source: branches/2646_DifferentialEvolution/HeuristicLab.Algorithms.GDE3/GDE3.cs @ 16472

#region License Information
/* HeuristicLab
 * Copyright (C) 2002-2016 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
 *
 * This file is part of HeuristicLab.
 *
 * Implementation based on the GDE3 implementation in jMetal Framework https://github.com/jMetal/jMetal
 *
 * HeuristicLab is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * HeuristicLab is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
 */
#endregion
using System;
using System.Linq;
using System.Collections.Generic;
using HeuristicLab.Analysis;
using HeuristicLab.Common;
using HeuristicLab.Core;
using HeuristicLab.Data;
using HeuristicLab.Encodings.RealVectorEncoding;
using HeuristicLab.Operators;
using HeuristicLab.Optimization;
using HeuristicLab.Optimization.Operators;
using HeuristicLab.Parameters;
using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
using HeuristicLab.PluginInfrastructure;
using HeuristicLab.Problems.MultiObjectiveTestFunctions;
using HeuristicLab.Random;
using System.Threading;
using HeuristicLab.Algorithms.GDE3;

namespace HeuristicLab.Algoritms.GDE3 {

  [Item("Generalized Differential Evolution (GDE3)", "A generalized differential evolution algorithm.")]
  [StorableClass]
  [Creatable(CreatableAttribute.Categories.PopulationBasedAlgorithms, Priority = 400)]
  public class GDE3 : BasicAlgorithm {
    public override Type ProblemType {
      get { return typeof(MultiObjectiveBasicProblem<RealVectorEncoding>); }
    }
    public new MultiObjectiveTestFunctionProblem Problem {
      get { return (MultiObjectiveTestFunctionProblem)base.Problem; }
      set { base.Problem = value; }
    }

    public ILookupParameter<DoubleMatrix> BestKnownFrontParameter {
      get {
        return (ILookupParameter<DoubleMatrix>)Parameters["BestKnownFront"];
      }
    }

    private readonly IRandom _random = new MersenneTwister();
    private int evals;
    private double IGDSumm;

    #region ParameterNames
    private const string MaximumGenerationsParameterName = "Maximum Generations";
    private const string MaximumEvaluationsParameterName = "Maximum Evaluations";
    private const string CrossoverProbabilityParameterName = "CrossoverProbability";
    private const string PopulationSizeParameterName = "PopulationSize";
    private const string ScalingFactorParameterName = "ScalingFactor";

    #endregion

    #region ParameterProperties
    public IFixedValueParameter<IntValue> MaximumGenerationsParameter {
      get { return (IFixedValueParameter<IntValue>)Parameters[MaximumGenerationsParameterName]; }
    }
    public IFixedValueParameter<IntValue> MaximumEvaluationsParameter {
      get { return (IFixedValueParameter<IntValue>)Parameters[MaximumEvaluationsParameterName]; }
    }
    private ValueParameter<IntValue> PopulationSizeParameter {
      get { return (ValueParameter<IntValue>)Parameters[PopulationSizeParameterName]; }
    }
    public ValueParameter<DoubleValue> CrossoverProbabilityParameter {
      get { return (ValueParameter<DoubleValue>)Parameters[CrossoverProbabilityParameterName]; }
    }
    public ValueParameter<DoubleValue> ScalingFactorParameter {
      get { return (ValueParameter<DoubleValue>)Parameters[ScalingFactorParameterName]; }
    }
    #endregion

    #region Properties
    public int MaximumGenerations {
      get { return MaximumGenerationsParameter.Value.Value; }
      set { MaximumGenerationsParameter.Value.Value = value; }
    }

    public int MaximumEvaluations {
      get { return MaximumEvaluationsParameter.Value.Value; }
      set { MaximumEvaluationsParameter.Value.Value = value; }
    }

    public Double CrossoverProbability {
      get { return CrossoverProbabilityParameter.Value.Value; }
      set { CrossoverProbabilityParameter.Value.Value = value; }
    }
    public Double ScalingFactor {
      get { return ScalingFactorParameter.Value.Value; }
      set { ScalingFactorParameter.Value.Value = value; }
    }
    public IntValue PopulationSize {
      get { return PopulationSizeParameter.Value; }
      set { PopulationSizeParameter.Value = value; }
    }
    #endregion

