{
 "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": 1,
   "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[1mPrecompiling\u001b[22m\u001b[39m project...\n",
      "\u001b[32m  ✓ \u001b[39mTestOptinum\n",
      "  1 dependency successfully precompiled in 6 seconds (158 already precompiled)\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[1mPrecompiling\u001b[22m\u001b[39m project...\n",
      "\u001b[32m  ✓ \u001b[39mTestOptinum\n",
      "  1 dependency successfully precompiled in 3 seconds (158 already precompiled)\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": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "readKnapInstance (generic function with 1 method)"
      ]
     },
     "execution_count": 1,
     "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": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TestsSondabilite_relaxlin (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function TestsSondabilite_relaxlin(x, price, weight, capacity, BestProfit, Bestsol, affich)\n",
    "    TA, TO, TR = false, false, false\n",
    "    if (!Constraints(x, weight, capacity)) # Test de faisabilite\n",
    "        TA = true\n",
    "        if affich\n",
    "            println(\"TA\")\n",
    "        end\n",
    "    elseif (Objective(x, price) <= BestProfit) # Test d'optimalite\n",
    "        TO = true\n",
    "        if affich\n",
    "            println(\"TO\")\n",
    "        end\n",
    "    elseif (AllDef(x)) # Test de resolution\n",
    "        TR = true\n",
    "        if affich\n",
    "            println(\"TR : solution \", \" de profit \", Objective(x, price))\n",
    "        end\n",
    "        if (Objective(x, price) >= BestProfit) # Le profit de la solution trouvée est meilleur que les autres\n",
    "            if affich\n",
    "                println(\"\\t-> Cette solution a un meilleur profit.\")\n",
    "            end\n",
    "            # On remplace la solution et le profit par les nouvelles valeurs\n",
    "            Bestsol = x\n",
    "            BestProfit = Objective(x, price)\n",
    "        else\n",
    "            if affich\n",
    "                println(\"\\t-> Cette solution est moins bonne.\")\n",
    "            end\n",
    "        end\n",
    "    else\n",
    "        if affich \n",
    "            println(\"non sondable\")\n",
    "        end\n",
    "    end\n",
    "    if affich\n",
    "        println(\"\\n\")\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": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ExplorerAutreNoeud_relaxlin (generic function with 1 method)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "function SeparerNoeud_relaxlin(price, listvars, listvals)\n",
    "    # Le noeud est non-sondable. Appliquer le critère de séparation pour le séparer en sous-noeuds \n",
    "\n",
    "    # Cas du noeud le plus à gauche\n",
    "\n",
    "    # On sépare le noeud actuel en 2 sous-noeuds\n",
    "    predX = pop!(listvars)\n",
    "    nextX0 = copy(predX)\n",
    "    nextX1 = copy(predX)\n",
    "\n",
    "    # On initialise leurs valeurs à zéro\n",
    "    val0 = 0\n",
    "    val1 = 0\n",
    "\n",
    "    # On fixe la nouvelle variable des deux sous-noeuds\n",
    "    n = length(predX)\n",
    "    for i in 1:n\n",
    "        if predX[i] == -1\n",
    "            # L'un a zéro\n",
    "            nextX0[i] = 0\n",
    "            # L'autre a un\n",
    "            nextX1[i] = 1\n",
    "\n",
    "            # On calcule leurs valeurs\n",
    "            val0 = Objective(nextX0, price)\n",
    "            val1 = Objective(nextX1, price)\n",
    "            break\n",
    "        end\n",
    "    end\n",
    "    # On ajoute les sous-noeuds a la pile des noeuds a explorer\n",
    "    push!(listvars, nextX1)\n",
    "    push!(listvars, nextX0)\n",
    "\n",
    "    # On ajoute aussi leurs valeurs\n",
    "    push!(listvals, val1)\n",
    "    push!(listvals, val0)\n",
    "\n",
    "    listvars, listvals\n",
    "end\n",
    "\n",
    "\n",
    "function ExplorerAutreNoeud_relaxlin(listvars, listvals)\n",
    "    # Le noeud est sondable, on l'enlève de la pile des noeuds à sonder\n",
    "    \n",
    "    stop = false\n",
