1 | #region License Information
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2 | /* HeuristicLab
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3 | * Copyright (C) 2002-2013 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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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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24 | using System.Linq;
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25 |
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26 | namespace HeuristicLab.Analysis.AlgorithmBehavior.Analyzers {
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27 | /*
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28 | * Calculate Convex Hull using Linear Programming as described in
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29 | * J.B. Rosen et. al., 1989, Efficient computation of convex hull in Rd
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30 | * and
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31 | * P.M. Pardalos et. al., 1995,
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32 | * Linear programming approaches to the convex hull problem in Rm
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33 | *
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34 | */
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35 | public static class LPHull {
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36 | public static List<double[]> Calculate(double[][] inputs) {
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37 | List<double[]> C = new List<double[]>();
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38 | List<double[]> E = new List<double[]>();
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39 |
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40 | //Phase 1
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41 | double[][] A = SortA(inputs);
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42 |
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43 | //Phase 2
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44 | C.Add(A[0]);
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45 | for (int i = 1; i < A.Length; i++) {
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46 | if (EXT(C, A[i])) {
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47 | C.Add(A[i]);
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48 | }
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49 | }
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50 |
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51 | //Phase 3
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52 | for (int i = 0; i < C.Count; i++) {
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53 | //TODO: this is not very efficient
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54 | if (EXT(ExcludeRow(C, i), C[i], i)) {
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55 | E.Add(C[i]);
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56 | }
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57 | }
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58 |
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59 | return E;
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60 | }
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61 |
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62 | private static List<double[]> ExcludeRow(List<double[]> matrix, int row) {
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63 | List<double[]> result = new List<double[]>();
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64 |
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65 | for (int i = 0; i < matrix.Count; i++) {
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66 | if (i != row) {
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67 | var tmpRow = new double[matrix[i].Length];
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68 | result.Add(tmpRow);
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69 | for (int j = 0; j < matrix[i].Length; j++) {
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70 | tmpRow[j] = matrix[i][j];
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71 | }
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72 | }
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73 | }
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74 |
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75 | return result;
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76 | }
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77 |
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78 | //sort A decreasing by distance to center of polytope
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79 | public static double[][] SortA(double[][] A) {
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80 | //TODO: sort inplace
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81 | int length = A[0].Length;
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82 | double[] maxs = new double[length];
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83 | double[] mins = new double[length];
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84 | double[][] sortedA = new double[A.Length][];
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85 |
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86 | for (int i = 0; i < maxs.Length; i++) {
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87 | maxs[i] = double.MinValue;
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88 | mins[i] = double.MaxValue;
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89 | }
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90 |
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91 | for (int i = 0; i < A.Length; i++) {
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92 | for (int j = 0; j < A[i].Length; j++) {
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93 | if (A[i][j] > maxs[j]) maxs[j] = A[i][j];
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94 | if (A[i][j] < mins[j]) mins[j] = A[i][j];
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95 | }
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96 | }
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97 |
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98 | double[] d = new double[length];
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99 | double[] r = new double[length];
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100 |
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101 | //calculate center
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102 | for (int i = 0; i < length; i++) {
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103 | d[i] = (maxs[i] + mins[i]) / 2.0;
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104 | }
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105 |
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106 | //calculate length of sides of rectangle
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107 | for (int i = 0; i < length; i++) {
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108 | r[i] = maxs[i] - mins[i];
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109 | }
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110 |
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111 | VertexComparer comparer = new VertexComparer();
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112 | comparer.d = d;
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113 | comparer.r = r;
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114 | sortedA = A.OrderByDescending(x => x, comparer).ToArray();
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115 |
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116 | return sortedA;
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117 | }
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118 |
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119 | /// <summary>
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120 | /// Checks if alpha is an extreme point (lies on convex hull) of A.
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121 | /// Returns true if alpha is an extreme point, else false.
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122 | /// </summary>
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123 | private static bool EXT(List<double[]> A, double[] alpha, int aIdx = -1) {
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124 | alglib.minbleicstate state;
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125 | double diffstep = 1.0e-6;
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126 | int N = alpha.Length;
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127 | int K = A.Count;
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128 |
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129 |
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130 | double[] init = new double[N];
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131 | double[] lowerBound = new double[N];
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132 | double[] upperBound = new double[N];
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133 | double[] x;
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134 | alglib.minbleicreport rep;
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135 | double[,] c = new double[K + 1, N + 1];
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136 | int[] ct = new int[K + 1]; //init with 0, means equal
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137 |
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138 | for (int i = 0; i < N; i++) {
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139 | //TODO: this should be a feasible solution
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140 | init[i] = 1.0;
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141 | lowerBound[i] = 0.0;
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142 | upperBound[i] = double.MaxValue;
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143 | }
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144 |
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145 | //last column gets b
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146 | for (int i = 0; i < K; i++) {
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147 | c[i, N] = alpha[i];
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148 | }
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149 | //sum(x) == 1 constraint
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150 | for (int i = 0; i < N + 1; i++) {
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151 | c[K, i] = 1.0;
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152 | }
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153 |
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154 | for (int i = 0; i < K; i++) {
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155 | for (int j = 0; j < N; j++) {
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156 | c[j, i] = A[i][j];
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157 | }
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158 | }
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159 |
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160 | alglib.minbleiccreatef(init, diffstep, out state);
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161 | alglib.minbleicsetbc(state, lowerBound, upperBound);
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162 | alglib.minbleicsetlc(state, c, ct);
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163 | alglib.minbleicsetcond(state, 0.0, 0.0, 0.0, 0);
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164 | alglib.minbleicoptimize(state, Func, null, new Tuple<List<double[]>, int>(A, aIdx));
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165 | alglib.minbleicresults(state, out x, out rep);
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166 |
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167 | return x.Sum() > 0;
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168 | }
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169 |
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170 | private static void Func(double[] x, ref double func, object obj) {
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171 | Tuple<List<double[]>, int> data = obj as Tuple<List<double[]>, int>;
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172 | int aIdx = data.Item2;
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173 | List<double[]> A = data.Item1;
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174 |
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175 | //TODO: I have no idea what I'm doing...
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176 | func = 0.0;
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177 | for (int i = 0; i < A.Count; i++) {
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178 | if (i != aIdx) {
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179 | for (int j = 0; j < A[i].Length; j++) {
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180 | func += A[i][j] * x[i];
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181 | }
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182 | }
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183 | }
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184 | }
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185 | }
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186 | }
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