310 lines
9.1 KiB
Julia
310 lines
9.1 KiB
Julia
import Pkg;
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Pkg.add("GraphRecipes");
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Pkg.add("Plots");
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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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"""Open and read a KnapFile.
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Args: \\
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- filename (String): the name of the file to read.
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Returns: \\
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- price (Vector{Integer}): prices of items to put in the KnapSack. \\
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- weight (Vector{Integer}): weights of items to put in the KnapSack. \\
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- capacity (Integer): the maximum capacity of the KnapSack.
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"""
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function readKnapInstance(filename)
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price = []
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weight = []
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capacity = -1
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open(filename) do f
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for i = 1:3
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tok = split(readline(f))
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if (tok[1] == "ListPrices=")
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for i = 2:(length(tok)-1)
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push!(price, parse(Int64, tok[i]))
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end
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elseif (tok[1] == "ListWeights=")
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for i = 2:(length(tok)-1)
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push!(weight, parse(Int64, tok[i]))
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end
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elseif (tok[1] == "Capacity=")
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capacity = parse(Int64, tok[2])
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else
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println("Unknown read :", tok)
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end
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end
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end
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return price, weight, capacity
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end
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"""Test if a node should be pruned.
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Args: \\
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- x (Vector{Integer}): the node to be tested. \\
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- price (Vector{Integer}): prices of items to put in the KnapSack. \\
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- weight (Vector{Integer}): weights of items to put in the KnapSack. \\
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- capacity (Integer): the maximum capacity of the KnapSack. \\
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- BestProfit (Integer): the current BestProfit value. \\
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- Bestsol (Integer): the current BestSol values. \\
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- affich (Bool): determine if the function should print to stdout.
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Returns: \\
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- TA (Bool): true if the node is feasible. \\
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- TO (Bool): true if the node is optimal. \\
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- TR (Bool): true if the node is resolvable. \\
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- BestProfit (Integer): the updated value of BestProfit. \\
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- Bestsol (Vector{Integer}): the updated values of BestSol.
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"""
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function TestsSondabilite_relaxlin(x, price, weight, capacity, BestProfit, Bestsol, affich)
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TA, TO, TR = false, false, false
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if (!Constraints(x, weight, capacity)) # Test de faisabilite
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TA = true
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if affich
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println("TA\n")
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end
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elseif (Objective(x, price) <= BestProfit) # Test d'optimalite
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TO = true
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if affich
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println("TO\n")
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end
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elseif (AllDef(x)) # Test de resolution
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TR = true
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if affich
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println("TR : solution ", " de profit ", Objective(x, price), "\n")
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end
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if (Objective(x, price) >= BestProfit) # Le profit de la solution trouvée est meilleur que les autres
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if affich
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println("\t-> Cette solution a un meilleur profit.\n")
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end
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# On remplace la solution et le profit par les nouvelles valeurs
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Bestsol = x
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BestProfit = Objective(x, price)
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else
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if affich
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println("\t-> Cette solution est moins bonne.\n")
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end
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end
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elseif affich
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println("non sondable\n")
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end
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return TA, TO, TR, Bestsol, BestProfit
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end
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"""Split a node in two.
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Args: \\
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- price (Vector{Integer}): prices of items to put in the KnapSack. \\
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- listvars (Vector{Vector{Integer}}): the current values of listvars. \\
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- listvals (Vector{Integer}): the current values of listvals.
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Returns: \\
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- listvars (Vector{Vector{Integer}}): the updated values of listvars. \\
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- listvals (Vector{Integer}): the updated values of listvals.
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"""
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function SeparerNoeud_relaxlin(price, listvars, listvals)
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# Le noeud est non-sondable. Appliquer le critère de séparation pour le séparer en sous-noeuds
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# Cas du noeud le plus à gauche
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# On sépare le noeud actuel en 2 sous-noeuds
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predX = pop!(listvars)
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nextX0 = copy(predX)
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nextX1 = copy(predX)
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# On initialise leurs valeurs à zéro
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val0 = 0
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val1 = 0
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# On fixe la nouvelle variable des deux sous-noeuds
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n = length(predX)
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for i = 1:n
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if predX[i] == -1
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# L'un a zéro
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nextX0[i] = 0
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# L'autre a un
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nextX1[i] = 1
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# On calcule leurs valeurs
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val0 = Objective(nextX0, price)
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val1 = Objective(nextX1, price)
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break
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end
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end
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# On ajoute les sous-noeuds a la pile des noeuds a explorer
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push!(listvars, nextX0)
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push!(listvars, nextX1)
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# On ajoute aussi leurs valeurs
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push!(listvals, val0)
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push!(listvals, val1)
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return listvars, listvals
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end
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"""Pop node fom the list to explore another node.
