1039 lines
101 KiB
Plaintext
1039 lines
101 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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"# TP 2-3 : Branch-and-bound applied to a knapsack problem"
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]
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},
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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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"### Initialisation (à faire une seule fois)"
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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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"import Pkg; \n",
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"Pkg.add(\"GraphRecipes\"); Pkg.add(\"Plots\"); \n",
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"using GraphRecipes, Plots #only used to visualize the search tree at the end of the branch-and-bound"
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]
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},
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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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"### Récupération des données"
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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": 2,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"readKnaptxtInstance (generic function with 1 method)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"function readKnaptxtInstance(filename)\n",
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" price=[]\n",
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" weight=[]\n",
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" KnapCap=[]\n",
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" open(filename) do f\n",
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" for i in 1:3\n",
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" tok = split(readline(f))\n",
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" if (tok[1] == \"ListPrices=\")\n",
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" for i in 2:(length(tok)-1)\n",
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" push!(price,parse(Int64, tok[i]))\n",
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" end\n",
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" elseif(tok[1] == \"ListWeights=\")\n",
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" for i in 2:(length(tok)-1)\n",
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" push!(weight,parse(Int64, tok[i]))\n",
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" end\n",
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" elseif(tok[1] == \"Capacity=\")\n",
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" push!(KnapCap, parse(Int64, tok[2]))\n",
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" else\n",
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" println(\"Unknown read :\", tok)\n",
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" end \n",
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" end\n",
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" end\n",
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" capacity=KnapCap[1]\n",
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" return price, weight, capacity\n",
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"end"
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]
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},
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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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"### Procédure d'application des tests de sondabilités TA, TO et TR pour le cas de la relaxation linéaire"
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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": 3,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"TestsSondabilite_relaxlin (generic function with 1 method)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"function TestsSondabilite_relaxlin(model2, x, varsbin, BestProfit, Bestsol)\n",
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" TA, TO, TR = false, false, false\n",
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" if (termination_status(model2) == MOI.INFEASIBLE)#Test de faisabilite\n",
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" TA=true\n",
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" println(\"TA\")\n",
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" elseif (objective_value(model2) <= BestProfit) #Test d'optimalite\n",
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" TO=true\n",
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" println(\"TO\")\n",
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" elseif ( prod(abs.([round.(v, digits=0) for v in value.(varsbin)]-value.(varsbin)) .<= fill(10^-5, size(varsbin))) \n",
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" ) #Test de resolution\n",
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" TR=true\n",
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" println(\"TR\")\n",
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" #if (value(benef) >= BestProfit)\n",
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" if (objective_value(model2) >= BestProfit)\n",
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" Bestsol = value.(x)\n",
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" #BestProfit=value(benef)\n",
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" BestProfit=objective_value(model2)\n",
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" end\n",
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" else\n",
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" println(\"non sondable\")\n",
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" end\n",
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" TA, TO, TR, Bestsol, BestProfit\n",
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"end"
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]
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},
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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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"### Procédure de séparation et stratégie d'exploration permettant de se placer au prochain noeud à traiter"
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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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"data": {
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"text/plain": [
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"ExplorerAutreNoeud_relaxlin (generic function with 1 method)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"\n",
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"function SeparerNoeud_relaxlin(varsshouldbebinary, listvars, listvals)\n",
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" # le noeud est non-sondable. Appliquer le critère de séparation pour le séparer en sous-noeuds \n",
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" # et choisir un noeud-fils le plus à gauche \n",
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" \n",
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" #find a fractionnal variable\n",
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" i, var = 1, 0\n",
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" while ((i <= length(varsshouldbebinary)) && (var==0))\n",
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" #if (varsshouldbebinary[i] ∉ listvars)\n",
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" if (abs(round(value(varsshouldbebinary[i]), digits=0) - value(varsshouldbebinary[i]) ) >= 10^-5)\n",
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" var=varsshouldbebinary[i]\n",
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" end\n",
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" i+=1\n",
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" end\n",
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" \n",
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" #=\n",
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" #find most fractionnal variable ?\n",
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" i, var, maxfrac = -1, 0, 0.0\n",
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" for i in 1:length(varsshouldbebinary)\n",
