source: branches/GeneralizedQAP/HeuristicLab.Problems.GeneralizedQuadraticAssignment/3.3/Operators/Crossovers/GQAPPathRelinking.cs @ 15572

#region License Information
/* HeuristicLab
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#endregion

using System;
using System.Collections.Generic;
using System.Linq;
using HeuristicLab.Common;
using HeuristicLab.Core;
using HeuristicLab.Data;
using HeuristicLab.Encodings.IntegerVectorEncoding;
using HeuristicLab.Parameters;
using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
using HeuristicLab.Random;

namespace HeuristicLab.Problems.GeneralizedQuadraticAssignment {
  /// <summary>
  /// This is an implementation of the algorithm described in Mateus, G.R., Resende, M.G.C. & Silva, R.M.A. J Heuristics (2011) 17: 527. https://doi.org/10.1007/s10732-010-9144-0
  /// </summary>
  [Item("GQAPPathRelinking", "Operator that performs path relinking between two solutions. It is described in Mateus, G., Resende, M., and Silva, R. 2011. GRASP with path-relinking for the generalized quadratic assignment problem. Journal of Heuristics 17, Springer Netherlands, pp. 527-565.")]
  [StorableClass]
  public class GQAPPathRelinking : GQAPCrossover, IQualitiesAwareGQAPOperator {

    public IScopeTreeLookupParameter<DoubleValue> QualityParameter {
      get { return (IScopeTreeLookupParameter<DoubleValue>)Parameters["Quality"]; }
    }
    public IScopeTreeLookupParameter<Evaluation> EvaluationParameter {
      get { return (IScopeTreeLookupParameter<Evaluation>)Parameters["Evaluation"]; }
    }
    public IValueParameter<PercentValue> CandidateSizeFactorParameter {
      get { return (IValueParameter<PercentValue>)Parameters["CandidateSizeFactor"]; }
    }
    public IValueLookupParameter<BoolValue> GreedyParameter {
      get { return (IValueLookupParameter<BoolValue>)Parameters["Greedy"]; }
    }

    [StorableConstructor]
    protected GQAPPathRelinking(bool deserializing) : base(deserializing) { }
    protected GQAPPathRelinking(GQAPPathRelinking original, Cloner cloner) : base(original, cloner) { }
    public GQAPPathRelinking()
      : base() {
      Parameters.Add(new ScopeTreeLookupParameter<DoubleValue>("Quality", ""));
      Parameters.Add(new ScopeTreeLookupParameter<Evaluation>("Evaluation", GQAP.EvaluationDescription));
      Parameters.Add(new ValueParameter<PercentValue>("CandidateSizeFactor", "(η) Determines the size of the set of feasible moves in each path-relinking step relative to the maximum size. A value of 50% means that only half of all possible moves are considered each step.", new PercentValue(0.5)));
      Parameters.Add(new ValueLookupParameter<BoolValue>("Greedy", "Whether to use a greedy selection strategy or a probabilistic one.", new BoolValue(true)));
    }

    public override IDeepCloneable Clone(Cloner cloner) {
      return new GQAPPathRelinking(this, cloner);
    }

    public static GQAPSolution Apply(IRandom random,
      IntegerVector source, Evaluation sourceEval,
      IntegerVector target, Evaluation targetEval,
      GQAPInstance problemInstance, double candidateSizeFactor,
      out int evaluatedSolutions, bool greedy = true) {
      evaluatedSolutions = 0;
      var demands = problemInstance.Demands;
      var capacities = problemInstance.Capacities;
      var cmp = new IntegerVectorEqualityComparer();
      
      var sFit = problemInstance.ToSingleObjective(sourceEval);
      var tFit = problemInstance.ToSingleObjective(targetEval);
      GQAPSolution pi_star = sFit < tFit
        ? new GQAPSolution((IntegerVector)source.Clone(), (Evaluation)sourceEval.Clone())
        : new GQAPSolution((IntegerVector)target.Clone(), (Evaluation)targetEval.Clone()); // line 1 of Algorithm 4
      double pi_star_Fit = problemInstance.ToSingleObjective(pi_star.Evaluation); // line 2 of Algorithm 4
      
      var pi_prime = (IntegerVector)source.Clone(); // line 3 of Algorithm 4
      //var fix = new bool[demands.Length]; // line 3 of Algorithm 4, note that according to the description it is not necessary to track the fixed equipments
      var nonFix = Enumerable.Range(0, demands.Length).ToList(); // line 3 of Algorithm 4
      var phi = new List<int>(IntegerVectorEqualityComparer.GetDifferingIndices(pi_prime, target)); // line 4 of Algorithm 4