    #region ResultsProperties
    private double ResultsBestQuality {
      get { return ((DoubleValue)Results["Best Quality"].Value).Value; }
      set { ((DoubleValue)Results["Best Quality"].Value).Value = value; }
    }

    private double ResultsIGDMean {
      get { return ((DoubleValue)Results["IGDMeanValue"].Value).Value; }
      set { ((DoubleValue)Results["IGDMeanValue"].Value).Value = value; }
    }

    private double ResultsIGDBest {
      get { return ((DoubleValue)Results["IGDBestValue"].Value).Value; }
      set { ((DoubleValue)Results["IGDBestValue"].Value).Value = value; }
    }

    private double ResultsIGDWorst {
      get { return ((DoubleValue)Results["IGDWorstValue"].Value).Value; }
      set { ((DoubleValue)Results["IGDWorstValue"].Value).Value = value; }
    }

    private double ResultsInvertedGenerationalDistance {
      get { return ((DoubleValue)Results["InvertedGenerationalDistance"].Value).Value; }
      set { ((DoubleValue)Results["InvertedGenerationalDistance"].Value).Value = value; }
    }

    private double ResultsHypervolume {
      get { return ((DoubleValue)Results["HyperVolumeValue"].Value).Value; }
      set { ((DoubleValue)Results["HyperVolumeValue"].Value).Value = value; }
    }

    private DoubleMatrix ResultsBestFront {
      get { return (DoubleMatrix)Results["Best Front"].Value; }
      set { Results["Best Front"].Value = value; }
    }

    private int ResultsEvaluations {
      get { return ((IntValue)Results["Evaluations"].Value).Value; }
      set { ((IntValue)Results["Evaluations"].Value).Value = value; }
    }
    private int ResultsGenerations {
      get { return ((IntValue)Results["Generations"].Value).Value; }
      set { ((IntValue)Results["Generations"].Value).Value = value; }
    }
    private double ResultsGenerationalDistance {
      get { return ((DoubleValue)Results["GenerationalDistance"].Value).Value; }
      set { ((DoubleValue)Results["GenerationalDistance"].Value).Value = value; }
    }

    private double ResultsSpacing {
      get { return ((DoubleValue)Results["Spacing"].Value).Value; }
      set { ((DoubleValue)Results["Spacing"].Value).Value = value; }
    }

    private double ResultsCrowding {
      get { return ((DoubleValue)Results["Crowding"].Value).Value; }
      set { ((DoubleValue)Results["Crowding"].Value).Value = value; }
    }

    #endregion

    [StorableConstructor]
    protected GDE3(bool deserializing) : base(deserializing) { }

    protected GDE3(GDE3 original, Cloner cloner)
      : base(original, cloner) {
    }

    public override IDeepCloneable Clone(Cloner cloner) {
      return new GDE3(this, cloner);
    }

    public GDE3() {
      Parameters.Add(new FixedValueParameter<IntValue>(MaximumGenerationsParameterName, "", new IntValue(1000)));
      Parameters.Add(new FixedValueParameter<IntValue>(MaximumEvaluationsParameterName, "", new IntValue(Int32.MaxValue)));
      Parameters.Add(new ValueParameter<IntValue>(PopulationSizeParameterName, "The size of the population of solutions.", new IntValue(100)));
      Parameters.Add(new ValueParameter<DoubleValue>(CrossoverProbabilityParameterName, "The value for crossover rate", new DoubleValue(0.5)));
      Parameters.Add(new ValueParameter<DoubleValue>(ScalingFactorParameterName, "The value for scaling factor", new DoubleValue(0.5)));
      Parameters.Add(new LookupParameter<DoubleMatrix>("BestKnownFront", "The currently best known Pareto front"));
    }

    protected override void Run(CancellationToken cancellationToken) {
      // Set up the results display
      Results.Add(new Result("Generations", new IntValue(0)));
      Results.Add(new Result("Evaluations", new IntValue(0)));
      Results.Add(new Result("Best Front", new DoubleMatrix()));
      Results.Add(new Result("Crowding", new DoubleValue(0)));
      Results.Add(new Result("InvertedGenerationalDistance", new DoubleValue(0)));
      Results.Add(new Result("GenerationalDistance", new DoubleValue(0)));
      Results.Add(new Result("HyperVolumeValue", new DoubleValue(0)));
      Results.Add(new Result("IGDMeanValue", new DoubleValue(0)));
      Results.Add(new Result("IGDBestValue", new DoubleValue(Int32.MaxValue)));
      Results.Add(new Result("IGDWorstValue", new DoubleValue(0)));