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" if (abs(round(value(varsshouldbebinary[i]), digits=0) - value(varsshouldbebinary[i]) ) >= maxfrac) \n",
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" #if a variable is more fractinonal\n",
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" var=varsshouldbebinary[i]\n",
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" maxfrac=abs(round(value(varsshouldbebinary[i]), digits=0) - value(varsshouldbebinary[i]) )\n",
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" #println(i, \" \", var, \" \", maxfrac)\n",
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" end\n",
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" end\n",
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" =#\n",
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" \n",
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"\n",
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" set_lower_bound(var,1.0)\n",
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" set_upper_bound(var,1.0)\n",
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"\n",
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" push!(listvars,var) #stocker l'identite de la variable choisie pour la séparation\n",
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" push!(listvals,1.0) #stocker la branche choisie, identifiee par la valeur de la variable choisie\n",
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" listvars, listvals\n",
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"end\n",
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"\n",
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"\n",
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"function ExplorerAutreNoeud_relaxlin(listvars, listvals, listnodes)\n",
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" #this node is sondable, go back to parent node then right child if possible\n",
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" \n",
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" stop=false\n",
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" #check if we are not at the root node\n",
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" if (length(listvars)>= 1)\n",
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" #go back to parent node\n",
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" var=pop!(listvars)\n",
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" theval=pop!(listvals)\n",
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" tmp=pop!(listnodes)\n",
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" set_lower_bound(var,0.0)\n",
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" set_upper_bound(var,1.0)\n",
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"\n",
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" #go to right child if possible, otherwise go back to parent\n",
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" while ( (theval==0.0) && (length(listvars)>= 1))\n",
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" var=pop!(listvars)\n",
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" theval=pop!(listvals)\n",
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" tmp=pop!(listnodes)\n",
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" set_lower_bound(var,0.0) \n",
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" set_upper_bound(var,1.0)\n",
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" end\n",
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" if theval==1.0\n",
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" set_lower_bound(var,0.0)\n",
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" set_upper_bound(var,0.0)\n",
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" push!(listvars,var)\n",
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" push!(listvals,0.0)\n",
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" else\n",
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" println(\"\\nFINISHED\")\n",
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" stop=true\n",
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" end\n",
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" else\n",
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" #the root node was sondable\n",
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" println(\"\\nFINISHED\")\n",
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" stop=true\n",
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" end\n",
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" listvars, listvals, listnodes, stop \n",
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"end"
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]
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},
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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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"### Création de la relaxation linéaire (= modèle associé au noeud 0): <span style=\"color:red\"> SECTION A SUPPRIMER !!!! </span>\n",
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"\n",
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"<span style=\"color:red\"> Cette section est à commenter/supprimer et remplacer par vos propres calculs de bornes supérieures et autres, par exemple basées sur les bornes 1 et 2 vues en cours, ou d'autres calculs de bornes de votre choix/conception validés au préalable par votre encadrant/e de TP </span>"
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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": 5,
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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 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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"Pkg.add(\"Clp\");\n",
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"using JuMP, Clp"
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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": 6,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"CreationModeleLP (generic function with 1 method)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"function CreationModeleLP(price, weight, capacity)\n",
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"# ROOT NODE\n",
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" \n",
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" model2 = Model(Clp.Optimizer) # set optimizer\n",
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" set_optimizer_attribute(model2, \"LogLevel\", 0) #don't display anything during solve\n",
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" set_optimizer_attribute(model2, \"Algorithm\", 4) #LP solver chosen is simplex\n",
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"\n",
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" # define x variables as CONTINUOUS (recall that it is not possible to define binary variables in Clp)\n",
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" @variable(model2, 0 <= x[i in 1:4] <= 1)\n",
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" varsshouldbebinary=[x[1] x[2] x[3] x[4]]\n",
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"\n",
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" # define objective function\n",
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" @objective(model2, Max, sum(price[i]*x[i] for i in 1:4))\n",
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"\n",
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" # define the capacity constraint \n",
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" @constraint(model2, sum(weight[i]*x[i] for i in 1:4) <= capacity)\n",
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"\n",
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" println(model2)\n",
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"\n",
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" return model2, x, varsshouldbebinary\n",
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"end\n"
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]
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},
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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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"### Boucle principale : résoudre la relaxation linéaire, appliquer les tests de sondabilité, identifier le prochain noeud, répéter."
