1 | using System;
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2 | using System.Collections.Generic;
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3 | using System.Linq;
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4 | using System.Threading;
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5 | using HEAL.Attic;
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6 | using HeuristicLab.Common;
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7 | using HeuristicLab.Core;
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8 | using HeuristicLab.Data;
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9 | using HeuristicLab.Encodings.RealVectorEncoding;
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10 | using HeuristicLab.Optimization;
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11 | using HeuristicLab.Parameters;
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12 | using HeuristicLab.Random;
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13 |
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14 | namespace HeuristicLab.Algorithms.NSGA3
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15 | {
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16 | /// <summary>
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17 | /// The Reference Point Based Non-dominated Sorting Genetic Algorithm III was introduced in Deb
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18 | /// et al. 2013. An Evolutionary Many-Objective Optimization Algorithm Using Reference Point
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19 | /// Based Non-dominated Sorting Approach. IEEE Transactions on Evolutionary Computation, 18(4),
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20 | /// pp. 577-601.
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21 | /// </summary>
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22 | [Item("NSGA-III", "The Reference Point Based Non-dominated Sorting Genetic Algorithm III was introduced in Deb et al. 2013. An Evolutionary Many-Objective Optimization Algorithm Using Reference Point Based Non-dominated Sorting Approach. IEEE Transactions on Evolutionary Computation, 18(4), pp. 577-601.")]
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23 | [Creatable(Category = CreatableAttribute.Categories.PopulationBasedAlgorithms, Priority = 136)]
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24 | [StorableType("07C745F7-A8A3-4F99-8B2C-F97E639F9AC3")]
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25 | public class NSGA3 : BasicAlgorithm
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26 | {
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27 | private const double EPSILON = 10e-6; // a tiny number that is greater than 0
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28 |
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29 | public override bool SupportsPause => false;
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30 |
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31 | #region ProblemProperties
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32 |
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33 | public override Type ProblemType
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34 | {
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35 | get { return typeof(MultiObjectiveBasicProblem<RealVectorEncoding>); }
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36 | }
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37 |
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38 | public new MultiObjectiveBasicProblem<RealVectorEncoding> Problem
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39 | {
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40 | get { return (MultiObjectiveBasicProblem<RealVectorEncoding>)base.Problem; }
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41 | set { base.Problem = value; }
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42 | }
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43 |
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44 | #endregion ProblemProperties
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45 |
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46 | #region Storable fields
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47 |
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48 | [Storable]
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49 | private IRandom random;
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50 |
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51 | [Storable]
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52 | private int generation;
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53 |
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54 | [Storable]
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55 | private List<Solution> solutions;
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56 |
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57 | #endregion Storable fields
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58 |
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59 | #region ParameterAndResultsNames
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60 |
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61 | // Parameter Names
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62 |
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63 | private const string SeedName = "Seed";
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64 | private const string SetSeedRandomlyName = "SetSeedRandomly";
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65 | private const string PopulationSizeName = "PopulationSize";
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66 | private const string CrossoverProbabilityName = "CrossOverProbability";
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67 | private const string MutationProbabilityName = "MutationProbability";
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68 | private const string MaximumGenerationsName = "MaximumGenerations";
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69 | private const string DominateOnEqualQualitiesName = "DominateOnEqualQualities";
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70 |
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71 | // Results Names
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72 |
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73 | private const string GeneratedReferencePointsResultName = "Generated Reference Points";
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74 | private const string CurrentFrontResultName = "Pareto Front"; // Do not touch this
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75 |
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76 | #endregion ParameterAndResultsNames
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77 |
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78 | #region ParameterProperties
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79 |
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80 | private IFixedValueParameter<IntValue> SeedParameter
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81 | {
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82 | get { return (IFixedValueParameter<IntValue>)Parameters[SeedName]; }
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83 | }
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84 |
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85 | private IFixedValueParameter<BoolValue> SetSeedRandomlyParameter
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86 | {
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87 | get { return (IFixedValueParameter<BoolValue>)Parameters[SetSeedRandomlyName]; }
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88 | }
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89 |
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90 | private IFixedValueParameter<IntValue> PopulationSizeParameter