      Results.Add(new Result("Spacing", new DoubleValue(0)));
      Results.Add(new Result("Scatterplot", typeof(IMOFrontModel)));
      var table = new DataTable("Qualities");
      table.Rows.Add(new DataRow("Best Quality"));
      Results.Add(new Result("Qualities", table));

      //setup the variables
      List<SolutionSet> population;
      List<SolutionSet> offspringPopulation;
      SolutionSet[] parent;
      double IGDSumm = 0;

      //initialize population
      population = new List<SolutionSet>(PopulationSizeParameter.Value.Value);

      for(int i = 0; i < PopulationSizeParameter.Value.Value; ++i) {
        var m = createIndividual();
        m.Quality = Problem.Evaluate(m.Population, _random);
        //the test function is constrained
        if(m.Quality.Length > Problem.Objectives) {
          m.OverallConstrainViolation = m.Quality[Problem.Objectives];
        } else {
          m.OverallConstrainViolation = 0;
        }
        population.Add(m);
      }

      this.initProgress();
      int generations = 1;

      while(ResultsEvaluations < MaximumEvaluationsParameter.Value.Value
         && !cancellationToken.IsCancellationRequested) {
        var populationSize = PopulationSizeParameter.Value.Value;

        // Create the offSpring solutionSet
        offspringPopulation = new List<SolutionSet>(PopulationSizeParameter.Value.Value * 2);

        for(int i = 0; i < populationSize; i++) {
          // Obtain parents. Two parameters are required: the population and the 
          //                 index of the current individual
          parent = selection(population, i);

          SolutionSet child;
          // Crossover. The parameters are the current individual and the index of the array of parents 
          child = reproduction(population[i], parent);

          child.Quality = Problem.Evaluate(child.Population, _random);

          this.updateProgres();

          //the test function is constrained
          if(child.Quality.Length > Problem.Objectives) {
            child.OverallConstrainViolation = child.Quality[Problem.Objectives];
          } else {
            child.OverallConstrainViolation = 0;
          }

          // Dominance test
          int result;
          result = compareDomination(population[i], child);

          if(result == -1) { // Solution i dominates child
            offspringPopulation.Add(population[i]);
          } else if(result == 1) { // child dominates
            offspringPopulation.Add(child);
          } else { // the two solutions are non-dominated
            offspringPopulation.Add(child);
            offspringPopulation.Add(population[i]);
          }
        }

        // Ranking the offspring population
        List<SolutionSet>[] ranking = computeRanking(offspringPopulation);
        population = crowdingDistanceSelection(ranking);
        generations++;
        ResultsGenerations = generations;
        displayResults(population);
      }
    }

    public override bool SupportsPause { get { return false; } } // XXX does it actually support pause?

    private void displayResults(List<SolutionSet> population) {
      List<SolutionSet>[] rankingFinal = computeRanking(population);

      int objectives = Problem.Objectives;
      var optimalfront = Problem.TestFunction.OptimalParetoFront(objectives);

      double[][] opf = new double[0][];
      if(optimalfront != null) {
        opf = optimalfront.Select(s => s.ToArray()).ToArray();
      }

      //compute the final qualities and population
      double[][] qualitiesFinal = new double[rankingFinal[0].Count][];
      double[][] populationFinal = new double[rankingFinal[0].Count][];

      for(int i = 0; i < rankingFinal[0].Count; ++i) {
        qualitiesFinal[i] = new double[Problem.Objectives];
        populationFinal[i] = new double[Problem.Objectives];
        for(int j = 0; j < Problem.Objectives; ++j) {
          populationFinal[i][j] = rankingFinal[0][i].Population[j];
          qualitiesFinal[i][j] = rankingFinal[0][i].Quality[j];
        }
      }
      IEnumerable<double[]> en = qualitiesFinal;
      IEnumerable<double[]> frontVectors = NonDominatedSelect.selectNonDominatedVectors(qualitiesFinal, Problem.TestFunction.Maximization(objectives), true);
      //update the results