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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": 7,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"SolveKnapInstance (generic function with 1 method)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"\n",
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"function SolveKnapInstance(filename)\n",
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"\n",
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" if (split(filename,\"/\")[end] != \"test.opb\")\n",
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" println(\"This version of the code works only for the test instance !!!!\")\n",
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" else\n",
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" price, weight, capacity = readKnaptxtInstance(filename)\n",
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" model2, x, varsshouldbebinary = CreationModeleLP(price, weight, capacity)\n",
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" \n",
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" #create the structure to memorize the search tree for visualization at the end\n",
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" trParentnodes=Int64[] #will store orig node of arc in search tree\n",
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" trChildnodes=Int64[] #will store destination node of arc in search tree\n",
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" trNamenodes=[] #will store names of nodes in search tree\n",
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" \n",
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" #intermediate structure to navigate in the search tree\n",
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" listvars=[]\n",
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" listvals=[]\n",
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" listnodes=[]\n",
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"\n",
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" BestProfit=-1\n",
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" Bestsol=[]\n",
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"\n",
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" current_node_number=0\n",
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" stop = false\n",
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"\n",
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" while (!stop)\n",
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"\n",
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" println(\"\\nNode number \", current_node_number, \": \\n-----\\n\", model2)\n",
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"\n",
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" #Update the search tree\n",
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" push!(trNamenodes,current_node_number+1) \n",
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" if (length(trNamenodes)>=2)\n",
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" push!(trParentnodes,listnodes[end]+1) # +1 because the 1st node is \"node 0\"\n",
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" push!(trChildnodes, current_node_number+1) # +1 because the 1st node is \"node 0\"\n",
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" end\n",
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" push!(listnodes, current_node_number)\n",
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"\n",
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"\n",
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" print(\"Solve model2 to compute the bounds of the current node: start ... \")\n",