      var B = new List<GQAPSolution>((int)Math.Ceiling(phi.Count * candidateSizeFactor));
      var B_fit = new List<double>(B.Capacity);
      while (phi.Count > 0) { // line 5 of Algorithm 4
        B.Clear(); // line 6 of Algorithm 4
        B_fit.Clear(); // line 6 of Algorithm 4 (B is split into two synchronized lists)
        foreach (var v in phi) { // line 7 of Algorithm 4
          int oldLocation = pi_prime[v];
          pi_prime[v] = target[v]; // line 8 of Algorithm 4
          var pi_dash = MakeFeasible(random, pi_prime, v, nonFix, demands, capacities); // line 9 of Algorithm 4
          pi_prime[v] = oldLocation; // not mentioned in Algorithm 4, but seems reasonable

          if (problemInstance.IsFeasible(pi_dash)) { // line 10 of Algorithm 4
            var pi_dash_eval = problemInstance.Evaluate(pi_dash);
            evaluatedSolutions++;
            var pi_dash_fit = problemInstance.ToSingleObjective(pi_dash_eval);

            if (B.Any(x => cmp.Equals(x.Assignment, pi_dash))) continue; // cond. 2 of line 12 and cond. 1 of line 16 in Algorithm 4

            if (B.Count >= candidateSizeFactor * phi.Count) { // line 11 of Algorithm 4
              var replacement = B_fit.Select((val, idx) => new { Index = idx, Fitness = val })
                                            .Where(x => x.Fitness >= pi_dash_fit) // cond. 1 in line 12 of Algorithm 4
                                            .Select(x => new { x.Index, x.Fitness, Similarity = HammingSimilarityCalculator.CalculateSimilarity(B[x.Index].Assignment, pi_dash) })
                                            .ToArray();
              if (replacement.Length > 0) {
                var mostSimilar = replacement.MaxItems(x => x.Similarity).SampleRandom(random).Index;
                B[mostSimilar].Assignment = pi_dash; // line 13 of Algorithm 4
                B[mostSimilar].Evaluation = pi_dash_eval; // line 13 of Algorithm 4
                B_fit[mostSimilar] = pi_dash_fit; // line 13 of Algorithm 4
              }
            } else { // line 16, condition has been checked above already
              B.Add(new GQAPSolution(pi_dash, pi_dash_eval)); // line 17 of Algorithm 4
              B_fit.Add(pi_dash_fit); // line 17 of Algorithm 4
            }
          }
        }
        if (B.Count > 0) { // line 21 of Algorithm 4
          GQAPSolution pi;
          // line 22 of Algorithm 4
          if (greedy) {
            pi = B.Select((val, idx) => new { Index = idx, Value = val }).MinItems(x => B_fit[x.Index]).SampleRandom(random).Value;
          } else {
            pi = B.SampleProportional(random, 1, B_fit.Select(x => 1.0 / x), false).First();
          }
          var diff = IntegerVectorEqualityComparer.GetDifferingIndices(pi.Assignment, target); // line 23 of Algorithm 4
          var I = phi.Except(diff); // line 24 of Algorithm 4
          var i = I.SampleRandom(random); // line 25 of Algorithm 4
          //fix[i] = true; // line 26 of Algorithm 4
          nonFix.Remove(i); // line 26 of Algorithm 4
          pi_prime = pi.Assignment; // line 27 of Algorithm 4
          var fit = problemInstance.ToSingleObjective(pi.Evaluation);
          if (fit < pi_star_Fit) { // line 28 of Algorithm 4
            pi_star_Fit = fit; // line 29 of Algorithm 4
            pi_star = pi; // line 30 of Algorithm 4
          }
        } else return pi_star;
        phi = new List<int>(IntegerVectorEqualityComparer.GetDifferingIndices(pi_prime, target));
      }

      return pi_star;
    }

    protected override IntegerVector Cross(IRandom random, ItemArray<IntegerVector> parents,
      GQAPInstance problemInstance) {

      var qualities = QualityParameter.ActualValue;
      var evaluations = EvaluationParameter.ActualValue;
      var betterParent = qualities[0].Value <= qualities[1].Value ? 0 : 1;
      var worseParent = 1 - betterParent;
      var source = parents[betterParent];
      var target = parents[worseParent];

      int evaluatedSolution;
      return Apply(random, source, evaluations[betterParent],
        target, evaluations[worseParent], problemInstance,
        CandidateSizeFactorParameter.Value.Value, out evaluatedSolution,
        GreedyParameter.ActualValue.Value).Assignment;
    }

