[10060] | 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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[10081] | 46 | C.Add(A[i]);
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| 47 | if (!EXT(C, A[i], C.Count - 1)) {
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| 48 | C.Remove(A[i]);
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[10060] | 49 | }
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| 50 | }
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| 51 |
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| 52 | //Phase 3
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| 53 | for (int i = 0; i < C.Count; i++) {
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[10081] | 54 | if (EXT(C, C[i], i)) {
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[10060] | 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 | //sort A decreasing by distance to center of polytope
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| 63 | public static double[][] SortA(double[][] A) {
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| 64 | int length = A[0].Length;
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| 65 | double[] maxs = new double[length];
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| 66 | double[] mins = new double[length];
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| 67 | double[][] sortedA = new double[A.Length][];
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| 68 |
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| 69 | for (int i = 0; i < maxs.Length; i++) {
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| 70 | maxs[i] = double.MinValue;
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| 71 | mins[i] = double.MaxValue;
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| 72 | }
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| 73 |
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| 74 | for (int i = 0; i < A.Length; i++) {
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| 75 | for (int j = 0; j < A[i].Length; j++) {
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| 76 | if (A[i][j] > maxs[j]) maxs[j] = A[i][j];
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| 77 | if (A[i][j] < mins[j]) mins[j] = A[i][j];
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| 78 | }
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| 79 | }
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| 80 |
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| 81 | double[] d = new double[length];
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| 82 | double[] r = new double[length];
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| 83 |
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| 84 | //calculate center
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| 85 | for (int i = 0; i < length; i++) {
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| 86 | d[i] = (maxs[i] + mins[i]) / 2.0;
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| 87 | }
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| 88 |
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| 89 | //calculate length of sides of rectangle
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| 90 | for (int i = 0; i < length; i++) {
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| 91 | r[i] = maxs[i] - mins[i];
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| 92 | }
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| 93 |
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| 94 | VertexComparer comparer = new VertexComparer();
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| 95 | comparer.d = d;
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| 96 | comparer.r = r;
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| 97 | sortedA = A.OrderByDescending(x => x, comparer).ToArray();
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| 98 |
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| 99 | return sortedA;
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| 100 | }
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| 101 |
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| 102 | /// <summary>
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| 103 | /// Checks if alpha is an extreme point (lies on convex hull) of A.
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| 104 | /// Returns true if alpha is an extreme point, else false.
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| 105 | /// </summary>
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[10081] | 106 | public static bool EXT(List<double[]> A, double[] alpha, int aIdx = -1) {
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[10060] | 107 | alglib.minbleicstate state;
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| 108 | int N = alpha.Length;
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| 109 | int K = A.Count;
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[10081] | 110 | double[] init = new double[K];
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| 111 | double[] lowerBound = new double[K];
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| 112 | double[] upperBound = new double[K];
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[10060] | 113 | double[] x;
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| 114 | alglib.minbleicreport rep;
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[10081] | 115 | double[,] c = new double[N + 1, K + 1];
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| 116 | int[] ct = new int[N + 1]; //init with 0, means equal
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[10060] | 117 |
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[10081] | 118 | for (int i = 0; i < K; i++) {
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[10082] | 119 | init[i] = 0.0;
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[10060] | 120 | lowerBound[i] = 0.0;
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| 121 | upperBound[i] = double.MaxValue;
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| 122 | }
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[10082] | 123 | init[aIdx] = 1.0;
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[10060] | 124 |
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| 125 | //last column gets b
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[10081] | 126 | for (int i = 0; i < N; i++) {
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| 127 | c[i, K] = alpha[i];
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[10060] | 128 | }
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| 129 | //sum(x) == 1 constraint
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[10081] | 130 | for (int i = 0; i < K + 1; i++) {
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| 131 | c[N, i] = 1.0;
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[10060] | 132 | }
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| 133 |
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[10081] | 134 | //other constraints
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[10060] | 135 | for (int i = 0; i < K; i++) {
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| 136 | for (int j = 0; j < N; j++) {
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| 137 | c[j, i] = A[i][j];
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| 138 | }
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| 139 | }
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| 140 |
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[10081] | 141 | alglib.minbleiccreate(init, out state);
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[10060] | 142 | alglib.minbleicsetbc(state, lowerBound, upperBound);
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| 143 | alglib.minbleicsetlc(state, c, ct);
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| 144 | alglib.minbleicsetcond(state, 0.0, 0.0, 0.0, 0);
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[10082] | 145 | alglib.minbleicoptimize(state, Func, null, aIdx);
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[10060] | 146 | alglib.minbleicresults(state, out x, out rep);
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| 147 |
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[10082] | 148 | if (rep.terminationtype < 0) throw new ArgumentException("minbleic terminated with error");
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| 149 | if (rep.terminationtype == 5) Console.WriteLine("max number of iterations reached in minbleic");
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| 150 | return x[aIdx] >= 1.0;
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[10060] | 151 | }
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| 152 |
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[10081] | 153 | private static void Func(double[] x, ref double func, double[] grad, object obj) {
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[10082] | 154 | int aIdx = (int)obj;
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[10060] | 155 |
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[10082] | 156 | func = x[aIdx];
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[10081] | 157 | for (int i = 0; i < grad.Length; i++) {
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| 158 | grad[i] = 0;
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| 159 | }
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| 160 | grad[aIdx] = 1;
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[10060] | 161 | }
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| 162 | }
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| 163 | }
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