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" status = optimize!(model2)\n",
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" println(\"... end\")\n",
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"\n",
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" print(\"\\nSolution relax lin\"); \n",
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" if (termination_status(model2) == MOI.INFEASIBLE)#(has_values(model2))\n",
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" print(\" : NOT AVAILABLE (probably infeasible or ressources limit reached)\")\n",
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" else\n",
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" [print(\"\\t\", name(v),\"=\",value(v)) for v in all_variables(model2)] \n",
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" end\n",
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" println(\" \"); println(\"\\nPrevious Solution memorized \", Bestsol, \" with bestprofit \", BestProfit, \"\\n\")\n",
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"\n",
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" TA, TO, TR, Bestsol, BestProfit = TestsSondabilite_relaxlin(model2, x, varsshouldbebinary, BestProfit, Bestsol)\n",
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"\n",
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" is_node_sondable = TA || TO || TR\n",
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"\n",
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" if (!is_node_sondable)\n",
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" listvars, listvals = SeparerNoeud_relaxlin(varsshouldbebinary, listvars, listvals)\n",
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" else\n",
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" listvars, listvals, listnodes, stop = ExplorerAutreNoeud_relaxlin(listvars, listvals, listnodes)\n",
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" end\n",
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"\n",
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" current_node_number = current_node_number + 1\n",
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" end\n",
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"\n",
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" println(\"\\n******\\n\\nOptimal value = \", BestProfit, \"\\n\\nOptimal x=\", Bestsol)\n",
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"\n",
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" return BestProfit, Bestsol, trParentnodes, trChildnodes, trNamenodes\n",
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" end\n",
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"\n",
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"end\n"
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]
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},
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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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"### Affichage du résultat final"
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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": 8,
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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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"Max 42 x[1] + 40 x[2] + 12 x[3] + 25 x[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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"7 x[1] + 4 x[2] + 3 x[3] + 5 x[4] ≤ 10.0\n",
|
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" x[1] ≥ 0.0\n",
|
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" x[2] ≥ 0.0\n",