      ResultsEvaluations = this.evals;
      ResultsBestFront = new DoubleMatrix(MultiObjectiveTestFunctionProblem.To2D(qualitiesFinal));
      ResultsCrowding = Crowding.Calculate(qualitiesFinal, Problem.TestFunction.Bounds(objectives));
      GenerationalDistanceCalculator distance = new GenerationalDistanceCalculator();
      ResultsInvertedGenerationalDistance = distance.CalculateGenerationalDistance(qualitiesFinal, opf, Problem.Objectives);
      ResultsHypervolume = Hypervolume.Calculate(frontVectors, Problem.TestFunction.ReferencePoint(objectives), Problem.TestFunction.Maximization(objectives));
      ResultsGenerationalDistance = GenerationalDistance.Calculate(qualitiesFinal, optimalfront, 1);
      Results["Scatterplot"].Value = new MOSolution(qualitiesFinal, populationFinal, opf, objectives);
      ResultsSpacing = Spacing.Calculate(qualitiesFinal);

      if(ResultsIGDBest > ResultsInvertedGenerationalDistance) {
        ResultsIGDBest = ResultsInvertedGenerationalDistance;
      }
      if(ResultsIGDWorst < ResultsInvertedGenerationalDistance) {
        ResultsIGDWorst = ResultsInvertedGenerationalDistance;
      }
      this.IGDSumm += ResultsInvertedGenerationalDistance;
      ResultsIGDMean = this.IGDSumm / ResultsGenerations;
    }

    private int getWorstIndex(List<SolutionSet> SolutionsList) {
      int result = 0;

      if((SolutionsList == null) || SolutionsList.Count == 0) {
        result = 0;
      } else {
        SolutionSet worstKnown = SolutionsList[0],
                    candidateSolution;
        int flag;
        for(int i = 1; i < SolutionsList.Count; i++) {
          candidateSolution = SolutionsList[i];
          flag = compareDomination(worstKnown, candidateSolution);
          if(flag == -1) {
            result = i;
            worstKnown = candidateSolution;
          }
        }
      }
      return result;
    }

    private SolutionSet createIndividual() {
      var dim = Problem.ProblemSize;
      var lb = Problem.Bounds[0, 0];
      var ub = Problem.Bounds[0, 1];
      var range = ub - lb;
      var v = new double[Problem.ProblemSize];
      SolutionSet solutionObject = new SolutionSet(PopulationSizeParameter.Value.Value);

      for(int i = 0; i < Problem.ProblemSize; ++i) {
        v[i] = _random.NextDouble() * range + lb;

      }
      solutionObject.createSolution(v);
      return solutionObject;
    }

    private SolutionSet createEmptyIndividual() {
      SolutionSet solutionObject = new SolutionSet(PopulationSizeParameter.Value.Value);
      var n = new RealVector(Problem.ProblemSize);
      solutionObject.Population = n;
      return solutionObject;
    }

    private void initProgress() {
      this.evals = PopulationSizeParameter.Value.Value;
    }

    private void updateProgres() {
      this.evals++;
    }

    private SolutionSet[] selection(List<SolutionSet> population, int i) {
      SolutionSet[] parents = new SolutionSet[3];
      int r0, r1, r2;
      //assure the selected vectors r0, r1 and r2 are different
      do {
        r0 = _random.Next(0, PopulationSizeParameter.Value.Value);
      } while(r0 == i);
      do {
        r1 = _random.Next(0, PopulationSizeParameter.Value.Value);
      } while(r1 == i || r1 == r0);
      do {
        r2 = _random.Next(0, PopulationSizeParameter.Value.Value);
      } while(r2 == i || r2 == r0 || r2 == r1);

      parents[0] = population[r0];
      parents[1] = population[r1];
      parents[2] = population[r2];

      return parents;
    }

    private SolutionSet reproduction(SolutionSet parent, SolutionSet[] parentsSolutions) {
      var individual = createEmptyIndividual();
      double rnbr = _random.Next(0, Problem.ProblemSize);
      for(int m = 0; m < Problem.ProblemSize; m++) {
        if(_random.NextDouble() < CrossoverProbabilityParameter.Value.Value || m == rnbr) {
          double value;
          value = parentsSolutions[2].Population[m] +
              ScalingFactorParameter.Value.Value * (parentsSolutions[0].Population[m] - parentsSolutions[1].Population[m]);
          //check the problem upper and lower bounds
          if(value > Problem.Bounds[0, 1]) value = Problem.Bounds[0, 1];
          if(value < Problem.Bounds[0, 0]) value = Problem.Bounds[0, 0];
          individual.Population[m] = value;
        } else {
          double value;
          value = parent.Population[m];
          individual.Population[m] = value;
        }
      }
      return individual;
    }