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91 | {
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92 | get { return (IFixedValueParameter<IntValue>)Parameters[PopulationSizeName]; }
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93 | }
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94 |
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95 | private IFixedValueParameter<PercentValue> CrossoverProbabilityParameter
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96 | {
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97 | get { return (IFixedValueParameter<PercentValue>)Parameters[CrossoverProbabilityName]; }
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98 | }
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99 |
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100 | private IFixedValueParameter<PercentValue> MutationProbabilityParameter
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101 | {
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102 | get { return (IFixedValueParameter<PercentValue>)Parameters[MutationProbabilityName]; }
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103 | }
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104 |
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105 | private IFixedValueParameter<IntValue> MaximumGenerationsParameter
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106 | {
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107 | get { return (IFixedValueParameter<IntValue>)Parameters[MaximumGenerationsName]; }
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108 | }
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109 |
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110 | private IFixedValueParameter<BoolValue> DominateOnEqualQualitiesParameter
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111 | {
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112 | get { return (IFixedValueParameter<BoolValue>)Parameters[DominateOnEqualQualitiesName]; }
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113 | }
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114 |
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115 | #endregion ParameterProperties
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116 |
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117 | #region Properties
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118 |
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119 | public IntValue Seed => SeedParameter.Value;
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120 |
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121 | public BoolValue SetSeedRandomly => SetSeedRandomlyParameter.Value;
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122 |
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123 | public IntValue PopulationSize => PopulationSizeParameter.Value;
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124 |
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125 | public PercentValue CrossoverProbability => CrossoverProbabilityParameter.Value;
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126 |
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127 | public PercentValue MutationProbability => MutationProbabilityParameter.Value;
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128 |
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129 | public IntValue MaximumGenerations => MaximumGenerationsParameter.Value;
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130 |
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131 | public BoolValue DominateOnEqualQualities => DominateOnEqualQualitiesParameter.Value;
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132 |
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133 | public List<List<Solution>> Fronts { get; private set; }
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134 |
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135 | public List<ReferencePoint> ReferencePoints { get; private set; }
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136 |
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137 | #endregion Properties
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138 |
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139 | #region ResultsProperties
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140 |
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141 | public DoubleMatrix ResultsGeneratedReferencePoints
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142 | {
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143 | get { return (DoubleMatrix)Results[GeneratedReferencePointsResultName].Value; }
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144 | set { Results[GeneratedReferencePointsResultName].Value = value; }
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145 | }
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146 |
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147 | public DoubleMatrix ResultsSolutions
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148 | {
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149 | get { return (DoubleMatrix)Results[CurrentFrontResultName].Value; }
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150 | set { Results[CurrentFrontResultName].Value = value; }
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151 | }
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152 |
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153 | #endregion ResultsProperties
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154 |
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155 | #region Constructors
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156 |
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157 | public NSGA3() : base()
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158 | {
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159 | Parameters.Add(new FixedValueParameter<IntValue>(SeedName, "The random seed used to initialize the new pseudo random number generator.", new IntValue(0)));
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160 | Parameters.Add(new FixedValueParameter<BoolValue>(SetSeedRandomlyName, "True if the random seed should be set to a random value, otherwise false.", new BoolValue(true)));
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161 | Parameters.Add(new FixedValueParameter<IntValue>(PopulationSizeName, "The size of the population of Individuals.", new IntValue(100)));
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162 | Parameters.Add(new FixedValueParameter<PercentValue>(CrossoverProbabilityName, "The probability that the crossover operator is applied on two parents.", new PercentValue(0.9)));
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163 | Parameters.Add(new FixedValueParameter<PercentValue>(MutationProbabilityName, "The probability that the mutation operator is applied on a Individual.", new PercentValue(0.05)));
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164 | Parameters.Add(new FixedValueParameter<IntValue>(MaximumGenerationsName, "The maximum number of generations which should be processed.", new IntValue(1000)));
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165 | Parameters.Add(new FixedValueParameter<BoolValue>(DominateOnEqualQualitiesName, "Flag which determines wether Individuals with equal quality values should be treated as dominated.", new BoolValue(false)));
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166 | }
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167 |
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168 | // Persistence uses this ctor to improve deserialization efficiency. If we would use the
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169 | // default ctor instead this would completely initialize the object (e.g. creating
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170 | // parameters) even though the data is later overwritten by the stored data.
