Add third notebook using CPLEX callbacks.
This commit is contained in:
Mikaël Capelle
parent
06b0f2b5d9
commit
d11d5ede42
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@ -47,7 +47,7 @@
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"... # TODO\n",
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"\n",
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"solution = tsp.solve()\n",
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"print(\"z* =\", solution.objective_value)"
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"print(\"z* =\", solution.objective_value)\n"
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]
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},
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{
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@ -90,7 +90,7 @@
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"... # TODO: Copy your model from the first question here.\n",
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"\n",
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"solution = tsp.solve()\n",
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"print(\"z* =\", solution.objective_value)"
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"print(\"z* =\", solution.objective_value)\n"
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]
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},
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{
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@ -147,7 +147,7 @@
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"... # TODO: Model for the warehouse allocation.\n",
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"\n",
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"solution = wa.solve()\n",
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"print(\"z* =\", solution.objective_value)"
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"print(\"z* =\", solution.objective_value)\n"
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]
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},
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{
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@ -230,7 +230,7 @@
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"\n",
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"# Check your method:\n",
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"wa, z, y = create_master_problem(N, M, f, c)\n",
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"print(wa.export_as_lp_string())"
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"print(wa.export_as_lp_string())\n"
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]
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},
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{
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@ -270,7 +270,7 @@
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"\n",
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" Return: The optimality constraint added.\n",
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" \"\"\"\n",
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" return ... # TODO"
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" return ... # TODO\n"
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]
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},
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{
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@ -312,7 +312,7 @@
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" The feasibility constraint added.\n",
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" \"\"\"\n",
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" # TODO:\n",
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" return"
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" return\n"
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]
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},
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{
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@ -370,7 +370,7 @@
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"\n",
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"# Check your method (assuming y = [1 1 1 ... 1]):\n",
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"dsp, v, u = create_dual_subproblem(N, M, f, c, [1] * M)\n",
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"print(dsp.export_as_lp_string())"
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"print(dsp.export_as_lp_string())\n"
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]
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},
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{
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@ -466,7 +466,7 @@
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"\n",
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" ... # TODO\n",
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"\n",
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"print(\"Done.\")"
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"print(\"Done.\")\n"
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]
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},
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{
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@ -509,7 +509,7 @@
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.2"
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"version": "3.9.13"
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}
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},
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"nbformat": 4,
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@ -0,0 +1,163 @@
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"from typing import Sequence\n",
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"\n",
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"\n",
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"def find_subtours(x: Sequence[Sequence[int]]) -> Sequence[Sequence[int]]:\n",
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" \"\"\"\n",
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" Extracts subtours from the given 2D-array.\n",
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"\n",
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" Args:\n",
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" x: A two-dimensional array corresponding to the x variable in the TSP formulation, where\n",
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" x[i][j] is 1 if arc (i, j) is used.\n",
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"\n",
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" Returns:\n",
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" A list of subtours, where each subtour is a list.\n",
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" \"\"\"\n",
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" N = len(x)\n",
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" marked = [False] * N\n",
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" subtours: list[list[int]] = []\n",
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"\n",
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" while not all(marked):\n",
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" # Index of the first non-marked city:\n",
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" istart = min(range(N), key=lambda j: marked[j])\n",
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"\n",
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" # Create the subtour:\n",
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" subtour = [istart]\n",
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"\n",
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" while True:\n",
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" i = istart\n",
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" for i, b in enumerate(x[subtour[-1]]):\n",
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" if b:\n",
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" break\n",
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"\n",
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" if i == istart:\n",
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" break\n",
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"\n",
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" subtour.append(i)\n",
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"\n",
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" for i in subtour:\n",
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" marked[i] = True\n",
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"\n",
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" subtours.append(subtour)\n",
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"\n",
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" return subtours\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 44,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"699.0\n"
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]
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}
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],
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"source": [
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"from docplex.mp.model import Model\n",
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"from docplex.mp.callbacks.cb_mixin import ConstraintCallbackMixin\n",
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"from cplex.callbacks import LazyConstraintCallback\n",
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"from docplex.mp.solution import SolveSolution\n",
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"import numpy as np\n",
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"from numpy.typing import NDArray\n",
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"\n",
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"import tsp.data\n",
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"\n",
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"\n",
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"class SubtourConstraintCallback(ConstraintCallbackMixin, LazyConstraintCallback):\n",
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" x: NDArray\n",
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"\n",
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" def __init__(self, env):\n",
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" LazyConstraintCallback.__init__(self, env)\n",
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" ConstraintCallbackMixin.__init__(self)\n",
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"\n",
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" self.nb_callback = 0\n",
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" self.nb_subtours = 0\n",
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"\n",
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" self.single_subtour_per_call = False\n",
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"\n",
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" def __call__(self):\n",
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" n = len(self.x)\n",
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"\n",
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" x_list = self.x.flatten().tolist()\n",
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"\n",
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" sol: SolveSolution = self.make_solution_from_vars(x_list)\n",
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"\n",
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" xvals = np.array(sol.get_values(x_list)).reshape(self.x.shape).astype(int)\n",
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" subtours = find_subtours(xvals)\n",
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"\n",
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" if len(subtours) == 1:\n",
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" return\n",
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"\n",
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" self.nb_callback += 1\n",
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"\n",
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" for subtour in subtours:\n",
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" xs = [\n",
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" self.x[i, j].index\n",
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" for i in subtour\n",
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" for j in range(n)\n",
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" if j not in subtour\n",
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" ]\n",
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" self.add([xs, [1] * len(xs)], \"G\", 1)\n",
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"\n",
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" self.nb_subtours += 1\n",
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"\n",
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" if self.single_subtour_per_call:\n",
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" break\n",
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"\n",
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"\n",
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"with Model(name=\"TSP\") as m:\n",
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" dist = tsp.data.grid42\n",
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" n = len(dist)\n",
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"\n",
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" x = np.array([m.binary_var_list(n, name=f\"x_{i}\") for i in range(n)])\n",
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"\n",
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" for i in range(n):\n",
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" m.add_constraint(x[i, :].sum() == 1)\n",
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" m.add_constraint(x[:, i].sum() == 1)\n",
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" m.add_constraint(x[i, i] == 0)\n",
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"\n",
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" m.set_objective(\"min\", (x * dist).sum())\n",
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"\n",
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" cb: SubtourConstraintCallback = m.register_callback(SubtourConstraintCallback)\n",
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" cb.x = x\n",
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"\n",
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" s = m.solve()\n",
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"\n",
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" print(cb.nb_subtours)\n",
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" print(s.get_objective_value())\n"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "INSA",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.9.13"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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