    "    if (length(listvars) > 1)\n",
    "        # On passe au noeud suivant\n",
    "        var = pop!(listvars)\n",
    "        val = pop!(listvals)\n",
    "    else\n",
    "        # Il n'y a pas d'autre noeud\n",
    "        println(\"\\nFINISHED\")\n",
    "        stop = true\n",
    "    end\n",
    "\n",
    "    listvars, listvals, stop \n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AllDef (generic function with 1 method)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fonction objectif que l'on souhaite maximiser/minimiser (évalué dans le meilleur des cas)\n",
    "Objective(x, price) = \n",
    "    sum(\n",
    "        if x[i] < 0\n",
    "            price[i]\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 (dans le meilleur des cas)\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",
    "# Fonction qui nous dis si toutes les variables de x sont fixées\n",
    "function AllDef(x)\n",
    "    for i in 1:length(x)\n",
    "        if x[i] < 0\n",
    "            return false\n",
    "        end\n",
    "    end\n",
    "    return true\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Capacity : 994 | Number of objects : 50\n",
      "\n",
      "----------\n",
      "Node n°1001 :  \n",
      "\n",
      "Previous Solution memorized  with bestprofit 994\n",
      "\n",
      "non sondable\n",
      "\n",
      "\n",
      "\n",
      "FINISHED\n",
      "\n",
      "******\n",
      "\n",
      "Optimal value = 994\n",
      "\n",
      "Optimal x=[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n"
     ]
    }
   ],
   "source": [
    "function SolveKnapInstance(filename)\n",
    "\n",
    "    price, weight, capacity = readKnapInstance(filename)\n",
    "\n",
    "    println(\"Capacity : \", capacity, \" | Number of objects : \", length(price), \"\\n\")\n",
    "\n",
    "    # Liste des variable pour naviguer de noeuds en noeuds\n",
    "    listvars=[]\n",
    "    listvals=[]\n",
    "\n",
    "    # La meilleur solution et sa valeur\n",
    "    BestProfit=-1\n",
    "    Bestsol=[]\n",
    "\n",
    "    # Compter le nombre de noeud explorés\n",
    "    current_node_number = 0\n",
    "\n",
    "    stop = false\n",
    "    affich = false\n",
    "\n",
    "    # On ajoute le premier noeud à explorer (la racine)\n",
    "    push!(listvars, [-1 for p in price])\n",
    "    push!(listvals, Objective(last(listvars), price))\n",
    "\n",
    "    while (!stop)\n",
    "        # Le noeud actuel\n",
    "        x = last(listvars)\n",
    "\n",
    "        if affich\n",
    "            print(\"----------\\nNode n°\", current_node_number, \" : \")\n",
    "            println(\" \")\n",
    "            println(\"\\nPrevious Solution memorized \", \" with bestprofit \", BestProfit, \"\\n\")\n",
    "        end\n",
    "\n",
    "        # Test de sondabilité du noeud actuel\n",
    "        #   -> On mets a jour la solution et sa valeur si besoin\n",
    "        TA, TO, TR, Bestsol, BestProfit = TestsSondabilite_relaxlin(x, price, weight, capacity, BestProfit, Bestsol, affich)\n",
    "        \n",
    "        is_node_sondable = TA || TO || TR\n",
    "        if (!is_node_sondable)\n",
    "            # Le noeud n'est pas sondable, on le sépare en 2 sous-noeuds\n",
    "            listvars, listvals = SeparerNoeud_relaxlin(price, listvars, listvals)\n",
    "        else\n",
    "            # Le noeud est sondable, on passe au noeud suivant\n",
    "            listvars, listvals, stop = ExplorerAutreNoeud_relaxlin(listvars, listvals)\n",
    "        end\n",
    "\n",
    "        # On évite de spammer l'output donc  on n'affiche pas tout les résultats\n",
    "        if current_node_number % 1000000 == 100\n",
    "            affich = true\n",
    "        else\n",
    "            affich = false\n",
    "        end\n",
    "\n",
    "        current_node_number += 1\n",
    "    end\n",
    "\n",
    "    println(\"\\n******\\n\\nOptimal value = \", BestProfit, \"\\n\\nOptimal x=\", Bestsol)\n",
    "\n",
    "end\n",
    "\n",
    "SolveKnapInstance(\"data/subset_sum/knapPI_6_50_1000_1_-994.opb\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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