{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# TP 2-3 : Branch-and-bound applied to a knapsack problem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Initialisation (à faire une seule fois)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General`\n", "\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n", "\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", "\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n", "\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": [ "import Pkg; \n", "Pkg.add(\"GraphRecipes\"); Pkg.add(\"Plots\"); \n", "using GraphRecipes, Plots #only used to visualize the search tree at the end of the branch-and-bound" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Récupération des données" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(Any[42, 40, 12, 25], Any[7, 4, 3, 5], 10)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function readKnapInstance(filename)\n", " price=[]\n", " weight=[]\n", " capacity = -1\n", " open(filename) do f\n", " for i in 1:3\n", " tok = split(readline(f))\n", " if (tok[1] == \"ListPrices=\")\n", " for i in 2:(length(tok)-1)\n", " push!(price,parse(Int64, tok[i]))\n", " end\n", " elseif (tok[1] == \"ListWeights=\")\n", " for i in 2:(length(tok)-1)\n", " push!(weight,parse(Int64, tok[i]))\n", " end\n", " elseif (tok[1] == \"Capacity=\")\n", " capacity = parse(Int64, tok[2])\n", " else\n", " println(\"Unknown read :\", tok)\n", " end \n", " end\n", " end\n", " \n", " return price, weight, capacity\n", "end\n", "\n", "# readKnapInstance(\"data/test.opb\")\n", "# readKnapInstance(\"data/almost_strongly_correlated/knapPI_5_50_1000_1_-2096.opb\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Procédure d'application des tests de sondabilités TA, TO et TR pour le cas de la relaxation linéaire" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "TestsSondabilite_relaxlin (generic function with 1 method)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function TestsSondabilite_relaxlin(x, price, weight, capacity, varsbin, BestProfit, Bestsol)\n", " TA, TO, TR = false, false, false\n", " if (!Constraints(x, weight, capacity)) # Test de faisabilite\n", " TA = true\n", " println(\"TA\")\n", " elseif (Objective(x, price) <= BestProfit) # Test d'optimalite\n", " TO = true\n", " println(\"TO\")\n", " elseif (AllDef(x)) # Test de resolution\n", " TR = true\n", " println(\"TR\")\n", " #if (value(benef) >= BestProfit)\n", " if (Objective(x, price) >= BestProfit)\n", " Bestsol = x\n", " #BestProfit=value(benef)\n", " BestProfit = Objective(x, price)\n", " end\n", " else\n", " println(\"non sondable\")\n", " end\n", " TA, TO, TR, Bestsol, BestProfit\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Procédure de séparation et stratégie d'exploration permettant de se placer au prochain noeud à traiter" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "ExplorerAutreNoeud_relaxlin (generic function with 1 method)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\n", "function SeparerNoeud_relaxlin(varsshouldbebinary, listvars, listvals)\n", " # le noeud est non-sondable. Appliquer le critère de séparation pour le séparer en sous-noeuds et choisir un noeud-fils le plus à gauche \n", " \n", " # Cas du noeud le plus à gauche\n", " predX = first(listvars)\n", " nextX0 = predX\n", " for xi in predX\n", " \n", " end\n", "\n", "\n", " push!(listvars,var) #stocker l'identite de la variable choisie pour la séparation\n", " push!(listvals,1.0) #stocker la branche choisie, identifiee par la valeur de la variable choisie\n", " listvars, listvals\n", "end\n", "\n", "\n", "function ExplorerAutreNoeud_relaxlin(listvars, listvals, listnodes)\n", " #this node is sondable, go back to parent node then right child if possible\n", " \n", " stop=false\n", " #check if we are not at the root node\n", " if (length(listvars)>= 1)\n", " #go back to parent node\n", " var=pop!(listvars)\n", " theval=pop!(listvals)\n", " tmp=pop!(listnodes)\n", " set_lower_bound(var,0.0)\n", " set_upper_bound(var,1.0)\n", "\n", " #go to right child if possible, otherwise go back to parent\n", " while ( (theval==0.0) && (length(listvars)>= 1))\n", " var=pop!(listvars)\n", " theval=pop!(listvals)\n", " tmp=pop!(listnodes)\n", " set_lower_bound(var,0.0) \n", " set_upper_bound(var,1.0)\n", " end\n", " if theval==1.0\n", " set_lower_bound(var,0.0)\n", " set_upper_bound(var,0.0)\n", " push!(listvars,var)\n", " push!(listvals,0.0)\n", " else\n", " println(\"\\nFINISHED\")\n", " stop=true\n", " end\n", " else\n", " #the root node was sondable\n", " println(\"\\nFINISHED\")\n", " stop=true\n", " end\n", " listvars, listvals, listnodes, stop \n", "end" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Constraints (generic function with 1 method)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# fonction objectif que l'on souhaite maximiser/minimiser\n", "Objective(x, price) = \n", " sum(\n", " if x[i] < 0\n", " 1\n", " else\n", " price[i]*x[i] \n", " end\n", " for i in 1:length(x)\n", " )\n", "\n", "# fonction permettant de vérfier toutes les contraintes du modèle\n", "Constraints(x, weight, capacity) =\n", " sum(\n", " if x[i] < 0\n", " 0\n", " else \n", " weight[i]*x[i]\n", " end\n", " for i in 1:length(x)\n", " ) <= capacity\n", "\n", "\n", "AllDef(x) =\n", " for xi in x\n", " if xi < 0\n", " return false\n", " end\n", " end\n", " return true" ] } ], "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 }