[15080] | 1 | #region License Information
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| 2 | /* HeuristicLab
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[16728] | 3 | * Copyright (C) 2002-2019 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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[15080] | 4 | *
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| 5 | * This file is part of HeuristicLab.
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| 6 | *
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| 7 | * HeuristicLab is free software: you can redistribute it and/or modify
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| 8 | * it under the terms of the GNU General Public License as published by
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| 9 | * the Free Software Foundation, either version 3 of the License, or
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| 10 | * (at your option) any later version.
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| 11 | *
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| 12 | * HeuristicLab is distributed in the hope that it will be useful,
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| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 15 | * GNU General Public License for more details.
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| 16 | *
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| 17 | * You should have received a copy of the GNU General Public License
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| 18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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| 19 | */
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| 20 | #endregion
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| 21 |
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| 22 | using System;
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| 23 | using System.Collections.Generic;
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[16728] | 24 | using HEAL.Attic;
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[15080] | 25 |
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| 26 | namespace HeuristicLab.Optimization {
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[16728] | 27 | [StorableType("d76eb753-5088-4490-ad18-e78d3629c60b")]
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[15080] | 28 | public enum DominationResult { Dominates, IsDominated, IsNonDominated };
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| 29 |
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| 30 | public static class DominationCalculator<T> {
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| 31 | /// <summary>
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| 32 | /// Calculates the best pareto front only. The fast non-dominated sorting algorithm is used
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| 33 | /// as described in Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002).
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| 34 | /// A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II.
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| 35 | /// IEEE Transactions on Evolutionary Computation, 6(2), 182-197.
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| 36 | /// </summary>
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| 37 | /// <remarks>
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| 38 | /// When there are plateaus in the fitness landscape several solutions might have exactly
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| 39 | /// the same fitness vector. In this case parameter <paramref name="dominateOnEqualQualities"/>
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| 40 | /// can be set to true to avoid plateaus becoming too attractive for the search process.
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| 41 | /// </remarks>
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| 42 | /// <param name="solutions">The solutions of the population.</param>
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| 43 | /// <param name="qualities">The qualities resp. fitness for each solution.</param>
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| 44 | /// <param name="maximization">The objective in each dimension.</param>
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| 45 | /// <param name="dominateOnEqualQualities">Whether solutions of exactly equal quality should dominate one another.</param>
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| 46 | /// <returns>The pareto front containing the best solutions and their associated quality resp. fitness.</returns>
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| 47 | public static List<Tuple<T, double[]>> CalculateBestParetoFront(T[] solutions, double[][] qualities, bool[] maximization, bool dominateOnEqualQualities = true) {
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| 48 | int populationSize = solutions.Length;
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| 49 |
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| 50 | Dictionary<T, List<int>> dominatedIndividuals;
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| 51 | int[] dominationCounter, rank;
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| 52 | return CalculateBestFront(solutions, qualities, maximization, dominateOnEqualQualities, populationSize, out dominatedIndividuals, out dominationCounter, out rank);
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| 53 | }
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| 54 |
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| 55 | /// <summary>
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| 56 | /// Calculates all pareto fronts. The first in the list is the best front.
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| 57 | /// The fast non-dominated sorting algorithm is used as described in
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| 58 | /// Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002).
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| 59 | /// A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II.
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| 60 | /// IEEE Transactions on Evolutionary Computation, 6(2), 182-197.
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| 61 | /// </summary>
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| 62 | /// <remarks>
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| 63 | /// When there are plateaus in the fitness landscape several solutions might have exactly
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| 64 | /// the same fitness vector. In this case parameter <paramref name="dominateOnEqualQualities"/>
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| 65 | /// can be set to true to avoid plateaus becoming too attractive for the search process.
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| 66 | /// </remarks>
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| 67 | /// <param name="solutions">The solutions of the population.</param>
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| 68 | /// <param name="qualities">The qualities resp. fitness for each solution.</param>
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| 69 | /// <param name="maximization">The objective in each dimension.</param>
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| 70 | /// <param name="rank">The rank of each of the solutions, corresponds to the front it is put in.</param>
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| 71 | /// <param name="dominateOnEqualQualities">Whether solutions of exactly equal quality should dominate one another.</param>
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| 72 | /// <returns>A sorted list of the pareto fronts from best to worst.</returns>
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| 73 | public static List<List<Tuple<T, double[]>>> CalculateAllParetoFronts(T[] solutions, double[][] qualities, bool[] maximization, out int[] rank, bool dominateOnEqualQualities = true) {
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| 74 | int populationSize = solutions.Length;
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| 75 |
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| 76 | Dictionary<T, List<int>> dominatedIndividuals;
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| 77 | int[] dominationCounter;
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| 78 | var fronts = new List<List<Tuple<T, double[]>>>();
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| 79 | fronts.Add(CalculateBestFront(solutions, qualities, maximization, dominateOnEqualQualities, populationSize, out dominatedIndividuals, out dominationCounter, out rank));
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| 80 | int i = 0;
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| 81 | while (i < fronts.Count && fronts[i].Count > 0) {
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| 82 | var nextFront = new List<Tuple<T, double[]>>();
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| 83 | foreach (var p in fronts[i]) {
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| 84 | List<int> dominatedIndividualsByp;
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| 85 | if (dominatedIndividuals.TryGetValue(p.Item1, out dominatedIndividualsByp)) {
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| 86 | for (int k = 0; k < dominatedIndividualsByp.Count; k++) {
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| 87 | int dominatedIndividual = dominatedIndividualsByp[k];
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| 88 | dominationCounter[dominatedIndividual] -= 1;
