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

#region License Information
/* HeuristicLab
 * Copyright (C) 2002-2016 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
 *
 * This file is part of HeuristicLab.
 *
 * HeuristicLab is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * HeuristicLab is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
 */
#endregion

using HeuristicLab.Common;
using HeuristicLab.Core;
using HeuristicLab.Data;
using HeuristicLab.Encodings.PermutationEncoding;
using HeuristicLab.Optimization;
using HeuristicLab.Parameters;
using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
using HeuristicLab.Problems.QuadraticAssignment;
using HeuristicLab.Random;
using System;
using System.Collections.Generic;
using System.Linq;

namespace HeuristicLab.Problems.CharacteristicAnalysis.QAP {
  [Item("Directed Walk (QAP-specific)", "")]
  [StorableClass]
  public class QAPDirectedWalk : CharacteristicCalculator {
    
    public IFixedValueParameter<IntValue> PathsParameter {
      get { return (IFixedValueParameter<IntValue>)Parameters["Paths"]; }
    }

    public IFixedValueParameter<BoolValue> BestImprovementParameter {
      get { return (IFixedValueParameter<BoolValue>)Parameters["BestImprovement"]; }
    }

    public IValueParameter<IntValue> SeedParameter {
      get { return (IValueParameter<IntValue>)Parameters["Seed"]; }
    }

    public int Paths {
      get { return PathsParameter.Value.Value; }
      set { PathsParameter.Value.Value = value; }
    }

    public bool BestImprovement {
      get { return BestImprovementParameter.Value.Value; }
      set { BestImprovementParameter.Value.Value = value; }
    }

    public int? Seed {
      get { return SeedParameter.Value != null ? SeedParameter.Value.Value : (int?)null; }
      set { SeedParameter.Value = value.HasValue ? new IntValue(value.Value) : null; }
    }

    [StorableConstructor]
    private QAPDirectedWalk(bool deserializing) : base(deserializing) { }
    private QAPDirectedWalk(QAPDirectedWalk original, Cloner cloner) : base(original, cloner) { }
    public QAPDirectedWalk() {
      characteristics.AddRange(new[] { "Swap2.Sharpness", "Swap2.Bumpiness", "Swap2.Flatness", "Swap2.Steadiness" }
        .Select(x => new StringValue(x)).ToList());
      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)));
      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)));
      Parameters.Add(new OptionalValueParameter<IntValue>("Seed", "The seed for the random number generator."));
    }

    public override IDeepCloneable Clone(Cloner cloner) {
      return new QAPDirectedWalk(this, cloner);
    }

    public override bool CanCalculate() {
      return Problem is QuadraticAssignmentProblem;
    }

    public override IEnumerable<IResult> Calculate() {
      var pathCount = Paths;
      var random = Seed.HasValue ? new MersenneTwister((uint)Seed.Value) : new MersenneTwister();
      var bestImprovement = BestImprovement;
      var qap = (QuadraticAssignmentProblem)Problem;
      var N = qap.Weights.Rows;
      var start = new Permutation(PermutationTypes.Absolute, N, random);
      var end = start;
      List<double> ips = new List<double>(), ups = new List<double>(), sd2 = new List<double>();
      var pathsD1 = new List<List<Tuple<double, double>>>();
      for (var i = 0; i < pathCount; i++) {
        var trajD1 = new List<Tuple<double, double>>();
        pathsD1.Add(trajD1);

        if ((i + 1) % N == 0) {
          start = new Permutation(PermutationTypes.Absolute, N, random);
          end = start;
        }
        end = (Permutation)end.Clone();
        Rot1(end);

        var hist = new Tuple<Permutation, double>[5];
        var walkDist = 0.0;
        var prevVal = double.NaN;
        var sumD2 = 0.0;
        var inflectionPoints = 0;
        var undulationPoints = 0;
        var countPoints = 0;
        var counter = 0;
        var path = bestImprovement ? BestImprovementWalk(qap, start, QAPEvaluator.Apply(start, qap.Weights, qap.Distances), end)
                                  : FirstImprovementWalk(qap, start, QAPEvaluator.Apply(start, qap.Weights, qap.Distances), end, random);
        foreach (var next in path) {
          if (hist[0] != null) {
            var dist = Dist(next.Item1, hist[0].Item1);
            walkDist += dist;
          }
          // from the past 5 values we can calculate the 2nd derivative
          // first derivative in point 2 as differential between points 1 and 3
          // first derivative in point 4 as differential between points 3 and 5
          // second derivative in point 3 as differential between the first derivatives in points 2 and 4
          hist[4] = hist[3];
          hist[3] = hist[2];
          hist[2] = hist[1];
          hist[1] = hist[0];
          hist[0] = next;
          counter++;

          if (counter < 3) continue;
          var grad1 = (hist[0].Item2 - hist[2].Item2) / Dist(hist[0].Item1, hist[2].Item1);

          if (!double.IsNaN(grad1) && !double.IsInfinity(grad1))
            trajD1.Add(Tuple.Create(walkDist, grad1));