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Args: \\
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- price (Vector{Integer}): prices of items to put in the KnapSack. \\
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- listvars (Vector{Vector{Integer}}): the current values of listvars. \\
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- listvals (Vector{Integer}): the current values of listvals.
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Returns: \\
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- listvars (Vector{Vector{Integer}}): the updated values of listvars. \\
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- listvals (Vector{Integer}): the updated values of listvals. \\
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- stop (Bool): true if the tree search is finished.
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"""
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function ExplorerAutreNoeud_relaxlin(listvars, listvals)
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# Le noeud est sondable, on l'enlève de la pile des noeuds à sonder
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stop = false
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if (length(listvars) > 1)
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# On passe au noeud suivant
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var = pop!(listvars)
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val = pop!(listvals)
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else
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# Il n'y a pas d'autre noeud
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stop = true
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end
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return listvars, listvals, stop
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end
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# Fonction objectif que l'on souhaite maximiser/minimiser (évalué dans le meilleur des cas)
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Objective(x, price) =
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sum(
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if x[i] < 0
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price[i]
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else
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price[i] * x[i]
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end
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for i = 1:length(x)
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)
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# Fonction permettant de vérfier toutes les contraintes du modèle (dans le meilleur des cas)
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Constraints(x, weight, capacity) =
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sum(
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if x[i] < 0
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0
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else
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weight[i] * x[i]
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end
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for i = 1:length(x)
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) <= capacity
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# Fonction qui nous dis si toutes les variables de x sont fixées
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function AllDef(x)
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for i = 1:length(x)
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if x[i] < 0
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return false
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end
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end
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return true
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end
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"""Solve the KnapSack problem for the data contained in `filename`.
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Args: \\
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- filename (String): the name of the file to read.
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Returns: \\
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- trParentnodes (Vector{Integer}): the parents nodes, to plot the tree.
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- trChildnodes (Vector{Integer}): the child nodes, to plot the tree.
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- trNamenodes (Vector{Integer}): the name of the nodes, to plot the tree.
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"""
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function SolveKnapInstance(filename)
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stop = false
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affich = false
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# Extraction des données
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price, weight, capacity = readKnapInstance(filename)
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if affich
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println("Capacity : ", capacity, " | Number of objects : ", length(price), "\n")
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end
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# Pour dessiner le graph
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trParentnodes = Int64[]
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trChildnodes = Int64[]
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trNamenodes = []
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# Liste des variable pour naviguer de noeuds en noeuds
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listvars = []
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listvals = []
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listnodes = []
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# La meilleur solution et sa valeur
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BestProfit = -1
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Bestsol = []
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# Compter le nombre de noeud explorés
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current_node_number = 0
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# On ajoute le premier noeud à explorer (la racine)
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push!(listvars, [-1 for p in price])
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push!(listvals, Objective(last(listvars), price))
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push!(listnodes, 1)
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push!(trNamenodes, 0)
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newnodeid = 2
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while (!stop)
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# Le noeud actuel
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x = last(listvars)
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if affich && current_node_number % 10000 == 0
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println("----------\nNode n°", current_node_number, " :\n")
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println("Previous Solution memorized ", " with bestprofit ", BestProfit, "\n")
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end
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# Test de sondabilité du noeud actuel
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# -> On mets a jour la solution et sa valeur si besoin
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TA, TO, TR, Bestsol, BestProfit = TestsSondabilite_relaxlin(x, price, weight, capacity, BestProfit, Bestsol, affich)
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is_node_sondable = TA || TO || TR
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if (!is_node_sondable)
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# Le noeud n'est pas sondable, on le sépare en 2 sous-noeuds
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listvars, listvals = SeparerNoeud_relaxlin(price, listvars, listvals)
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curnode = pop!(listnodes)
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push!(trParentnodes, curnode)
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push!(trParentnodes, curnode)
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push!(listnodes, newnodeid + 1)
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push!(listnodes, newnodeid)
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push!(trChildnodes, newnodeid)
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push!(trChildnodes, newnodeid + 1)
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push!(trNamenodes, newnodeid - 1)
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push!(trNamenodes, newnodeid)
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newnodeid += 2
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else
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# Le noeud est sondable, on passe au noeud suivant
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listvars, listvals, stop = ExplorerAutreNoeud_relaxlin(listvars, listvals)
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pop!(listnodes)
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end
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current_node_number += 1
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end
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if affich
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println("\n******\n\nOptimal value = ", BestProfit, "\n\nOptimal x = ", Bestsol)
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end
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return trParentnodes, trChildnodes, trNamenodes
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end
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trParentnodes, trChildnodes, trNamenodes = SolveKnapInstance("data/circle/knapPI_16_10000_1000_5_-912198.opb")
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# graphplot(trParentnodes, trChildnodes, names = trNamenodes, method = :tree) |