source: branches/PerformanceComparison/HeuristicLab.OptimizationExpertSystem.Common/3.3/ProblemCharacteristicAnalysis/QAP/QAPBestDirectedWalk.cs @ 13861

Last change on this file since 13861 was 13861, checked in by abeham, 5 years ago

#2457: added directed walk for qap

File size: 10.6 KB
Line 
1#region License Information
2/* HeuristicLab
3 * Copyright (C) 2002-2016 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
4 *
5 * This file is part of HeuristicLab.
6 *
7 * HeuristicLab is free software: you can redistribute it and/or modify
8 * it under the terms of the GNU General Public License as published by
9 * the Free Software Foundation, either version 3 of the License, or
10 * (at your option) any later version.
11 *
12 * HeuristicLab is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
15 * GNU General Public License for more details.
16 *
17 * You should have received a copy of the GNU General Public License
18 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
19 */
20#endregion
21
22using HeuristicLab.Common;
23using HeuristicLab.Core;
24using HeuristicLab.Data;
25using HeuristicLab.Encodings.PermutationEncoding;
26using HeuristicLab.Optimization;
27using HeuristicLab.Parameters;
28using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
29using HeuristicLab.Problems.QuadraticAssignment;
30using HeuristicLab.Random;
31using System;
32using System.Collections.Generic;
33using System.Linq;
34
35namespace HeuristicLab.Problems.CharacteristicAnalysis.QAP {
36  [Item("Directed Walk (QAP-specific)", "")]
37  [StorableClass]
38  public class QAPDirectedWalk : CharacteristicCalculator {
39   
40    public IFixedValueParameter<IntValue> PathsParameter {
41      get { return (IFixedValueParameter<IntValue>)Parameters["Paths"]; }
42    }
43
44    public IFixedValueParameter<BoolValue> BestImprovementParameter {
45      get { return (IFixedValueParameter<BoolValue>)Parameters["BestImprovement"]; }
46    }
47
48    public IValueParameter<IntValue> SeedParameter {
49      get { return (IValueParameter<IntValue>)Parameters["Seed"]; }
50    }
51
52    public int Paths {
53      get { return PathsParameter.Value.Value; }
54      set { PathsParameter.Value.Value = value; }
55    }
56
57    public bool BestImprovement {
58      get { return BestImprovementParameter.Value.Value; }
59      set { BestImprovementParameter.Value.Value = value; }
60    }
61
62    public int? Seed {
63      get { return SeedParameter.Value != null ? SeedParameter.Value.Value : (int?)null; }
64      set { SeedParameter.Value = value.HasValue ? new IntValue(value.Value) : null; }
65    }
66
67    [StorableConstructor]
68    private QAPDirectedWalk(bool deserializing) : base(deserializing) { }
69    private QAPDirectedWalk(QAPDirectedWalk original, Cloner cloner) : base(original, cloner) { }
70    public QAPDirectedWalk() {
71      characteristics.AddRange(new[] { "Swap2.Sharpness", "Swap2.Bumpiness", "Swap2.Flatness", "Swap2.Steadiness" }
72        .Select(x => new StringValue(x)).ToList());
73      Parameters.Add(new FixedValueParameter<IntValue>("Paths", "The number of paths to explore (a path is a set of solutions that connect two randomly chosen solutions).", new IntValue(50)));
74      Parameters.Add(new FixedValueParameter<BoolValue>("BestImprovement", "Whether the best of all alternatives should be chosen for each step in the path or just the first improving (least degrading) move should be made.", new BoolValue(true)));
75      Parameters.Add(new OptionalValueParameter<IntValue>("Seed", "The seed for the random number generator."));
76    }
77
78    public override IDeepCloneable Clone(Cloner cloner) {
79      return new QAPDirectedWalk(this, cloner);
80    }
81
82    public override bool CanCalculate() {
83      return Problem is QuadraticAssignmentProblem;
