TP-recherche-operationnelle/notebook.ipynb

{
 "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"
   ]
  }
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