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| 89 | if (dominationCounter[dominatedIndividual] == 0) {
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| 90 | rank[dominatedIndividual] = i + 1;
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| 91 | nextFront.Add(Tuple.Create(solutions[dominatedIndividual], qualities[dominatedIndividual]));
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| 92 | }
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| 93 | }
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| 94 | }
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| 95 | }
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| 96 | i += 1;
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| 97 | fronts.Add(nextFront);
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| 98 | }
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| 99 | return fronts;
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| 100 | }
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| 101 |
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[15086] | 102 | private static List<Tuple<T, double[]>> CalculateBestFront(T[] solutions, double[][] qualities, bool[] maximization, bool dominateOnEqualQualities, int populationSize, out Dictionary<T, List<int>> dominatedIndividuals, out int[] dominationCounter, out int[] rank) {
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[15080] | 103 | var front = new List<Tuple<T, double[]>>();
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| 104 | dominatedIndividuals = new Dictionary<T, List<int>>();
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| 105 | dominationCounter = new int[populationSize];
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| 106 | rank = new int[populationSize];
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| 107 | for (int pI = 0; pI < populationSize - 1; pI++) {
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[15086] | 108 | var p = solutions[pI];
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[15080] | 109 | List<int> dominatedIndividualsByp;
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| 110 | if (!dominatedIndividuals.TryGetValue(p, out dominatedIndividualsByp))
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| 111 | dominatedIndividuals[p] = dominatedIndividualsByp = new List<int>();
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| 112 | for (int qI = pI + 1; qI < populationSize; qI++) {
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| 113 | var test = Dominates(qualities[pI], qualities[qI], maximization, dominateOnEqualQualities);
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| 114 | if (test == DominationResult.Dominates) {
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| 115 | dominatedIndividualsByp.Add(qI);
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| 116 | dominationCounter[qI] += 1;
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| 117 | } else if (test == DominationResult.IsDominated) {
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| 118 | dominationCounter[pI] += 1;
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[15086] | 119 | if (!dominatedIndividuals.ContainsKey(solutions[qI]))
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| 120 | dominatedIndividuals.Add(solutions[qI], new List<int>());
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| 121 | dominatedIndividuals[solutions[qI]].Add(pI);
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[15080] | 122 | }
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| 123 | if (pI == populationSize - 2
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| 124 | && qI == populationSize - 1
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| 125 | && dominationCounter[qI] == 0) {
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| 126 | rank[qI] = 0;
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[15086] | 127 | front.Add(Tuple.Create(solutions[qI], qualities[qI]));
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[15080] | 128 | }
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| 129 | }
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| 130 | if (dominationCounter[pI] == 0) {
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| 131 | rank[pI] = 0;
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| 132 | front.Add(Tuple.Create(p, qualities[pI]));
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| 133 | }
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| 134 | }
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| 135 | return front;
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| 136 | }
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| 137 |
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| 138 | /// <summary>
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| 139 | /// Calculates the domination result of two solutions which are given in form
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| 140 | /// of their quality resp. fitness vector.
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| 141 | /// </summary>
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| 142 | /// <param name="left">The fitness of the solution that is to be compared.</param>
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| 143 | /// <param name="right">The fitness of the solution which is compared against.</param>
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| 144 | /// <param name="maximizations">The objective in each dimension.</param>
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| 145 | /// <param name="dominateOnEqualQualities">Whether the result should be Dominates in case both fitness vectors are exactly equal</param>
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| 146 | /// <returns>Dominates if left dominates right, IsDominated if right dominates left and IsNonDominated otherwise.</returns>
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| 147 | public static DominationResult Dominates(double[] left, double[] right, bool[] maximizations, bool dominateOnEqualQualities) {
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| 148 | //mkommend Caution: do not use LINQ.SequenceEqual for comparing the two quality arrays (left and right) due to performance reasons
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| 149 | if (dominateOnEqualQualities) {
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| 150 | var equal = true;
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| 151 | for (int i = 0; i < left.Length; i++) {
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| 152 | if (left[i] != right[i]) {
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| 153 | equal = false;
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| 154 | break;
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| 155 | }
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| 156 | }
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| 157 | if (equal) return DominationResult.Dominates;
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| 158 | }
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| 159 |
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| 160 | bool leftIsBetter = false, rightIsBetter = false;
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| 161 | for (int i = 0; i < left.Length; i++) {
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| 162 | if (IsDominated(left[i], right[i], maximizations[i])) rightIsBetter = true;
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| 163 | else if (IsDominated(right[i], left[i], maximizations[i])) leftIsBetter = true;
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| 164 | if (leftIsBetter && rightIsBetter) break;
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| 165 | }
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| 166 |
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| 167 | if (leftIsBetter && !rightIsBetter) return DominationResult.Dominates;
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| 168 | if (!leftIsBetter && rightIsBetter) return DominationResult.IsDominated;
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| 169 | return DominationResult.IsNonDominated;
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| 170 | }
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| 171 |
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| 172 | /// <summary>
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| 173 | /// A simple check if the quality resp. fitness in <paramref name="left"/> is better than
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| 174 | /// that given in <paramref name="right"/>.
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| 175 | /// </summary>
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| 176 | /// <param name="left">The first fitness value</param>
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| 177 | /// <param name="right">The second fitness value</param>
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| 178 | /// <param name="maximization">The objective direction</param>
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| 179 | /// <returns>True if left is better than right, false if it is not.</returns>
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| 180 | public static bool IsDominated(double left, double right, bool maximization) {
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| 181 | return maximization && left < right
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| 182 | || !maximization && left > right;
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| 183 | }
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| 184 | }
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| 185 | }
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