Cleaned up symmetric TSP, which can now solve the full-sized model

Author: gglockner

traveling_salesman/tsp.ipynb

@@ -136,11 +136,9 @@
     "\n",
     "Consider a salesperson that needs to visit customers at each state capital of the continental US. The salesperson wants to identify the shortest route that goes to all the state capitals.\n",
     "\n",
-    "This modeling example requires to import the following libraries.\n",
-    "* **math** access to mathematical functions.\n",
-    "* **itertools** implements a number of iterator building blocks.\n",
-    "* **folium** creates maps.\n",
-    "* **gurobipy** calls Gurobi algorithms to solve MIP models.\n"
+    "This modeling example requires the following libraries that are not part of the standard Python distribution:\n",
+    "* **folium**: to create maps.\n",
+    "* **gurobipy**: provides Gurobi algorithms to solve MIP models.\n"
    ]
   },
   {
@@ -153,7 +151,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -174,18 +172,18 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Preprocessing\n",
-    "The following function calculates the distance of each pair of state capitals combination."
+    "### Data computation\n",
+    "The following function calculates the distance for each pair of state capitals. Since we are solving the _symmetric_ traveling salesman problem, we use _combinations_ of cities."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "import math\n",
-    "from itertools import combinations,product\n",
+    "from itertools import combinations\n",
     "\n",
     "# Compute pairwise distance matrix\n",
     "\n",
@@ -195,7 +193,39 @@
     "    diff = (c1[0]-c2[0], c1[1]-c2[1])\n",
     "    return math.sqrt(diff[0]*diff[0]+diff[1]*diff[1])\n",
     "\n",
-    "dist = {(c1, c2): distance(c1, c2) for c1, c2 in product(capitals, capitals) if c1 != c2}"
+    "dist = {(c1, c2): distance(c1, c2) for c1, c2 in combinations(capitals, 2)}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Model Code\n",
+    "We now write the model for the TSP, by defining decision variables, constraints, and objective function. Because this is the _symmetric_ traveling salesman problem, we can make it more efficient by setting the _object_ x[j,i] to x[i,j], instead of a constraint."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import gurobipy as gp\n",
+    "from gurobipy import GRB\n",
+    "\n",
+    "# tested with Python 3.7 & Gurobi 9.0.0\n",
+    "\n",
+    "m = gp.Model()\n",
+    "\n",
+    "# Variables: is city 'i' adjacent to city 'j' on the tour?\n",
+    "vars = m.addVars(dist.keys(), obj=dist, vtype=GRB.BINARY, name='x')\n",
+    "\n",
+    "# Symmetric direction: Copy the object\n",
+    "for i, j in vars.keys():\n",
+    "    vars[j, i] = vars[i, j]  # edge in opposite direction\n",
+    "\n",
+    "# Constraints: two edges incident to each city\n",
+    "cons = m.addConstrs(vars.sum(c, '*') == 2 for c in capitals)"
    ]
   },
   {
@@ -208,7 +238,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -225,23 +255,8 @@
     "        if len(tour) < len(capitals):\n",
     "            # add subtour elimination constr. for every pair of cities in subtour\n",
     "            model.cbLazy(gp.quicksum(model._vars[i, j] for i, j in combinations(tour, 2))\n",
-    "                         <= len(tour)-1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Finding Shortest Route\n",
-    "The following function determines the shortest route from a given set of edges."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [],
-   "source": [
+    "                         <= len(tour)-1)\n",
+    "\n",
     "# Given a tuplelist of edges, find the shortest subtour\n",
     "\n",
     "def subtour(edges):\n",
@@ -265,91 +280,18 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Model Deployment\n",
-    "We now determine the model for the TSP, by defining decision variables, constraints, and objective function. Next, we start the optimization and Gurobi finds the optimal route for the TSP. "
