1  #region License Information


2  /* HeuristicLab


3  * Copyright (C) 20022016 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 


22  using HeuristicLab.Common;


23  using HeuristicLab.Core;


24  using HeuristicLab.Data;


25  using HeuristicLab.Encodings.PermutationEncoding;


26  using HeuristicLab.Optimization;


27  using HeuristicLab.Parameters;


28  using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;


29  using HeuristicLab.Problems.QuadraticAssignment;


30  using HeuristicLab.Random;


31  using System;


32  using System.Collections.Generic;


33  using System.Linq;


34 


35  namespace HeuristicLab.Problems.CharacteristicAnalysis.QAP {


36  [Item("Directed Walk (QAPspecific)", "")]


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  IRandom random = Seed.HasValue ? new MersenneTwister((uint)Seed.Value) : new MersenneTwister();


88  var qap = (QuadraticAssignmentProblem)Problem;


89  var pathCount = Paths;


90 


91  var perm = new Permutation(PermutationTypes.Absolute, qap.Weights.Rows, random);


92  var permutations = new List<Permutation> { perm };


93  while (permutations.Count < pathCount + 1) {


94  perm = (Permutation)permutations.Last().Clone();


95  BiasedShuffle(perm, random);


96  permutations.Add(perm);


97  }


98 


99  var trajectories = Run(random, (QuadraticAssignmentProblem)Problem, permutations, BestImprovement).ToList();


100  var firstDerivatives = trajectories.Select(path => ApproximateDerivative(path).ToList()).ToList();


101  var secondDerivatives = firstDerivatives.Select(d1 => ApproximateDerivative(d1).ToList()).ToList();


102 


103  var props = GetCharacteristics(trajectories, firstDerivatives, secondDerivatives).ToDictionary(x => x.Item1, x => x.Item2);


104  foreach (var chara in characteristics.CheckedItems.Select(x => x.Value.Value)) {


105  if (chara == "Swap2.Sharpness") yield return new Result("Swap2.Sharpness", new DoubleValue(props["Sharpness"]));


106  if (chara == "Swap2.Bumpiness") yield return new Result("Swap2.Bumpiness", new DoubleValue(props["Bumpiness"]));


107  if (chara == "Swap2.Flatness") yield return new Result("Swap2.Flatness", new DoubleValue(props["Flatness"]));


108  if (chara == "Swap2.Steadiness") yield return new Result("Swap2.Steadiness", new DoubleValue(props["Steadiness"]));


109  }


110  }


111 


112  public static IEnumerable<List<Tuple<Permutation, double>>> Run(IRandom random, QuadraticAssignmentProblem qap, IEnumerable<Permutation> permutations, bool bestImprovement = true) {


113  var iter = permutations.GetEnumerator();


114  if (!iter.MoveNext()) yield break;


115 


116  var start = iter.Current;


117  while (iter.MoveNext()) {


118  var end = iter.Current;


119 


120  var walk = (bestImprovement ? BestDirectedWalk(qap, start, end) : FirstDirectedWalk(random, qap, start, end)).ToList();


121  var max = walk.Max(x => x.Item2);


122  var min = walk.Min(x => x.Item2);


123  if (max > min)


124  yield return walk.Select(x => Tuple.Create(x.Item1, (x.Item2  min) / (max  min))).ToList();


125  else yield return walk.Select(x => Tuple.Create(x.Item1, 0.0)).ToList();


126  start = end;


127  } // end paths


128  }


129 


130  private IEnumerable<Tuple<string, double>> GetCharacteristics(List<List<Tuple<Permutation, double>>> f, List<List<Tuple<Permutation, double>>> f1, List<List<Tuple<Permutation, double>>> f2) {


131  var sharpness = f2.Average(x => Area(x));


132  var bumpiness = 0.0;


133  var flatness = 0.0;


134  var downPointing = f1.Where(x => x.Min(y => y.Item2) < 0).ToList();


135 


136  var steadiness = 0.0;


137  foreach (var path in downPointing) {


138  steadiness += ComBelowZero(path);


139  }


140  if (downPointing.Count > 0) steadiness /= downPointing.Count;


141 


142  for (var p = 0; p < f2.Count; p++) {


143  var bump = 0;


144  var flat = 0;


145  for (var i = 0; i < f2[p].Count  1; i++) {


146  if ((f2[p][i].Item2 > 0 && f2[p][i + 1].Item2 < 0)  (f2[p][i].Item2 < 0 && f2[p][i + 1].Item2 > 0)) {


147  bump++;


148  } else if (f2[p][i].Item2 == 0) {


149  flat++;


150  }


151  }


152  bumpiness += bump / (f2[p].Count  1.0);


153  flatness += flat / (f2[p].Count  1.0);


154  }


155  bumpiness /= f2.Count;


156  flatness /= f2.Count;


157  return new[] {


158  Tuple.Create("Sharpness", sharpness),


159  Tuple.Create("Bumpiness", bumpiness),


160  Tuple.Create("Flatness", flatness),


161  Tuple.Create("Steadiness", steadiness)


162  };


163  }


164 


165  public static IEnumerable<Tuple<Permutation, double>> BestDirectedWalk(QuadraticAssignmentProblem qap, Permutation start, Permutation end) {