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171 | [StorableConstructor]
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172 | public NSGA3(StorableConstructorFlag _) : base(_) { }
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173 |
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174 | // Each clonable item must have a cloning ctor (deep cloning, the cloner is used to handle
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175 | // cyclic object references). Don't forget to call the cloning ctor of the base class
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176 | public NSGA3(NSGA3 original, Cloner cloner) : base(original, cloner)
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177 | {
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178 | // todo: don't forget to clone storable fields
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179 | random = cloner.Clone(original.random);
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180 | solutions = new List<Solution>(original.solutions?.Select(cloner.Clone));
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181 | }
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182 |
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183 | public override IDeepCloneable Clone(Cloner cloner)
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184 | {
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185 | return new NSGA3(this, cloner);
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186 | }
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187 |
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188 | #endregion Constructors
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189 |
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190 | #region Initialization
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191 |
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192 | protected override void Initialize(CancellationToken cancellationToken)
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193 | {
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194 | base.Initialize(cancellationToken);
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195 |
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196 | InitFields();
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197 | InitReferencePoints();
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198 | InitResults();
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199 | Analyze();
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200 | }
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201 |
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202 | private void InitFields()
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203 | {
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204 | random = new MersenneTwister();
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205 | generation = 0;
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206 | InitSolutions();
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207 | }
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208 |
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209 | private void InitSolutions()
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210 | {
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211 | int minBound = 0;
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212 | int maxBound = 1;
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213 |
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214 | // Initialise solutions
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215 | solutions = new List<Solution>(PopulationSize.Value);
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216 | for (int i = 0; i < PopulationSize.Value; i++)
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217 | {
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218 | RealVector randomRealVector = new RealVector(Problem.Encoding.Length, random, minBound, maxBound);
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219 |
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220 | solutions.Add(new Solution(StorableConstructorFlag.Default)
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221 | {
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222 | Chromosome = randomRealVector
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223 | });
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224 | solutions[i].Fitness = Evaluate(solutions[i].Chromosome);
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225 | }
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226 | }
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227 |
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228 | private void InitReferencePoints()
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229 | {
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230 | // Generate reference points and add them to results
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231 | int nDiv = 5; // todo: figure out the correct number of divisions
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232 | ReferencePoints = ReferencePoint.GenerateReferencePoints(Problem.Encoding.Length, nDiv);
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233 | ResultsGeneratedReferencePoints = Utility.ConvertToDoubleMatrix(ReferencePoints);
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234 | }
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235 |
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236 | private void InitResults()
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237 | {
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238 | Results.Add(new Result(GeneratedReferencePointsResultName, "The initially generated reference points", Utility.ConvertToDoubleMatrix(ReferencePoints)));
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239 | Results.Add(new Result(CurrentFrontResultName, "The Pareto Front", new DoubleMatrix()));
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240 | }
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241 |
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242 | #endregion Initialization
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243 |
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244 | #region Overriden Methods
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245 |
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246 | protected override void Run(CancellationToken cancellationToken)
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247 | {
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248 | ReferencePoints = new List<ReferencePoint>(); // todo: use existing list of reference points
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249 | while (generation != MaximumGenerations.Value)
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250 | {
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251 | ToNextGeneration();
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252 | generation++;
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253 | }
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254 | }
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255 |
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256 | #endregion Overriden Methods
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257 |
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258 | #region Private Methods
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259 |
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260 | private void Analyze()
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261 | {
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262 | ResultsSolutions = solutions.Select(s => s.Chromosome.ToArray()).ToMatrix();
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263 | Problem.Analyze(
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264 | solutions.Select(s => (Individual)new SingleEncodingIndividual(Problem.Encoding, new Scope { Variables = { new Variable(Problem.Encoding.Name, s.Chromosome) } })).ToArray(),
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265 | solutions.Select(s => s.Fitness).ToArray(),
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266 | Results,
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267 | random
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268 | );
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269 | }
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270 |
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271 | /// <summary>
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272 | /// Returns the fitness of the given <paramref name="chromosome" /> by applying the Evaluate
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273 | /// method of the Problem.
