Add third notebook using CPLEX callbacks.

tp2-modeling-and-benders.ipynb

@@ -47,7 +47,7 @@
     "...  # TODO\n",
     "\n",
     "solution = tsp.solve()\n",
-    "print(\"z* =\", solution.objective_value)"
+    "print(\"z* =\", solution.objective_value)\n"
    ]
   },
   {
@@ -90,7 +90,7 @@
     "...  # TODO: Copy your model from the first question here.\n",
     "\n",
     "solution = tsp.solve()\n",
-    "print(\"z* =\", solution.objective_value)"
+    "print(\"z* =\", solution.objective_value)\n"
    ]
   },
   {
@@ -147,7 +147,7 @@
     "...  # TODO: Model for the warehouse allocation.\n",
     "\n",
     "solution = wa.solve()\n",
-    "print(\"z* =\", solution.objective_value)"
+    "print(\"z* =\", solution.objective_value)\n"
    ]
   },
   {
@@ -230,7 +230,7 @@
     "\n",
     "# Check your method:\n",
     "wa, z, y = create_master_problem(N, M, f, c)\n",
-    "print(wa.export_as_lp_string())"
+    "print(wa.export_as_lp_string())\n"
    ]
   },
   {
@@ -270,7 +270,7 @@
     "\n",
     "    Return: The optimality constraint added.\n",
     "    \"\"\"\n",
-    "    return ...  # TODO"
+    "    return ...  # TODO\n"
    ]
   },
   {
@@ -312,7 +312,7 @@
     "        The feasibility constraint added.\n",
     "    \"\"\"\n",
     "    # TODO:\n",
-    "    return"
+    "    return\n"
    ]
   },
   {
@@ -370,7 +370,7 @@
     "\n",
     "# Check your method (assuming y = [1 1 1 ... 1]):\n",
     "dsp, v, u = create_dual_subproblem(N, M, f, c, [1] * M)\n",
-    "print(dsp.export_as_lp_string())"
+    "print(dsp.export_as_lp_string())\n"
    ]
   },
   {
@@ -466,7 +466,7 @@
     "\n",
     "    ...  # TODO\n",
     "\n",
-    "print(\"Done.\")"
+    "print(\"Done.\")\n"
    ]
   },
   {
@@ -509,7 +509,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.2"
+   "version": "3.9.13"
   }
  },
  "nbformat": 4,

tp3-docplex-callback.ipynb

@@ -0,0 +1,163 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from typing import Sequence\n",
+    "\n",
+    "\n",
+    "def find_subtours(x: Sequence[Sequence[int]]) -> Sequence[Sequence[int]]:\n",
+    "    \"\"\"\n",
+    "    Extracts subtours from the given 2D-array.\n",
+    "\n",
+    "    Args:\n",
+    "        x: A two-dimensional array corresponding to the x variable in the TSP formulation, where\n",
+    "            x[i][j] is 1 if arc (i, j) is used.\n",
+    "\n",
+    "    Returns:\n",
+    "        A list of subtours, where each subtour is a list.\n",
+    "    \"\"\"\n",
+    "    N = len(x)\n",
+    "    marked = [False] * N\n",
+    "    subtours: list[list[int]] = []\n",
+    "\n",
+    "    while not all(marked):\n",
+    "        # Index of the first non-marked city:\n",
+    "        istart = min(range(N), key=lambda j: marked[j])\n",
+    "\n",
+    "        # Create the subtour:\n",
+    "        subtour = [istart]\n",
+    "\n",
+    "        while True:\n",
+    "            i = istart\n",
+    "            for i, b in enumerate(x[subtour[-1]]):\n",
+    "                if b:\n",
+    "                    break\n",
+    "\n",
+    "            if i == istart:\n",
+    "                break\n",
+    "\n",
+    "            subtour.append(i)\n",
+    "\n",
+    "        for i in subtour:\n",
+    "            marked[i] = True\n",
+    "\n",
+    "        subtours.append(subtour)\n",
+    "\n",
+    "    return subtours\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "699.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "from docplex.mp.model import Model\n",
+    "from docplex.mp.callbacks.cb_mixin import ConstraintCallbackMixin\n",
+    "from cplex.callbacks import LazyConstraintCallback\n",
+    "from docplex.mp.solution import SolveSolution\n",
+    "import numpy as np\n",
+    "from numpy.typing import NDArray\n",
+    "\n",
+    "import tsp.data\n",
+    "\n",
+    "\n",
+    "class SubtourConstraintCallback(ConstraintCallbackMixin, LazyConstraintCallback):\n",
+    "    x: NDArray\n",
+    "\n",
+    "    def __init__(self, env):\n",
+    "        LazyConstraintCallback.__init__(self, env)\n",
+    "        ConstraintCallbackMixin.__init__(self)\n",
+    "\n",
+    "        self.nb_callback = 0\n",
+    "        self.nb_subtours = 0\n",
+    "\n",
+    "        self.single_subtour_per_call = False\n",
+    "\n",
+    "    def __call__(self):\n",
+    "        n = len(self.x)\n",
+    "\n",
+    "        x_list = self.x.flatten().tolist()\n",
+    "\n",
+    "        sol: SolveSolution = self.make_solution_from_vars(x_list)\n",
+    "\n",
+    "        xvals = np.array(sol.get_values(x_list)).reshape(self.x.shape).astype(int)\n",
+    "        subtours = find_subtours(xvals)\n",
+    "\n",
+    "        if len(subtours) == 1:\n",
+    "            return\n",
+    "\n",
+    "        self.nb_callback += 1\n",
+    "\n",
+    "        for subtour in subtours:\n",
+    "            xs = [\n",
+    "                self.x[i, j].index\n",
+    "                for i in subtour\n",
+    "                for j in range(n)\n",
+    "                if j not in subtour\n",
+    "            ]\n",
+    "            self.add([xs, [1] * len(xs)], \"G\", 1)\n",
+    "\n",
+    "            self.nb_subtours += 1\n",
+    "\n",
+    "            if self.single_subtour_per_call:\n",
+    "                break\n",
+    "\n",
+    "\n",
+    "with Model(name=\"TSP\") as m:\n",
+    "    dist = tsp.data.grid42\n",
+    "    n = len(dist)\n",
+    "\n",
+    "    x = np.array([m.binary_var_list(n, name=f\"x_{i}\") for i in range(n)])\n",
+    "\n",
+    "    for i in range(n):\n",
+    "        m.add_constraint(x[i, :].sum() == 1)\n",
+    "        m.add_constraint(x[:, i].sum() == 1)\n",
+    "        m.add_constraint(x[i, i] == 0)\n",
+    "\n",
+    "    m.set_objective(\"min\", (x * dist).sum())\n",
+    "\n",
+    "    cb: SubtourConstraintCallback = m.register_callback(SubtourConstraintCallback)\n",
+    "    cb.x = x\n",
+    "\n",
+    "    s = m.solve()\n",
+    "\n",
+    "    print(cb.nb_subtours)\n",
+    "    print(s.get_objective_value())\n"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "INSA",
+   "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": "3.9.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}