166  var N = qap.Weights.Rows;


167  var sol = start;


168  var fitness = QAPEvaluator.Apply(sol, qap.Weights, qap.Distances);


169  yield return Tuple.Create(sol, fitness);


170 


171  var invSol = GetInverse(sol);


172  // we require at most N1 steps to move from one permutation to another


173  for (var step = 0; step < N  1; step++) {


174  var bestFitness = double.MaxValue;


175  var bestIndex = 1;


176  sol = (Permutation)sol.Clone();


177  for (var index = 0; index < N; index++) {


178  if (sol[index] == end[index]) continue;


179  var fit = QAPSwap2MoveEvaluator.Apply(sol, new Swap2Move(index, invSol[end[index]]), qap.Weights, qap.Distances);


180  if (fit < bestFitness) { // QAP is minimization


181  bestFitness = fit;


182  bestIndex = index;


183  }


184  }


185  if (bestIndex >= 0) {


186  var prev = sol[bestIndex];


187  Swap2Manipulator.Apply(sol, bestIndex, invSol[end[bestIndex]]);


188  fitness += bestFitness;


189  yield return Tuple.Create(sol, fitness);


190  invSol[prev] = invSol[end[bestIndex]];


191  invSol[sol[bestIndex]] = bestIndex;


192  } else break;


193  }


194  }


195 


196  public static IEnumerable<Tuple<Permutation, double>> FirstDirectedWalk(IRandom random, QuadraticAssignmentProblem qap, Permutation start, Permutation end) {


197  var N = qap.Weights.Rows;


198  var sol = start;


199  var fitness = QAPEvaluator.Apply(sol, qap.Weights, qap.Distances);


200  yield return Tuple.Create(sol, fitness);


201 


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 N1 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 Area(IEnumerable<Tuple<Permutation, double>> path) {


232  var iter = path.GetEnumerator();


233  if (!iter.MoveNext()) return 0.0;


234  var area = 0.0;


235  var prev = iter.Current;


236  while (iter.MoveNext()) {


237  area += TrapezoidArea(prev, iter.Current);


238  prev = iter.Current;


239  }


240  return area;


241  }


242 


243  private static double TrapezoidArea(Tuple<Permutation, double> a, Tuple<Permutation, double> b) {


244  var area = 0.0;


245  var dist = Dist(a.Item1, b.Item1);


246  if ((a.Item2 <= 0 && b.Item2 <= 0)  (a.Item2 >= 0 && b.Item2 >= 0))


247  area += dist * (Math.Abs(a.Item2) + Math.Abs(b.Item2)) / 2.0;


248  else {


249  var k = (b.Item2  a.Item2) / dist;


250  var d = a.Item2;


251  var x = d / k;


252  area += Math.Abs(x * a.Item2 / 2.0);


253  area += Math.Abs((dist  x) * b.Item2 / 2.0);


254  }


255  return area;


256  }


257 


258  private static double ComBelowZero(IEnumerable<Tuple<Permutation, double>> path) {


259  var area = 0.0;


260  var com = 0.0;


261  var nwalkDist = 0.0;


262  Tuple<Permutation, double> prev = null;


263  var iter = path.GetEnumerator();


264  while (iter.MoveNext()) {


265  var c = iter.Current;


266  if (prev != null) {


267  var ndist = Dist(prev.Item1, c.Item1) / (double)c.Item1.Length;


268  nwalkDist += ndist;


269  if (prev.Item2 < 0  c.Item2 < 0) {


270  var a = TrapezoidArea(prev, c) / (double)c.Item1.Length;


271  area += a;


272  com += (nwalkDist  (ndist / 2.0)) * a;


273  }


274  }


275  prev = c;


276  }


277  return com / area;


278  }


279 


280  private static IEnumerable<Tuple<Permutation, double>> ApproximateDerivative(IEnumerable<Tuple<Permutation, double>> data) {


281  Tuple<Permutation, double> prev = null, prev2 = null;


282  foreach (var d in data) {


283  if (prev == null) {


284  prev = d;


285  continue;


286  }


287  if (prev2 == null) {


288  prev2 = prev;


289  prev = d;


290  continue;


291  }


292  var dist = Dist(prev2.Item1, d.Item1);


293  yield return Tuple.Create(prev.Item1, (d.Item2  prev2.Item2) / (double)dist);


294  prev2 = prev;


295  prev = d;


296  }


297  }


298 


299  private static double Dist(Permutation a, Permutation b) {


300  var dist = 0;


301  for (var i = 0; i < a.Length; i++)


302  if (a[i] != b[i]) dist++;


303  return dist;


304  }


305 


306  private static int[] GetInverse(Permutation p) {


307  var inv = new int[p.Length];


308  for (var i = 0; i < p.Length; i++) {


309  inv[p[i]] = i;


310  }


311  return inv;


312  }


313 


314  // permutation must be strictly different in every position


315  private static void BiasedShuffle(Permutation p, IRandom random) {


316  for (var i = p.Length  1; i > 0; i) {


317  // Swap element "i" with a random earlier element (excluding itself)


318  var swapIndex = random.Next(i);


319  var h = p[swapIndex];


320  p[swapIndex] = p[i];


321  p[i] = h;


322  }


323  }


324  }


325  }

