TP-recherche-operationnelle/TP1/exo2/personnel.ipynb

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