source: branches/1614_GeneralizedQAP/HeuristicLab.Problems.GeneralizedQuadraticAssignment/3.3/SolutionCreators/GreedyRandomizedSolutionCreator.cs

#region License Information
/* HeuristicLab
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using System;
using System.Collections.Generic;
using System.Linq;
using System.Threading;
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;
using HEAL.Attic;

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("GreedyRandomizedSolutionCreator", "Creates a solution according to the procedure 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.")]
  [StorableType("44919EFC-AF47-4F0D-8EE4-F5AECBF776CA")]
  public class GreedyRandomizedSolutionCreator : GQAPStochasticSolutionCreator {

    public IValueLookupParameter<IntValue> MaximumTriesParameter {
      get { return (IValueLookupParameter<IntValue>)Parameters["MaximumTries"]; }
    }
    public IValueLookupParameter<BoolValue> CreateMostFeasibleSolutionParameter {
      get { return (IValueLookupParameter<BoolValue>)Parameters["CreateMostFeasibleSolution"]; }
    }

    [StorableConstructor]
    protected GreedyRandomizedSolutionCreator(StorableConstructorFlag _) : base(_) { }
    protected GreedyRandomizedSolutionCreator(GreedyRandomizedSolutionCreator original, Cloner cloner)
      : base(original, cloner) { }
    public GreedyRandomizedSolutionCreator()
      : base() {
      Parameters.Add(new ValueLookupParameter<IntValue>("MaximumTries", "The maximum number of tries to create a feasible solution after which an exception is thrown. If it is set to 0 or a negative value there will be an infinite number of attempts.", new IntValue(100000)));
      Parameters.Add(new ValueLookupParameter<BoolValue>("CreateMostFeasibleSolution", "If this is set to true the operator will always succeed, and outputs the solution with the least violation instead of throwing an exception.", new BoolValue(false)));
    }

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

    public static IntegerVector CreateSolution(IRandom random, GQAPInstance problemInstance,
      int maximumTries, bool createMostFeasibleSolution, CancellationToken cancelToken) {
      var weights = problemInstance.Weights;
      var distances = problemInstance.Distances;
      var installCosts = problemInstance.InstallationCosts;
      var demands = problemInstance.Demands;
      var capacities = problemInstance.Capacities.ToArray();
      var transportCosts = problemInstance.TransportationCosts;
      var equipments = demands.Length;
      var locations = capacities.Length;
      int tries = 0;
      var slack = new double[locations];
      double minViolation = double.MaxValue;
      int[] assignment = null;
      int[] bestAssignment = null;
      var F = new List<int>(equipments); // set of (initially) all facilities / equipments
      var CF = new List<int>(equipments); // set of chosen facilities / equipments
      var L = new List<int>(locations); // set of (initially) all locations
      var CL_list = new List<int>(locations); // list of chosen locations
      var CL_selected = new bool[locations]; // bool decision if location is chosen
      var T = new List<int>(equipments); // set of facilities / equpiments that can be assigned to the set of chosen locations (CL)
      var H = new double[locations]; // proportions for choosing locations in stage 1
      var W = new double[equipments]; // proportions for choosing facilities in stage 2
      var Z = new double[locations]; // proportions for choosing locations in stage 2
      
      for (var k = 0; k < equipments; k++) {
        for (var h = 0; h < equipments; h++) {
          if (k == h) continue;
          W[k] += weights[k, h];
        }
        W[k] *= demands[k];
      }

      while (maximumTries <= 0 || tries < maximumTries) {
        cancelToken.ThrowIfCancellationRequested();

        assignment = new int[equipments];

        Array.Copy(capacities, slack, locations); // line 2 of Algorihm 2
        CF.Clear(); // line 2 of Algorihm 2
        Array.Clear(CL_selected, 0, locations); // line 2 of Algorihm 2
        CL_list.Clear(); // line 2 of Algorihm 2
        T.Clear(); // line 2 of Algorihm 2

        F.Clear(); F.AddRange(Enumerable.Range(0, equipments)); // line 2 of Algorihm 2
        L.Clear(); L.AddRange(Enumerable.Range(0, locations)); // line 2 of Algorihm 2

        Array.Clear(H, 0, H.Length);

        double threshold = 1.0; // line 3 of Algorithm 2
        do { // line 4 of Algorithm 2
          if (L.Count > 0 && random.NextDouble() < threshold) { // line 5 of Algorithm 2
            // H is the proportion that a location is chosen
            // The paper doesn't mention what happens if the candidate list CL
            // does not contain an element in which case according to the formula
            // all H_k elements would be 0 which would be equal to random selection
            var HH = L.Select(x => H[x]);
            int l = L.SampleProportional(random, 1, HH, false, false).Single(); // line 6 of Algorithm 2
            L.Remove(l); // line 7 of Algorithm 2
            CL_list.Add(l); // line 7 of Algorithm 2
            CL_selected[l] = true; // line 7 of Algorithm 2
            // incrementally updating location weights
            foreach (var k in L)
              H[k] += capacities[k] * capacities[l] / distances[k, l];