|
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" x[3] ≥ 0.0\n",
|
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" x[4] ≥ 0.0\n",
|
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" x[1] ≤ 1.0\n",
|
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" x[2] ≤ 1.0\n",
|
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" x[3] ≤ 1.0\n",
|
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" x[4] ≤ 1.0\n",
|
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"\n",
|
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"\n",
|
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"Node number 0: \n",
|
|
"-----\n",
|
|
"Max 42 x[1] + 40 x[2] + 12 x[3] + 25 x[4]\n",
|
|
"Subject to\n",
|
|
" 7 x[1] + 4 x[2] + 3 x[3] + 5 x[4] ≤ 10.0\n",
|
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" x[1] ≥ 0.0\n",
|
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" x[2] ≥ 0.0\n",
|
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" x[3] ≥ 0.0\n",
|
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" x[4] ≥ 0.0\n",
|
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" x[1] ≤ 1.0\n",
|
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" x[2] ≤ 1.0\n",
|
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" x[3] ≤ 1.0\n",
|
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" x[4] ≤ 1.0\n",
|
|
"\n",
|
|
"Solve model2 to compute the bounds of the current node: start ... "
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
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"output_type": "stream",
|
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"text": [
|
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"... end\n",
|
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"\n",
|
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"Solution relax lin\t"
|
|
]
|
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},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
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"text": [
|
|
"x[1]=0.857142857142857\tx[2]=1.0\tx[3]=0.0\tx[4]=0.0 \n",
|
|
"\n",
|
|
"Previous Solution memorized "
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
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"text": [
|
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"Any[] with bestprofit -1\n",
|
|
"\n",
|
|
"non sondable"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n",
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"\n",
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"Node number "
|
|
]
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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: \n",
|
|
"-----\n",
|
|
"Max 42 x[1] + 40 x[2] + 12 x[3] + 25 x[4]\n",
|
|
"Subject to\n",
|
|
" 7 x[1] + 4 x[2] + 3 x[3] + 5 x[4] ≤ 10.0\n",
|
|
" x[1] ≥ 1.0\n",
|
|
" x[2] ≥ 0.0\n",
|
|
" x[3] ≥ 0.0\n",
|
|
" x[4] ≥ 0.0\n",
|
|
" x[1] ≤ 1.0\n",
|
|
" x[2] ≤ 1.0\n",
|
|
" x[3] ≤ 1.0\n",
|
|
" x[4] ≤ 1.0\n",
|
|
"\n",
|
|
"Solve model2 to compute the bounds of the current node: start ... ... end\n",
|
|
"\n",
|
|
"Solution relax lin\tx[1]=1.0\tx[2]=0.7500000000000001\tx[3]=0.0\tx[4]=0.0 \n",
|
|
"\n",
|
|
"Previous Solution memorized Any[] with bestprofit -1\n",
|
|
"\n",
|
|
"non sondable\n",
|
|
"\n",
|
|
"Node number 2: \n",
|
|
"-----\n",
|
|
"Max 42 x[1] + 40 x[2] + 12 x[3] + 25 x[4]\n",
|
|
"Subject to\n",
|
|
" 7 x[1] + 4 x[2] + 3 x[3] + 5 x[4] ≤ 10.0\n",
|
|
" x[1] ≥ 1.0\n",
|
|
" x[2] ≥ 1.0\n",
|
|
" x[3] ≥ 0.0\n",
|
|
" x[4] ≥ 0.0\n",
|
|
" x[1] ≤ 1.0\n",
|
|
" x[2] ≤ 1.0\n",
|
|
" x[3] ≤ 1.0\n",
|
|
" x[4] ≤ 1.0\n",
|
|
"\n",
|
|
"Solve model2 to compute the bounds of the current node: start ... ... end\n",
|
|
"\n",
|
|