          if (counter < 5) continue;
          countPoints++;
          var grad2 = (hist[2].Item2 - hist[4].Item2) / Dist(hist[2].Item1, hist[4].Item1);
          var dgrad = (grad1 - grad2) / Dist(hist[1].Item1, hist[3].Item1);

          if (double.IsNaN(dgrad) || double.IsInfinity(dgrad)) continue;
          if (!double.IsNaN(prevVal)) {
            if (prevVal < 0 && dgrad > 0 || prevVal > 0 && dgrad < 0)
              inflectionPoints++;
            else if (prevVal.IsAlmost(0) && dgrad.IsAlmost(0)
                || prevVal.IsAlmost(0) && !dgrad.IsAlmost(0)
                || !prevVal.IsAlmost(0) && dgrad.IsAlmost(0))
              undulationPoints++;
          }
          sumD2 += Math.Abs(grad1 - grad2);
          prevVal = dgrad;
        }
        start = end;
        ips.Add(inflectionPoints / (double)countPoints);
        ups.Add(undulationPoints / (double)countPoints);
        sd2.Add(sumD2 / walkDist);
      } // end paths
      var avgZero = pathsD1.Select(path => path.SkipWhile(v => v.Item2 < 0).First().Item1 / path.Last().Item1).Median();
      
      foreach (var chara in characteristics.CheckedItems.Select(x => x.Value.Value)) {
        if (chara == "Swap2.Sharpness") yield return new Result("Swap2.Sharpness", new DoubleValue(sd2.Average()));
        if (chara == "Swap2.Bumpiness") yield return new Result("Swap2.Bumpiness", new DoubleValue(ips.Average()));
        if (chara == "Swap2.Flatness") yield return new Result("Swap2.Flatness", new DoubleValue(ups.Average()));
        if (chara == "Swap2.Steadiness") yield return new Result("Swap2.Steadiness", new DoubleValue(avgZero));
      }
    }

    public IEnumerable<Tuple<Permutation, double>> BestImprovementWalk(QuadraticAssignmentProblem qap, Permutation start, double fitness, Permutation end) {
      var N = qap.Weights.Rows;
      var sol = start;
      var invSol = GetInverse(sol);
      // we require at most N-1 steps to move from one permutation to another
      for (var step = 0; step < N - 1; step++) {
        var bestFitness = double.MaxValue;
        var bestIndex = -1;
        sol = (Permutation)sol.Clone();
        for (var index = 0; index < N; index++) {
          if (sol[index] == end[index]) continue;
          var fit = QAPSwap2MoveEvaluator.Apply(sol, new Swap2Move(index, invSol[end[index]]), qap.Weights, qap.Distances);
          if (fit < bestFitness) { // QAP is minimization
            bestFitness = fit;
            bestIndex = index;
          }
        }
        if (bestIndex >= 0) {
          var prev = sol[bestIndex];
          Swap2Manipulator.Apply(sol, bestIndex, invSol[end[bestIndex]]);
          fitness += bestFitness;
          yield return Tuple.Create(sol, fitness);
          invSol[prev] = invSol[end[bestIndex]];
          invSol[sol[bestIndex]] = bestIndex;
        } else break;
      }
    }

    public IEnumerable<Tuple<Permutation, double>> FirstImprovementWalk(QuadraticAssignmentProblem qap, Permutation start, double fitness, Permutation end, IRandom random) {
      var N = qap.Weights.Rows;
      var sol = start;
      var invSol = GetInverse(sol);
      // randomize the order in which improvements are tried
      var order = Enumerable.Range(0, N).Shuffle(random).ToArray();
      // we require at most N-1 steps to move from one permutation to another
      for (var step = 0; step < N - 1; step++) {
        var bestFitness = double.MaxValue;
        var bestIndex = -1;
        sol = (Permutation)sol.Clone();
        for (var i = 0; i < N; i++) {
          var index = order[i];
          if (sol[index] == end[index]) continue;
          var fit = QAPSwap2MoveEvaluator.Apply(sol, new Swap2Move(index, invSol[end[index]]), qap.Weights, qap.Distances);
          if (fit < bestFitness) { // QAP is minimization
            bestFitness = fit;
            bestIndex = index;
            if (bestFitness < 0) break;
          }
        }
        if (bestIndex >= 0) {
          var prev = sol[bestIndex];
          Swap2Manipulator.Apply(sol, bestIndex, invSol[end[bestIndex]]);
          fitness += bestFitness;
          yield return Tuple.Create(sol, fitness);
          invSol[prev] = invSol[end[bestIndex]];
          invSol[sol[bestIndex]] = bestIndex;
        } else break;
      }
    }

    private static double Dist(Permutation a, Permutation b) {
      return a.Where((t, i) => t != b[i]).Count();
    }

    private static int[] GetInverse(Permutation p) {
      var inv = new int[p.Length];
      for (var i = 0; i < p.Length; i++) inv[p[i]] = i;
      return inv;
    }

    private static void Rot1(Permutation p) {
      var first = p[0];
      for (var i = 0; i < p.Length - 1; i++) p[i] = p[i + 1];
      p[p.Length - 1] = first;
    }
  }
}