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274 | /// </summary>
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275 | /// <param name="chromosome"></param>
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276 | /// <returns></returns>
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277 | private double[] Evaluate(RealVector chromosome)
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278 | {
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279 | return Problem.Evaluate(new SingleEncodingIndividual(Problem.Encoding, new Scope { Variables = { new Variable(Problem.Encoding.Name, chromosome) } }), random);
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280 | }
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281 |
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282 | private List<Solution> ToNextGeneration()
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283 | {
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284 | List<Solution> st = new List<Solution>();
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285 | List<Solution> qt = Mutate(Recombine(solutions));
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286 | List<Solution> rt = Utility.Concat(solutions, qt);
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287 | List<Solution> nextGeneration;
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288 |
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289 | // Do non-dominated sort
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290 | var qualities = Utility.ToFitnessMatrix(solutions);
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291 | // compute the pareto fronts using the DominationCalculator and discard the qualities
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292 | // part in the inner tuples
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293 | Fronts = DominationCalculator<Solution>.CalculateAllParetoFronts(rt.ToArray(), qualities, Problem.Maximization, out int[] rank, true)
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294 | .Select(list => new List<Solution>(list.Select(pair => pair.Item1))).ToList();
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295 |
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296 | int i = 0;
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297 | List<Solution> lf = null; // last front to be included
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298 | while (i < Fronts.Count && st.Count < PopulationSize.Value)
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299 | {
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300 | lf = Fronts[i];
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301 | st = Utility.Concat(st, lf);
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302 | i++;
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303 | }
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304 |
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305 | if (st.Count == PopulationSize.Value) // no selection needs to be done
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306 | nextGeneration = st;
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307 | else
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308 | {
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309 | int l = i - 1;
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310 | nextGeneration = new List<Solution>();
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311 | for (int f = 0; f < l; f++)
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312 | nextGeneration = Utility.Concat(nextGeneration, Fronts[f]);
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313 | Normalize(st);
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314 | Associate();
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315 | throw new NotImplementedException();
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316 | }
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317 |
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318 | throw new NotImplementedException();
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319 | }
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320 |
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321 | private void Normalize(List<Solution> population)
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322 | {
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323 | // Find the ideal point
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324 | double[] idealPoint = new double[Problem.Encoding.Length];
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325 | for (int j = 0; j < Problem.Encoding.Length; j++)
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326 | {
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327 | // Compute ideal point
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328 | idealPoint[j] = Utility.Min(s => s.Fitness[j], solutions);
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329 |
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330 | // Translate objectives
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331 | foreach (var solution in solutions)
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332 | solution.Fitness[j] -= idealPoint[j];
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333 | }
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334 |
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335 | // Find the extreme points
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336 | Solution[] extremePoints = new Solution[Problem.Encoding.Length];
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337 | for (int j = 0; j < Problem.Encoding.Length; j++)
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338 | {
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339 | // Compute extreme points
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340 | double[] weights = new double[Problem.Encoding.Length];
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341 | for (int i = 0; i < Problem.Encoding.Length; i++) weights[i] = EPSILON;
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342 | weights[j] = 1;
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343 | double func(Solution s) => ASF(s.Fitness, weights);
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344 | extremePoints[j] = Utility.ArgMin(func, solutions);
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345 | }
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346 |
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347 | // Compute intercepts
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348 | List<double> intercepts = GetIntercepts(extremePoints.ToList());
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349 |
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350 | // Normalize objectives
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351 | NormalizeObjectives(intercepts, idealPoint);
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352 |
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353 | // Associate reference points to solutions
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354 | Associate();
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355 | }
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356 |
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357 | private void NormalizeObjectives(List<double> intercepts, double[] idealPoint)
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358 | {
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359 | for (int f = 0; f < Fronts.Count; f++)
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360 | {
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361 | foreach (var solution in Fronts[f])
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362 | {
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363 | for (int i = 0; i < Problem.Encoding.Length; i++)
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364 | {
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365 | if (Math.Abs(intercepts[i] - idealPoint[i]) > EPSILON)
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366 | {
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367 | solution.Fitness[i] = solution.Fitness[i] / (intercepts[i] - idealPoint[i]);
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368 | }
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369 | else
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370 | {
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371 | solution.Fitness[i] = solution.Fitness[i] / EPSILON;
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372 | }
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373 | }
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374 | }
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375 | }
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376 | }
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377 |
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378 | private void Associate()
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379 | {
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380 | for (int f = 0; f < Fronts.Count; f++)
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381 | {
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382 | foreach (var solution in Fronts[f])
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383 | {
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384 | // find reference point for which the perpendicular distance to the current
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385 | // solution is the lowest
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386 | var rpAndDist = Utility.MinArgMin(rp => GetPerpendicularDistance(rp.Values, solution.Fitness), ReferencePoints);
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387 |
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388 | //// todo: use ArgMin here
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389 | //int min_rp = -1;
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390 | //double min_dist = double.MaxValue;
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391 | //for (int r = 0; r < referencePoints.Count; r++)
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392 | //{
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393 | // double d = GetPerpendicularDistance(referencePoints[r].Values, solution.Fitness);
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394 | // if (d < min_dist)
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395 | // {
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396 | // min_dist = d;
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397 | // min_rp = r;
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398 | // }
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399 | //}
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400 | if (f + 1 != Fronts.Count)
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401 | {
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402 | // Todo: Add member for reference point on index min_rp
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403 | throw new NotImplementedException();
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404 | }
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405 | else
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406 | {
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407 | // Todo: Add potential member for reference point on index min_rp
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408 | throw new NotImplementedException();
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409 | }
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410 | }
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411 | }
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412 | }
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413 |
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414 | private double GetPerpendicularDistance(double[] values, double[] fitness)
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415 | {
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416 | double numerator = 0;
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417 | double denominator = 0;
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418 | for (int i = 0; i < values.Length; i++)
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419 | {
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420 | numerator += values[i] * fitness[i];
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421 | denominator += Math.Pow(values[i], 2);
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422 | }
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423 | double k = numerator / denominator;
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424 |
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425 | double d = 0;
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426 | for (int i = 0; i < values.Length; i++)
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427 | {
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428 | d += Math.Pow(k * values[i] - fitness[i], 2);
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429 | }
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430 | return Math.Sqrt(d);
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431 | }
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432 |
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433 | private double ASF(double[] x, double[] weight)
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434 | {
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435 | List<int> dimensions = new List<int>();
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436 | for (int i = 0; i < Problem.Encoding.Length; i++) dimensions.Add(i);
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437 | double f(int dim) => x[dim] / weight[dim];
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438 | return Utility.Max(f, dimensions);
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439 | }
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440 |
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441 | private List<double> GetIntercepts(List<Solution> extremePoints)
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442 | {
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443 | // Check whether there are duplicate extreme points. This might happen but the original
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444 | // paper does not mention how to deal with it.