    private List<SolutionSet> crowdingDistanceSelection(List<SolutionSet>[] ranking) {
      List<SolutionSet> population = new List<SolutionSet>();
      int rankingIndex = 0;
      while(populationIsNotFull(population)) {
        if(subFrontFillsIntoThePopulation(ranking, rankingIndex, population)) {
          addRankedSolutionToPopulation(ranking, rankingIndex, population);
          rankingIndex++;
        } else {
          crowdingDistanceAssignment(ranking[rankingIndex]);
          addLastRankedSolutionToPopulation(ranking, rankingIndex, population);
        }
      }
      return population;
    }

    private void addLastRankedSolutionToPopulation(List<SolutionSet>[] ranking, int rankingIndex, List<SolutionSet> population) {
      List<SolutionSet> currentRankedFront = ranking[rankingIndex];
      //descending sort and add the front with highest crowding distance to the population
      currentRankedFront.Sort((x, y) => -x.CrowdingDistance.CompareTo(y.CrowdingDistance));
      int i = 0;
      while(population.Count < PopulationSizeParameter.Value.Value) {
        population.Add(currentRankedFront[i]);
        i++;
      }
    }

    private void crowdingDistanceAssignment(List<SolutionSet> rankingSubfront) {
      int size = rankingSubfront.Count;

      if(size == 0)
        return;

      if(size == 1) {
        rankingSubfront[0].CrowdingDistance = double.PositiveInfinity;
        return;
      }

      if(size == 2) {
        rankingSubfront[0].CrowdingDistance = double.PositiveInfinity;
        rankingSubfront[1].CrowdingDistance = double.PositiveInfinity;
        return;
      }

      //Use a new SolutionSet to evite alter original solutionSet
      List<SolutionSet> front = new List<SolutionSet>(size);
      for(int i = 0; i < size; i++) {
        front.Add(rankingSubfront[i]);
      }

      for(int i = 0; i < size; i++)
        front[i].CrowdingDistance = 0.0;

      double objetiveMaxn;
      double objetiveMinn;
      double distance;

      for(int i = 0; i < Problem.Objectives; i++) {
        // Sort the front population by the objective i          
        front.Sort((x, y) => x.Quality[i].CompareTo(y.Quality[i]));
        objetiveMinn = front[0].Quality[i];
        objetiveMaxn = front[front.Count - 1].Quality[i];

        //Set crowding distance for the current front           
        front[0].CrowdingDistance = double.PositiveInfinity;
        front[size - 1].CrowdingDistance = double.PositiveInfinity;

        for(int j = 1; j < size - 1; j++) {
          distance = front[j + 1].Quality[i] - front[j - 1].Quality[i];
          distance = distance / (objetiveMaxn - objetiveMinn);
          distance += front[j].CrowdingDistance;
          front[j].CrowdingDistance = distance;
        }
      }
    }

    private void addRankedSolutionToPopulation(List<SolutionSet>[] ranking, int rankingIndex, List<SolutionSet> population) {
      foreach(SolutionSet solution in ranking[rankingIndex]) {
        population.Add(solution);
      }
    }

    private bool subFrontFillsIntoThePopulation(List<SolutionSet>[] ranking, int rankingIndex, List<SolutionSet> population) {
      return ranking[rankingIndex].Count < (PopulationSizeParameter.Value.Value - population.Count);
    }

    private bool populationIsNotFull(List<SolutionSet> population) {
      return population.Count < PopulationSizeParameter.Value.Value;
    }

    private List<SolutionSet>[] computeRanking(List<SolutionSet> tmpList) {
      // dominateMe[i] contains the number of solutions dominating i        
      int[] dominateMe = new int[tmpList.Count];

      // iDominate[k] contains the list of solutions dominated by k
      List<int>[] iDominate = new List<int>[tmpList.Count];

      // front[i] contains the list of individuals belonging to the front i
      List<int>[] front = new List<int>[tmpList.Count + 1];

      // flagDominate is an auxiliar encodings.variable
      int flagDominate;