84    }
85
86    public override IEnumerable<IResult> Calculate() {
87      var pathCount = Paths;
88      var random = Seed.HasValue ? new MersenneTwister((uint)Seed.Value) : new MersenneTwister();
89      var bestImprovement = BestImprovement;
90      var qap = (QuadraticAssignmentProblem)Problem;
91      var N = qap.Weights.Rows;
92      var start = new Permutation(PermutationTypes.Absolute, N, random);
93      var end = start;
94      List<double> ips = new List<double>(), ups = new List<double>(), sd2 = new List<double>();
95      var pathsD1 = new List<List<Tuple<double, double>>>();
96      for (var i = 0; i < pathCount; i++) {
97        var trajD1 = new List<Tuple<double, double>>();
98        pathsD1.Add(trajD1);
99
100        if ((i + 1) % N == 0) {
101          start = new Permutation(PermutationTypes.Absolute, N, random);
102          end = start;
103        }
104        end = (Permutation)end.Clone();
105        Rot1(end);
106
107        var hist = new Tuple<Permutation, double>[5];
108        var walkDist = 0.0;
109        var prevVal = double.NaN;
110        var sumD2 = 0.0;
111        var inflectionPoints = 0;
112        var undulationPoints = 0;
113        var countPoints = 0;
114        var counter = 0;
115        var path = bestImprovement ? BestImprovementWalk(qap, start, QAPEvaluator.Apply(start, qap.Weights, qap.Distances), end)
116                                  : FirstImprovementWalk(qap, start, QAPEvaluator.Apply(start, qap.Weights, qap.Distances), end, random);
117        foreach (var next in path) {
118          if (hist[0] != null) {
119            var dist = Dist(next.Item1, hist[0].Item1);
120            walkDist += dist;
121          }
122          // from the past 5 values we can calculate the 2nd derivative
123          // first derivative in point 2 as differential between points 1 and 3
124          // first derivative in point 4 as differential between points 3 and 5
125          // second derivative in point 3 as differential between the first derivatives in points 2 and 4
126          hist[4] = hist[3];
127          hist[3] = hist[2];
128          hist[2] = hist[1];
129          hist[1] = hist[0];
130          hist[0] = next;
131          counter++;
132
133          if (counter < 3) continue;
134          var grad1 = (hist[0].Item2 - hist[2].Item2) / Dist(hist[0].Item1, hist[2].Item1);
135
136          if (!double.IsNaN(grad1) && !double.IsInfinity(grad1))
137            trajD1.Add(Tuple.Create(walkDist, grad1));
138
139          if (counter < 5) continue;
140          countPoints++;
141          var grad2 = (hist[2].Item2 - hist[4].Item2) / Dist(hist[2].Item1, hist[4].Item1);
142          var dgrad = (grad1 - grad2) / Dist(hist[1].Item1, hist[3].Item1);
143
144          if (double.IsNaN(dgrad) || double.IsInfinity(dgrad)) continue;
145          if (!double.IsNaN(prevVal)) {
146            if (prevVal < 0 && dgrad > 0 || prevVal > 0 && dgrad < 0)
147              inflectionPoints++;
148            else if (prevVal.IsAlmost(0) && dgrad.IsAlmost(0)
149                || prevVal.IsAlmost(0) && !dgrad.IsAlmost(0)
150                || !prevVal.IsAlmost(0) && dgrad.IsAlmost(0))
151              undulationPoints++;
152          }
153          sumD2 += Math.Abs(grad1 - grad2);
154          prevVal = dgrad;
155        }
156        start = end;
157        ips.Add(inflectionPoints / (double)countPoints);
158        ups.Add(undulationPoints / (double)countPoints);
159        sd2.Add(sumD2 / walkDist);
160      } // end paths
161      var avgZero = pathsD1.Select(path => path.SkipWhile(v => v.Item2 < 0).First().Item1 / path.Last().Item1).Median();
162     
163      foreach (var chara in characteristics.CheckedItems.Select(x => x.Value.Value)) {
164        if (chara == "Swap2.Sharpness") yield return new Result("Swap2.Sharpness", new DoubleValue(sd2.Average()));