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445 | bool duplicate = false;
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446 | for (int i = 0; !duplicate && i < extremePoints.Count; i++)
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447 | {
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448 | for (int j = i + 1; !duplicate && j < extremePoints.Count; j++)
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449 | {
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450 | // maybe todo: override Equals method of solution?
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451 | duplicate = extremePoints[i].Equals(extremePoints[j]);
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452 | }
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453 | }
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454 |
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455 | List<double> intercepts = new List<double>();
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456 |
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457 | if (duplicate)
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458 | { // cannot construct the unique hyperplane (this is a casual method to deal with the condition)
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459 | for (int f = 0; f < Problem.Encoding.Length; f++)
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460 | {
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461 | // extreme_points[f] stands for the individual with the largest value of
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462 | // objective f
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463 | intercepts.Add(extremePoints[f].Fitness[f]);
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464 | }
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465 | }
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466 | else
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467 | {
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468 | // Find the equation of the hyperplane
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469 | List<double> b = new List<double>(); //(pop[0].objs().size(), 1.0);
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470 | for (int i = 0; i < Problem.Encoding.Length; i++)
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471 | {
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472 | b.Add(1.0);
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473 | }
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474 |
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475 | List<List<double>> a = new List<List<double>>();
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476 | foreach (Solution s in extremePoints)
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477 | {
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478 | List<double> aux = new List<double>();
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479 | for (int i = 0; i < Problem.Encoding.Length; i++)
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480 | aux.Add(s.Fitness[i]);
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481 | a.Add(aux);
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482 | }
|
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483 | List<double> x = GaussianElimination(a, b);
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484 |
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485 | // Find intercepts
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486 | for (int f = 0; f < Problem.Encoding.Length; f++)
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487 | {
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488 | intercepts.Add(1.0 / x[f]);
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489 | }
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490 | }
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491 |
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492 | return intercepts;
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493 | }
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494 |
|
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495 | private List<double> GaussianElimination(List<List<double>> a, List<double> b)
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496 | {
|
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497 | List<double> x = new List<double>();
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498 |
|
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499 | int n = a.Count;
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500 | for (int i = 0; i < n; i++)
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501 | a[i].Add(b[i]);
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502 |
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503 | for (int @base = 0; @base < n - 1; @base++)
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504 | for (int target = @base + 1; target < n; target++)
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505 | {
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506 | double ratio = a[target][@base] / a[@base][@base];
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507 | for (int term = 0; term < a[@base].Count; term++)
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508 | a[target][term] = a[target][term] - a[@base][term] * ratio;
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509 | }
|
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510 |
|
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511 | for (int i = 0; i < n; i++)
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512 | x.Add(0.0);
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513 |
|
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514 | for (int i = n - 1; i >= 0; i--)
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515 | {
|
---|
516 | for (int known = i + 1; known < n; known++)
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517 | a[i][n] = a[i][n] - a[i][known] * x[known];
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518 | x[i] = a[i][n] / a[i][i];
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519 | }
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520 |
|
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521 | return x;
|
---|
522 | }
|
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523 |
|
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524 | private List<Solution> Recombine(List<Solution> solutions)
|
---|
525 | {
|
---|
526 | throw new NotImplementedException();
|
---|
527 | }
|
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528 |
|
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529 | private List<Solution> Mutate(List<Solution> solutions)
|
---|
530 | {
|
---|
531 | throw new NotImplementedException();
|
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532 | }
|
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533 |
|
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534 | #endregion Private Methods
|
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535 | }
|
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536 | } |
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