240 lines
7.4 KiB
Plaintext
240 lines
7.4 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Exemple de modèle et résolution du problème de Fabrication du perm"
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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": 1,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General`\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.6/Project.toml`\n",
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.6/Manifest.toml`\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.6/Project.toml`\n",
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.6/Manifest.toml`\n"
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]
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}
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],
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"source": [
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"#importer les packages utiles\n",
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"import Pkg;\n",
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"Pkg.add(\"Cbc\")\n",
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"Pkg.add(\"JuMP\")"
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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": 4,
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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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"Min perm[1,1] + 2 perm[1,2] + 3 perm[1,3] + 4 perm[1,4] + 2 perm[2,1] + 3 perm[2,2] + perm[2,3] + 4 perm[2,4] + 2 perm[3,1] + perm[3,2] + 3 perm[3,3] + 4 perm[3,4] + 4 perm[4,1] + 2 perm[4,2] + 3 perm[4,3] + perm[4,4]"
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]
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},
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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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"\n",
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"Subject to\n",
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" "
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]
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},
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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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"perm[1,1] + perm[1,2] + perm[1,3] + perm[1,4] = 1.0\n",
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" perm[1,1] + perm[2,1] + perm[3,1] + perm[4,1] = 1.0\n",
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" perm[2,1] + perm[2,2] + perm[2,3] + perm[2,4] = 1.0\n",
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" perm[1,2] + perm[2,2] + perm[3,2] + perm[4,2] = 1.0\n",
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" perm[3,1] + perm[3,2] + perm[3,3] + perm[3,4] = 1.0\n",
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" perm[1,3] + perm[2,3] + perm[3,3] + perm[4,3] = 1.0\n",
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" perm[4,1] + perm[4,2] + perm[4,3] + perm[4,4] = 1.0\n",
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" perm[1,4] + perm[2,4] + perm[3,4] + perm[4,4] = 1.0\n",
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" perm[1,1] binary\n",
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" perm[2,1] binary\n",
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" perm[3,1] binary\n",
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" perm[4,1] binary\n",
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" perm[1,2] binary\n",
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" perm[2,2] binary\n",
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" perm[3,2] binary\n",
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" perm[4,2] binary\n",
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" perm[1,3] binary\n",
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" perm[2,3] binary\n",
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" perm[3,3] binary\n",
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" perm[4,3] binary\n",
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" perm[1,4] binary\n",
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" perm[2,4] binary\n",
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" perm[3,4] binary\n",
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" perm[4,4] binary\n",
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"\n"
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]
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},
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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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"Welcome to the CBC MILP Solver \n",
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"Version: 2.10.5 \n",
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"Build Date: Jan 1 1970 \n",
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"\n",
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"command line - Cbc_C_Interface -solve -quit (default strategy 1)\n",
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"Continuous objective value is 4 - 0.00 seconds\n",
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"Cgl0004I processed model has 8 rows, 16 columns (16 integer (16 of which binary)) and 32 elements\n",
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"Cutoff increment increased from 1e-05 to 0.9999\n",
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"Cbc0038I Initial state - 0 integers unsatisfied sum - 0\n",
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"Cbc0038I Solution found of 4\n",
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"Cbc0038I Before mini branch and bound, 16 integers at bound fixed and 0 continuous\n",
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"Cbc0038I Mini branch and bound did not improve solution (0.01 seconds)\n",
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"Cbc0038I After 0.01 seconds - Feasibility pump exiting with objective of 4 - took 0.00 seconds\n",
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"Cbc0012I Integer solution of 4 found by feasibility pump after 0 iterations and 0 nodes (0.01 seconds)\n",
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"Cbc0001I Search completed - best objective 4, took 0 iterations and 0 nodes (0.01 seconds)\n",
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"Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost\n",
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"Cuts at root node changed objective from 4 to 4\n",
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"Probing was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
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"Gomory was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
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"Knapsack was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
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"Clique was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
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"MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
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"FlowCover was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
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"TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
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"ZeroHalf was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
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"\n",
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"Result - Optimal solution found\n",
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"\n",
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"Objective value: 4.00000000\n",
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"Enumerated nodes: 0\n",
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"Total iterations: 0\n",
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"Time (CPU seconds): 0.01\n",
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"Time (Wallclock seconds): 0.01\n",
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"\n",
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"Total time (CPU seconds): 0.01 (Wallclock seconds): 0.02\n",
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"\n"
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]
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}
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],
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"source": [
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"using Cbc\n",
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"using JuMP\n",
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"\n",
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"# data\n",
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"N = 4\n",
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"M = [\n",
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" 1 2 3 4\n",
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" 2 3 1 4\n",
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" 2 1 3 4\n",
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" 4 2 3 1\n",
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"]\n",
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"\n",
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"# set optimizer\n",
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"model = Model(Cbc.Optimizer)\n",
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"\n",
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"# define variables\n",
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"@variable(model, perm[1:N, 1:N], binary=true)\n",
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"\n",
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"# define objective function\n",
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"@objective(model, Min, sum(M[i, j] * perm[i, j] for i = 1:N for j = 1:N))\n",
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"\n",
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"# define constraints\n",
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"for i = 1:N\n",
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" @constraint(model, sum(perm[i, j] for j = 1:N) == 1)\n",
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" @constraint(model, sum(perm[j, i] for j = 1:N) == 1)\n",
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"end\n",
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"\n",
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"println(model)\n",
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"\n",
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"# run optimization\n",
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"optimize!(model)"
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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": 13,
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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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"Solution obtenue:\n"
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]
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},
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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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"1.0 0.0 0.0 0.0 \n",
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"0.0 0.0 1.0 0.0 \n",
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"0.0 1.0 0.0 0.0 \n",
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"0.0 0.0 0.0 1.0 \n"
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]
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}
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],
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"source": [
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"# print solution\n",
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"println(\"Solution obtenue:\")\n",
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"for i in 1:N\n",
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" for j in 1:N \n",
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" print(\"$(value(perm[i,j])) \")\n",
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" end\n",
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" println()\n",
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"end"
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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": "Julia 1.6.3",
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"language": "julia",
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"name": "julia-1.6"
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},
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"language_info": {
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"file_extension": ".jl",
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"mimetype": "application/julia",
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"name": "julia",
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"version": "1.6.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}
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