v in model.getVars():\n",
    "        if model.getVal(v) > 0.001:\n",
    "            print(v.name, \"=\", model.getVal(v))\n",
    "\n",
    "    x,u = model.data\n",
    "    sol = [i for (p,i) in sorted([(int(model.getVal(u[i])+.5),i) for i in range(1,n+1)])]\n",
    "    print(sol)\n",
    "    arcs = [(i,j) for (i,j) in x if model.getVal(x[i,j]) > .5]\n",
    "    sol = sequence(arcs)\n",
    "    print(sol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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