    /// <summary>
    /// Relocates equipments in the same location as <paramref name="equipment"/> to other locations in case the location
    /// is overutilized.
    /// </summary>
    /// <remarks>
    /// This method is performance critical, called very often and should run as fast as possible.
    /// </remarks>
    /// <param name="random">The random number generator.</param>
    /// <param name="pi">The current solution.</param>
    /// <param name="equipment">The equipment that was just assigned to a new location.</param>
    /// <param name="nonFix">The equipments that have not yet been fixed.</param>
    /// <param name="demands">The demands for all equipments.</param>
    /// <param name="capacities">The capacities of all locations.</param>
    /// <param name="maximumTries">The number of tries that should be done in relocating the equipments.</param>
    /// <returns>A feasible or infeasible solution</returns>
    private static IntegerVector MakeFeasible(IRandom random, IntegerVector pi, int equipment, List<int> nonFix, DoubleArray demands, DoubleArray capacities, int maximumTries = 1000) {
      int l = pi[equipment];
      var slack = ComputeSlack(pi, demands, capacities);
      if (slack[l] >= 0) // line 1 of Algorithm 5
        return (IntegerVector)pi.Clone(); // line 2 of Algorithm 5

      IntegerVector pi_prime = null;
      int k = 0; // line 4 of Algorithm 5
      var maxSlack = slack.Max(); // line 8-9 of Algorithm 5
      var slack_prime = (double[])slack.Clone();
      var maxSlack_prime = maxSlack;
      // note that FTL can be computed only once for all tries as all tries restart with the same solution
      var FTL = nonFix.Where(x => x != equipment && pi[x] == l && demands[x] <= maxSlack).ToList(); // line 8-9 of Algorithm 5
      var FTLweight = FTL.Select(x => demands[x]).ToList();
      while (k < maximumTries && slack_prime[l] < 0) {  // line 5 of Algorithm 5
        pi_prime = (IntegerVector)pi.Clone(); // line 6 of Algorithm 5
        // set T can only shrink and not grow, thus it is created outside the loop and only updated inside
        var T = new List<int>(FTL); // line 8-9 of Algorithm 5
        var weightT = new List<double>(FTLweight);
        do {  // line 7 of Algorithm 5
          if (T.Count > 0) { // line 10 of Algorithm 5
            var idx = Enumerable.Range(0, T.Count).SampleProportional(random, 1, weightT, false, false).First(); // line 11 of Algorithm 5
            int i = T[idx]; // line 11 of Algorithm 5
            var j = Enumerable.Range(0, capacities.Length)
              .Where(x => slack_prime[x] >= demands[i]) // line 12 of Algorithm 5
              .SampleRandom(random);  // line 13 of Algorithm 5
            pi_prime[i] = j; // line 14 of Algorithm 5
            T.RemoveAt(idx);
            weightT.RemoveAt(idx);
            var recomputeMaxSlack = slack_prime[j] == maxSlack_prime; // efficiency improvement: recompute max slack only if we assign to a location whose slack equals maxSlack
            slack_prime[j] -= demands[i]; // line 14 of Algorithm 5
            slack_prime[l] += demands[i]; // line 14 of Algorithm 5
            if (recomputeMaxSlack) {
              maxSlack_prime = slack_prime.Max();
              // T needs to be removed of equipments whose demand is higher than maxSlack only if maxSlack changes
              for (var h = 0; h < T.Count; h++) {
                var f = T[h];
                if (demands[f] > maxSlack_prime) {
                  T.RemoveAt(h);
                  weightT.RemoveAt(h);
                  h--;
                }
              }
            }
          } else break; // cond. 1 in line 16 of Algorithm 5
        } while (slack_prime[l] < 0); // cond. 2 in line 16 of Algorithm 5
        k++; // line 17 of Algorithm 5
        if (slack_prime[l] < 0) {
          // reset
          Array.Copy(slack, slack_prime, slack.Length);
          maxSlack_prime = maxSlack;
        }
      }
      return pi_prime; // line 19-23 of Algorithm 5
    }

    private static double[] ComputeSlack(IntegerVector assignment, DoubleArray demands, DoubleArray capacities) {
      var slack = capacities.ToArray();
      for (int i = 0; i < assignment.Length; i++) {
        slack[assignment[i]] -= demands[i];
      }
      return slack;
    }
  }
}