            T = new List<int>(WhereDemandEqualOrLess(F, GetMaximumSlack(slack, CL_selected), demands)); // line 8 of Algorithm 2
          }
          if (T.Count > 0) { // line 10 of Algorithm 2
            // W is the proportion that an equipment is chosen
            var WW = T.Select(x => W[x]);
            var f = T.SampleProportional(random, 1, WW, false, false) // line 11 of Algorithm 2
              .Single();
            T.Remove(f); // line 12 of Algorithm 2
            F.Remove(f); // line 12 of Algorithm 2
            CF.Add(f); // line 12 of Algorithm 2
            var R = WhereSlackGreaterOrEqual(CL_list, demands[f], slack).ToList(); // line 13 of Algorithm 2
            // Z is the proportion that a location is chosen in stage 2
            var l = R[0];
            if (R.Count > 1) { // optimization, calculate probabilistic weights only in case |R| > 1
              Array.Clear(Z, 0, R.Count);
              var zk = 0;
              foreach (var k in R) {
                // d is an increase in fitness if f would be assigned to location k
                var d = installCosts[f, k];
                foreach (var i in CF) {
                  if (assignment[i] == 0) continue; // i is unassigned
                  var j = assignment[i] - 1;
                  d += transportCosts * weights[f, i] * distances[k, j];
                }
                foreach (var h in CL_list) {
                  if (k == h) continue;
                  Z[zk] += slack[k] * capacities[h] / (d * distances[k, h]);
                }
                zk++;
              }
              l = R.SampleProportional(random, 1, Z.Take(R.Count), false, false).Single(); // line 14 of Algorithm 2
            }
            assignment[f] = l + 1; // line 15 of Algorithm 2
            slack[l] -= demands[f];
            T = new List<int>(WhereDemandEqualOrLess(F, GetMaximumSlack(slack, CL_selected), demands)); // line 16 of Algorithm 2
            threshold = 1.0 - (double)T.Count / Math.Max(F.Count, 1.0); // line 17 of Algorithm 2
          }
        } while (T.Count > 0 || L.Count > 0); // line 19 of Algorithm 2

        if (maximumTries > 0) tries++;

        if (F.Count == 0) {
          bestAssignment = assignment.Select(x => x - 1).ToArray();
          break;
        } else if (createMostFeasibleSolution) {
          // complete the solution and remember the one with least violation
          foreach (var l in L.ToArray()) {
            CL_list.Add(l);
            CL_selected[l] = true;
            L.Remove(l);
          }
          while (F.Count > 0) {
            var f = F.Select((v, i) => new { Index = i, Value = v }).MaxItems(x => demands[x.Value]).SampleRandom(random);
            var l = CL_list.MaxItems(x => slack[x]).SampleRandom(random);
            F.RemoveAt(f.Index);
            assignment[f.Value] = l + 1;
            slack[l] -= demands[f.Value];
          }
          double violation = slack.Select(x => x < 0 ? -x : 0).Sum();
          if (violation < minViolation) {
            bestAssignment = assignment.Select(x => x - 1).ToArray();
            minViolation = violation;
          }
        }
      }

      if (bestAssignment == null)
        throw new InvalidOperationException(String.Format("No solution could be found in {0} tries.", maximumTries));

      return new IntegerVector(bestAssignment);
    }

    protected override IntegerVector CreateRandomSolution(IRandom random, GQAPInstance problemInstance) {
      return CreateSolution(random, problemInstance,
        MaximumTriesParameter.ActualValue.Value,
        CreateMostFeasibleSolutionParameter.ActualValue.Value,
        CancellationToken);
    }

    private static IEnumerable<int> WhereDemandEqualOrLess(IEnumerable<int> facilities, double maximum, DoubleArray demands) {
      foreach (int f in facilities) {
        if (demands[f] <= maximum) yield return f;
      }
    }

    private static double GetMaximumSlack(double[] slack, bool[] CL) {
      var max = double.MinValue;
      for (var i = 0; i < slack.Length; i++) {
        if (CL[i] && max < slack[i]) max = slack[i];
      }
      return max;
    }

    private static IEnumerable<int> WhereSlackGreaterOrEqual(IEnumerable<int> locations, double minimum, double[] slack) {
      foreach (int l in locations) {
        if (slack[l] >= minimum) yield return l;
      }
    }
  }
}