165        if (chara == "Swap2.Bumpiness") yield return new Result("Swap2.Bumpiness", new DoubleValue(ips.Average()));
166        if (chara == "Swap2.Flatness") yield return new Result("Swap2.Flatness", new DoubleValue(ups.Average()));
167        if (chara == "Swap2.Steadiness") yield return new Result("Swap2.Steadiness", new DoubleValue(avgZero));
168      }
169    }
170
171    public IEnumerable<Tuple<Permutation, double>> BestImprovementWalk(QuadraticAssignmentProblem qap, Permutation start, double fitness, Permutation end) {
172      var N = qap.Weights.Rows;
173      var sol = start;
174      var invSol = GetInverse(sol);
175      // we require at most N-1 steps to move from one permutation to another
176      for (var step = 0; step < N - 1; step++) {
177        var bestFitness = double.MaxValue;
178        var bestIndex = -1;
179        sol = (Permutation)sol.Clone();
180        for (var index = 0; index < N; index++) {
181          if (sol[index] == end[index]) continue;
182          var fit = QAPSwap2MoveEvaluator.Apply(sol, new Swap2Move(index, invSol[end[index]]), qap.Weights, qap.Distances);
183          if (fit < bestFitness) { // QAP is minimization
184            bestFitness = fit;
185            bestIndex = index;
186          }
187        }
188        if (bestIndex >= 0) {
189          var prev = sol[bestIndex];
190          Swap2Manipulator.Apply(sol, bestIndex, invSol[end[bestIndex]]);
191          fitness += bestFitness;
192          yield return Tuple.Create(sol, fitness);
193          invSol[prev] = invSol[end[bestIndex]];
194          invSol[sol[bestIndex]] = bestIndex;
195        } else break;
196      }
197    }
198
199    public IEnumerable<Tuple<Permutation, double>> FirstImprovementWalk(QuadraticAssignmentProblem qap, Permutation start, double fitness, Permutation end, IRandom random) {
200      var N = qap.Weights.Rows;
201      var sol = start;
202      var invSol = GetInverse(sol);
203      // randomize the order in which improvements are tried
204      var order = Enumerable.Range(0, N).Shuffle(random).ToArray();
205      // we require at most N-1 steps to move from one permutation to another
206      for (var step = 0; step < N - 1; step++) {
207        var bestFitness = double.MaxValue;
208        var bestIndex = -1;
209        sol = (Permutation)sol.Clone();
210        for (var i = 0; i < N; i++) {
211          var index = order[i];
212          if (sol[index] == end[index]) continue;
213          var fit = QAPSwap2MoveEvaluator.Apply(sol, new Swap2Move(index, invSol[end[index]]), qap.Weights, qap.Distances);
214          if (fit < bestFitness) { // QAP is minimization
215            bestFitness = fit;
216            bestIndex = index;
217            if (bestFitness < 0) break;
218          }
219        }
220        if (bestIndex >= 0) {
221          var prev = sol[bestIndex];
222          Swap2Manipulator.Apply(sol, bestIndex, invSol[end[bestIndex]]);
223          fitness += bestFitness;
224          yield return Tuple.Create(sol, fitness);
225          invSol[prev] = invSol[end[bestIndex]];
226          invSol[sol[bestIndex]] = bestIndex;
227        } else break;
228      }
229    }
230
231    private static double Dist(Permutation a, Permutation b) {
232      return a.Where((t, i) => t != b[i]).Count();
233    }
234
235    private static int[] GetInverse(Permutation p) {
236      var inv = new int[p.Length];
237      for (var i = 0; i < p.Length; i++) inv[p[i]] = i;
238      return inv;
239    }
240
241    private static void Rot1(Permutation p) {
242      var first = p[0];
243      for (var i = 0; i < p.Length - 1; i++) p[i] = p[i + 1];
244      p[p.Length - 1] = first;
245    }
246  }
247}
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