+    "## Solve the model"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Using license file c:\\gurobi\\gurobi.lic\n",
-      "Changed value of parameter lazyConstraints to 1\n",
-      "   Prev: 0  Min: 0  Max: 1  Default: 0\n",
-      "Gurobi Optimizer version 9.1.0 build v9.1.0rc0 (win64)\n",
-      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
-      "Optimize a model with 2304 rows, 2256 columns and 6768 nonzeros\n",
-      "Model fingerprint: 0x029d7617\n",
-      "Variable types: 0 continuous, 2256 integer (2256 binary)\n",
-      "Coefficient statistics:\n",
-      "  Matrix range     [1e+00, 1e+00]\n",
-      "  Objective range  [6e-01, 5e+01]\n",
-      "  Bounds range     [1e+00, 1e+00]\n",
-      "  RHS range        [2e+00, 2e+00]\n",
-      "Presolve removed 2256 rows and 1128 columns\n",
-      "Presolve time: 0.01s\n",
-      "Presolved: 48 rows, 1128 columns, 2256 nonzeros\n",
-      "Variable types: 0 continuous, 1128 integer (1128 binary)\n",
-      "\n",
-      "Root relaxation: objective 3.223715e+02, 72 iterations, 0.00 seconds\n",
-      "\n",
-      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
-      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
-      "\n",
-      "     0     0  322.37153    0   12          -  322.37153      -     -    0s\n",
-      "     0     0  326.22035    0   18          -  326.22035      -     -    0s\n",
-      "     0     0  331.56424    0   16          -  331.56424      -     -    0s\n",
-      "     0     0  333.84959    0   14          -  333.84959      -     -    0s\n",
-      "     0     0  334.15410    0   33          -  334.15410      -     -    0s\n",
-      "H    0     0                     494.5024872  334.15410  32.4%     -    0s\n",
-      "     0     2  334.15410    0   33  494.50249  334.15410  32.4%     -    0s\n",
-      "*  131    58               9     363.5306008  336.61730  7.40%   5.0    0s\n",
-      "*  145    64               5     350.8980740  336.61730  4.07%   5.7    0s\n",
-      "\n",
-      "Cutting planes:\n",
-      "  Zero half: 8\n",
-      "  Lazy constraints: 32\n",
-      "\n",
-      "Explored 223 nodes (1444 simplex iterations) in 0.33 seconds\n",
-      "Thread count was 8 (of 8 available processors)\n",
-      "\n",
-      "Solution count 3: 350.898 363.531 494.502 \n",
-      "\n",
-      "Optimal solution found (tolerance 1.00e-04)\n",
-      "Best objective 3.508980740395e+02, best bound 3.508980740395e+02, gap 0.0000%\n",
-      "\n",
-      "User-callback calls 634, time in user-callback 0.10 sec\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
-    "import gurobipy as gp\n",
-    "from gurobipy import GRB\n",
-    "\n",
-    "# tested with Python 3.7 & Gurobi 9.0.0\n",
-    "\n",
-    "m = gp.Model()\n",
-    "\n",
-    "# Variables: is city 'i' adjacent to city 'j' on the tour?\n",
-    "\n",
-    "vars = m.addVars(dist.keys(), obj=dist, vtype=GRB.BINARY, name='e')\n",
-    "for i, j in vars.keys():\n",
-    "    m.addConstr(vars[j, i] == vars[i, j])  # edge in opposite direction\n",
-    "\n",
-    "# Constraints: two edges incident to each city\n",
-    "\n",
-    "m.addConstrs(vars.sum(c, '*') == 2 for c in capitals)\n",
-    "\n",
-    "# Optimize the model\n",
-    "\n",
     "m._vars = vars\n",
     "m.Params.lazyConstraints = 1\n",
-    "m.optimize(subtourelim)\n"
+    "m.optimize(subtourelim)"
    ]
   },
   {
@@ -363,7 +305,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -385,23 +327,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
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-      ],
-      "text/plain": [
-       "<folium.folium.Map at 0x1b8c6c73198>"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Map the solution\n",
     "\n",
@@ -469,7 +397,7 @@
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    "nbconvert_exporter": "python",
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+   "version": "3.8.2"
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