"Solution relax lin : NOT AVAILABLE (probably infeasible or ressources limit reached) \n",
|
|
"\n",
|
|
"Previous Solution memorized Any[] with bestprofit -1\n",
|
|
"\n",
|
|
"TA\n",
|
|
"\n",
|
|
"Node number 3: \n",
|
|
"-----\n",
|
|
"Max 42 x[1] + 40 x[2] + 12 x[3] + 25 x[4]\n",
|
|
"Subject to\n",
|
|
" 7 x[1] + 4 x[2] + 3 x[3] + 5 x[4] ≤ 10.0\n",
|
|
" x[1] ≥ 1.0\n",
|
|
" x[2] ≥ 0.0\n",
|
|
" x[3] ≥ 0.0\n",
|
|
" x[4] ≥ 0.0\n",
|
|
" x[1] ≤ 1.0\n",
|
|
" x[2] ≤ 0.0\n",
|
|
" x[3] ≤ 1.0\n",
|
|
" x[4] ≤ 1.0\n",
|
|
"\n",
|
|
"Solve model2 to compute the bounds of the current node: start ... ... end\n",
|
|
"\n",
|
|
"Solution relax lin\tx[1]=1.0\tx[2]=0.0\tx[3]=0.0\tx[4]=0.6 \n",
|
|
"\n",
|
|
"Previous Solution memorized Any[] with bestprofit -1\n",
|
|
"\n",
|
|
"non sondable\n",
|
|
"\n",
|
|
"Node number 4: \n",
|
|
"-----\n",
|
|
"Max 42 x[1] + 40 x[2] + 12 x[3] + 25 x[4]\n",
|
|
"Subject to\n",
|
|
" 7 x[1] + 4 x[2] + 3 x[3] + 5 x[4] ≤ 10.0\n",
|
|
" x[1] ≥ 1.0\n",
|
|
" x[2] ≥ 0.0\n",
|
|
" x[3] ≥ 0.0\n",
|
|
" x[4] ≥ 1.0\n",
|
|
" x[1] ≤ 1.0\n",
|
|
" x[2] ≤ 0.0\n",
|
|
" x[3] ≤ 1.0\n",
|
|
" x[4] ≤ 1.0\n",
|
|
"\n",
|
|
"Solve model2 to compute the bounds of the current node: start ... ... end\n",
|
|
"\n",
|
|
"Solution relax lin : NOT AVAILABLE (probably infeasible or ressources limit reached) \n",
|
|
"\n",
|
|
"Previous Solution memorized Any[] with bestprofit -1\n",
|
|
"\n",
|
|
"TA\n",
|
|
"\n",
|
|
"Node number 5: \n",
|
|
"-----\n",
|
|
"Max 42 x[1] + 40 x[2] + 12 x[3] + 25 x[4]\n",
|
|
"Subject to\n",
|
|
" 7 x[1] + 4 x[2] + 3 x[3] + 5 x[4] ≤ 10.0\n",
|
|
" x[1] ≥ 1.0\n",
|
|
" x[2] ≥ 0.0\n",
|
|
" x[3] ≥ 0.0\n",
|
|
" x[4] ≥ 0.0\n",
|
|
" x[1] ≤ 1.0\n",
|
|
" x[2] ≤ 0.0\n",
|
|
" x[3] ≤ 1.0\n",
|
|
" x[4] ≤ 0.0\n",
|
|
"\n",
|
|
"Solve model2 to compute the bounds of the current node: start ... ... end\n",
|
|
"\n",
|
|
"Solution relax lin\tx[1]=1.0\tx[2]=0.0\tx[3]=1.0\tx[4]=0.0 \n",
|
|
"\n",
|
|
"Previous Solution memorized Any[] with bestprofit -1\n",
|
|
"\n",
|
|
"TR\n",
|
|
"\n",
|
|
"Node number 6: \n",
|
|
"-----\n",
|
|
"Max 42 x[1] + 40 x[2] + 12 x[3] + 25 x[4]\n",
|
|
"Subject to\n",
|
|
" 7 x[1] + 4 x[2] + 3 x[3] + 5 x[4] ≤ 10.0\n",
|
|
" x[1] ≥ 0.0\n",
|
|
" x[2] ≥ 0.0\n",
|
|
" x[3] ≥ 0.0\n",
|
|
" x[4] ≥ 0.0\n",
|
|
" x[1] ≤ 0.0\n",
|
|
" x[2] ≤ 1.0\n",
|
|
" x[3] ≤ 1.0\n",
|
|
" x[4] ≤ 1.0\n",
|
|
"\n",
|
|
"Solve model2 to compute the bounds of the current node: start ... ... end\n",
|
|
"\n",
|
|
"Solution relax lin\tx[1]=0.0\tx[2]=1.0\tx[3]=0.3333333333333332\tx[4]=1.0 \n",
|
|
"\n",
|
|
"Previous Solution memorized "
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"[1.0, 0.0, 1.0, 0.0] with bestprofit 54.0\n",
|
|
"\n",
|
|
"non sondable\n",
|
|
"\n",
|
|
"Node number 7: \n",
|
|
"-----\n",
|
|
"Max 42 x[1] + 40 x[2] + 12 x[3] + 25 x[4]\n",
|
|
"Subject to\n",
|
|
" 7 x[1] + 4 x[2] + 3 x[3] + 5 x[4] ≤ 10.0\n",
|
|
" x[1] ≥ 0.0\n",
|
|
" x[2] ≥ 0.0\n",
|
|
" x[3] ≥ 1.0\n",
|
|
" x[4] ≥ 0.0\n",
|
|
" x[1] ≤ 0.0\n",
|
|
" x[2] ≤ 1.0\n",
|
|
" x[3] ≤ 1.0\n",
|
|
" x[4] ≤ 1.0\n",
|
|
"\n",
|
|
"Solve model2 to compute the bounds of the current node: start ... ... end\n",
|
|
"\n",
|
|
"Solution relax lin\tx[1]=0.0\tx[2]=1.0\tx[3]=1.0\tx[4]=0.6000000000000001 \n",
|
|
"\n",
|
|
"Previous Solution memorized [1.0, 0.0, 1.0, 0.0] with bestprofit 54.0\n",
|
|
"\n",
|
|
"non sondable\n",
|
|
"\n",
|
|
"Node number 8: \n",
|
|
"-----\n",
|
|
"Max 42 x[1] + 40 x[2] + 12 x[3] + 25 x[4]\n",
|
|
"Subject to\n",
|
|
" 7 x[1] + 4 x[2] + 3 x[3] + 5 x[4] ≤ 10.0\n",
|
|
" x[1] ≥ 0.0\n",
|
|
" x[2] ≥ 0.0\n",
|
|
" x[3] ≥ 1.0\n",
|
|
" x[4] ≥ 1.0\n",
|
|
" x[1] ≤ 0.0\n",
|
|
" x[2] ≤ 1.0\n",
|
|