      // Initialize the fronts 
      for(int i = 0; i < front.Length; i++) {
        front[i] = new List<int>();
      }

      //-> Fast non dominated sorting algorithm
      // Contribution of Guillaume Jacquenot
      for(int p = 0; p < tmpList.Count; p++) {
        // Initialize the list of individuals that i dominate and the number
        // of individuals that dominate me
        iDominate[p] = new List<int>();
        dominateMe[p] = 0;
      }
      for(int p = 0; p < (tmpList.Count - 1); p++) {
        // For all q individuals , calculate if p dominates q or vice versa
        for(int q = p + 1; q < tmpList.Count; q++) {
          flagDominate = compareConstraintsViolation(tmpList[p], tmpList[q]);
          if(flagDominate == 0) {
            flagDominate = compareDomination(tmpList[p], tmpList[q]);
          }
          if(flagDominate == -1) {
            iDominate[p].Add(q);
            dominateMe[q]++;
          } else if(flagDominate == 1) {
            iDominate[q].Add(p);
            dominateMe[p]++;
          }
        }
        // If nobody dominates p, p belongs to the first front
      }
      for(int i = 0; i < tmpList.Count; i++) {
        if(dominateMe[i] == 0) {
          front[0].Add(i);
          tmpList[i].Rank = 0;
        }
      }

      //Obtain the rest of fronts
      int k = 0;

      while(front[k].Count != 0) {
        k++;
        foreach(var it1 in front[k - 1]) {
          foreach(var it2 in iDominate[it1]) {
            int index = it2;
            dominateMe[index]--;
            if(dominateMe[index] == 0) {
              front[k].Add(index);
              tmpList[index].Rank = k;
            }
          }
        }
      }
      //<-

      var rankedSubpopulation = new List<SolutionSet>[k];
      //0,1,2,....,i-1 are front, then i fronts
      for(int j = 0; j < k; j++) {
        rankedSubpopulation[j] = new List<SolutionSet>(front[j].Count);
        foreach(var it1 in front[j]) {
          rankedSubpopulation[j].Add(tmpList[it1]);
        }
      }
      return rankedSubpopulation;
    }

    private int compareDomination(SolutionSet solution1, SolutionSet solution2) {
      int dominate1; // dominate1 indicates if some objective of solution1 
                     // dominates the same objective in solution2. dominate2
      int dominate2; // is the complementary of dominate1.

      dominate1 = 0;
      dominate2 = 0;

      int flag; //stores the result of the comparison

      // Test to determine whether at least a solution violates some constraint
      if(needToCompareViolations(solution1, solution2)) {
        return compareConstraintsViolation(solution1, solution2);
      }

      // Equal number of violated constraints. Applying a dominance Test then
      double value1, value2;
      for(int i = 0; i < Problem.Objectives; i++) {
        value1 = solution1.Quality[i];
        value2 = solution2.Quality[i];
        if(value1 < value2) {
          flag = -1;
        } else if(value2 < value1) {
          flag = 1;
        } else {
          flag = 0;
        }

        if(flag == -1) {
          dominate1 = 1;
        }

        if(flag == 1) {
          dominate2 = 1;
        }
      }

      if(dominate1 == dominate2) {
        return 0; //No one dominate the other
      }
      if(dominate1 == 1) {
        return -1; // solution1 dominate
      }
      return 1;    // solution2 dominate   
    }

    private bool needToCompareViolations(SolutionSet solution1, SolutionSet solution2) {
      bool needToCompare;
      needToCompare = (solution1.OverallConstrainViolation < 0) || (solution2.OverallConstrainViolation < 0);

      return needToCompare;
    }

    private int compareConstraintsViolation(SolutionSet solution1, SolutionSet solution2) {
      int result;
      double overall1, overall2;
      overall1 = solution1.OverallConstrainViolation;
      overall2 = solution2.OverallConstrainViolation;

      if((overall1 < 0) && (overall2 < 0)) {
        if(overall1 > overall2) {
          result = -1;
        } else if(overall2 > overall1) {
          result = 1;
        } else {
          result = 0;
        }
      } else if((overall1 == 0) && (overall2 < 0)) {
        result = -1;
      } else if((overall1 < 0) && (overall2 == 0)) {
        result = 1;
      } else {
        result = 0;
      }
      return result;
    }
  }
}