" x[3] ≤ 1.0\n",
|
|
" x[4] ≤ 1.0\n",
|
|
"\n",
|
|
"Solve model2 to compute the bounds of the current node: start ... ... end\n",
|
|
"\n",
|
|
"Solution relax lin\tx[1]=0.0\tx[2]=0.5\tx[3]=1.0\tx[4]=1.0 \n",
|
|
"\n",
|
|
"Previous Solution memorized [1.0, 0.0, 1.0, 0.0] with bestprofit 54.0\n",
|
|
"\n",
|
|
"non sondable\n",
|
|
"\n",
|
|
"Node number 9: \n",
|
|
"-----\n",
|
|
"Max 42 x[1] + 40 x[2] + 12 x[3] + 25 x[4]\n",
|
|
"Subject to\n",
|
|
" 7 x[1] + 4 x[2] + 3 x[3] + 5 x[4] ≤ 10.0\n",
|
|
" x[1] ≥ 0.0\n",
|
|
" x[2] ≥ 1.0\n",
|
|
" x[3] ≥ 1.0\n",
|
|
" x[4] ≥ 1.0\n",
|
|
" x[1] ≤ 0.0\n",
|
|
" x[2] ≤ 1.0\n",
|
|
" x[3] ≤ 1.0\n",
|
|
" x[4] ≤ 1.0\n",
|
|
"\n",
|
|
"Solve model2 to compute the bounds of the current node: start ... ... end\n",
|
|
"\n",
|
|
"Solution relax lin : NOT AVAILABLE (probably infeasible or ressources limit reached) \n",
|
|
"\n",
|
|
"Previous Solution memorized [1.0, 0.0, 1.0, 0.0] with bestprofit 54.0\n",
|
|
"\n",
|
|
"TA\n",
|
|
"\n",
|
|
"Node number 10: \n",
|
|
"-----\n",
|
|
"Max 42 x[1] + 40 x[2] + 12 x[3] + 25 x[4]\n",
|
|
"Subject to\n",
|
|
" 7 x[1] + 4 x[2] + 3 x[3] + 5 x[4] ≤ 10.0\n",
|
|
" x[1] ≥ 0.0\n",
|
|
" x[2] ≥ 0.0\n",
|
|
" x[3] ≥ 1.0\n",
|
|
" x[4] ≥ 1.0\n",
|
|
" x[1] ≤ 0.0\n",
|
|
" x[2] ≤ 0.0\n",
|
|
" x[3] ≤ 1.0\n",
|
|
" x[4] ≤ 1.0\n",
|
|
"\n",
|
|
"Solve model2 to compute the bounds of the current node: start ... ... end\n",
|
|
"\n",
|
|
"Solution relax lin\tx[1]=0.0\tx[2]=0.0\tx[3]=1.0\tx[4]=1.0 \n",
|
|
"\n",
|
|
"Previous Solution memorized [1.0, 0.0, 1.0, 0.0] with bestprofit 54.0\n",
|
|
"\n",
|
|
"TO\n",
|
|
"\n",
|
|
"Node number 11: \n",
|
|
"-----\n",
|
|
"Max 42 x[1] + 40 x[2] + 12 x[3] + 25 x[4]\n",
|
|
"Subject to\n",
|
|
" 7 x[1] + 4 x[2] + 3 x[3] + 5 x[4] ≤ 10.0\n",
|
|
" x[1] ≥ 0.0\n",
|
|
" x[2] ≥ 0.0\n",
|
|
" x[3] ≥ 1.0\n",
|
|
" x[4] ≥ 0.0\n",
|
|
" x[1] ≤ 0.0\n",
|
|
" x[2] ≤ 1.0\n",
|
|
" x[3] ≤ 1.0\n",
|
|
" x[4] ≤ 0.0\n",
|
|
"\n",
|
|
"Solve model2 to compute the bounds of the current node: start ... ... end\n",
|
|
"\n",
|
|
"Solution relax lin\tx[1]=0.0\tx[2]=1.0\tx[3]=1.0\tx[4]=0.0 \n",
|
|
"\n",
|
|
"Previous Solution memorized [1.0, 0.0, 1.0, 0.0] with bestprofit 54.0\n",
|
|
"\n",
|
|
"TO\n",
|
|
"\n",
|
|
"Node number 12: \n",
|
|
"-----\n",
|
|
"Max 42 x[1] + 40 x[2] + 12 x[3] + 25 x[4]\n",
|
|
"Subject to\n",
|
|
" 7 x[1] + 4 x[2] + 3 x[3] + 5 x[4] ≤ 10.0\n",
|
|
" x[1] ≥ 0.0\n",
|
|
" x[2] ≥ 0.0\n",
|
|
" x[3] ≥ 0.0\n",
|
|
" x[4] ≥ 0.0\n",
|
|
" x[1] ≤ 0.0\n",
|
|
" x[2] ≤ 1.0\n",
|
|
" x[3] ≤ 0.0\n",
|
|
" x[4] ≤ 1.0\n",
|
|
"\n",
|
|
"Solve model2 to compute the bounds of the current node: start ... ... end\n",
|
|
"\n",
|
|
"Solution relax lin\tx[1]=0.0\tx[2]=1.0\tx[3]=0.0\tx[4]=1.0 \n",
|
|
"\n",
|
|
"Previous Solution memorized [1.0, 0.0, 1.0, 0.0] with bestprofit 54.0\n",
|
|
"\n",
|
|
"TR\n",
|
|
"\n",
|
|
"FINISHED\n",
|
|
"\n",
|
|
"******\n",
|
|
"\n",
|
|
"Optimal value = 65.0\n",
|
|
"\n",
|
|
"Optimal x=[0.0, 1.0, 0.0, 1.0]\n",
|
|
"\n",
|
|
"******\n",
|
|
"\n",
|
|
"Optimal value = 65.0\n",
|
|
"\n",
|
|
"Optimal x=[0.0, 1.0, 0.0, 1.0]\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": 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|
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]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"BestProfit, Bestsol, trParentnodes, trChildnodes, trNamenodes = SolveKnapInstance(\"data/test.opb\")\n",
|
|
"println(\"\\n******\\n\\nOptimal value = \", BestProfit, \"\\n\\nOptimal x=\", Bestsol)\n",
|
|
"graphplot(trParentnodes, trChildnodes, names=trNamenodes, method=:tree)"
|
|
]
|
|
}
|
|
],
|
|
"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
|
|
}
|