source: branches/PerformanceComparison/HeuristicLab.Analysis.FitnessLandscape/3.3/ProblemCharacteristicAnalysis/QAP/QAPDirectedWalk.cs @ 14690

#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
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 * 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/>.
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#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;
using System.Threading;

namespace HeuristicLab.Analysis.FitnessLandscape {
  [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 IFixedValueParameter<BoolValue> LocalOptimaParameter {
      get { return (IFixedValueParameter<BoolValue>)Parameters["LocalOptima"]; }
    }

    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; }
    }

    public bool LocalOptima {
      get { return LocalOptimaParameter.Value.Value; }
      set { LocalOptimaParameter.Value.Value = value; }
    }

    [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."));
      Parameters.Add(new FixedValueParameter<BoolValue>("LocalOptima", "Whether to perform walks between local optima.", new BoolValue(false)));
    }

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

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

    public override IEnumerable<IResult> Calculate() {
      IRandom random = Seed.HasValue ? new MersenneTwister((uint)Seed.Value) : new MersenneTwister();
      var qap = (QuadraticAssignmentProblem)Problem;
      var pathCount = Paths;

      var perm = new Permutation(PermutationTypes.Absolute, qap.Weights.Rows, random);
      if (LocalOptima) {
        var fit = new DoubleValue(QAPEvaluator.Apply(perm, qap.Weights, qap.Distances));
        QAPExhaustiveSwap2LocalImprovement.ImproveFast(perm, qap.Weights, qap.Distances, fit, new IntValue(0), new IntValue(0), qap.Maximization.Value, int.MaxValue, CancellationToken.None);
      }
      var permutations = new List<Permutation> { perm };
      while (permutations.Count < pathCount + 1) {
        perm = (Permutation)permutations.Last().Clone();
        BiasedShuffle(perm, random);
        if (LocalOptima) {
          var fit = new DoubleValue(QAPEvaluator.Apply(perm, qap.Weights, qap.Distances));
          QAPExhaustiveSwap2LocalImprovement.ImproveFast(perm, qap.Weights, qap.Distances, fit, new IntValue(0), new IntValue(0), qap.Maximization.Value, int.MaxValue, CancellationToken.None);
        }
        if (HammingSimilarityCalculator.CalculateSimilarity(permutations.Last(), perm) < 0.75)
          permutations.Add(perm);
      }

      var trajectories = Run(random, (QuadraticAssignmentProblem)Problem, permutations, BestImprovement).ToList();
      var firstDerivatives = trajectories.Select(path => ApproximateDerivative(path).ToList()).ToList();
      var secondDerivatives = firstDerivatives.Select(d1 => ApproximateDerivative(d1).ToList()).ToList();
      
      var props = GetCharacteristics(trajectories, firstDerivatives, secondDerivatives).ToDictionary(x => x.Item1, x => x.Item2);
      foreach (var chara in characteristics.CheckedItems.Select(x => x.Value.Value)) {
        if (chara == "Swap2.Sharpness") yield return new Result("Swap2.Sharpness", new DoubleValue(props["Sharpness"]));
        if (chara == "Swap2.Bumpiness") yield return new Result("Swap2.Bumpiness", new DoubleValue(props["Bumpiness"]));
        if (chara == "Swap2.Flatness") yield return new Result("Swap2.Flatness", new DoubleValue(props["Flatness"]));
        if (chara == "Swap2.Steadiness") yield return new Result("Swap2.Steadiness", new DoubleValue(props["Steadiness"]));
      }
    }

    public static IEnumerable<IResult> Calculate(List<List<Tuple<Permutation, double>>> trajectories) {
      var firstDerivatives = trajectories.Select(path => ApproximateDerivative(path).ToList()).ToList();
      var secondDerivatives = firstDerivatives.Select(d1 => ApproximateDerivative(d1).ToList()).ToList();

      var props = GetCharacteristics(trajectories, firstDerivatives, secondDerivatives).ToDictionary(x => x.Item1, x => x.Item2);
      yield return new Result("Swap2.Sharpness", new DoubleValue(props["Sharpness"]));
      yield return new Result("Swap2.Bumpiness", new DoubleValue(props["Bumpiness"]));
      yield return new Result("Swap2.Flatness", new DoubleValue(props["Flatness"]));
      yield return new Result("Swap2.Steadiness", new DoubleValue(props["Steadiness"]));
    }

    public static IEnumerable<List<Tuple<Permutation, double>>> Run(IRandom random, QuadraticAssignmentProblem qap, IEnumerable<Permutation> permutations, bool bestImprovement = true) {
      var iter = permutations.GetEnumerator();
      if (!iter.MoveNext()) yield break;

      var min = qap.LowerBound.Value;
      var max = qap.AverageQuality.Value;

      var start = iter.Current;
      while (iter.MoveNext()) {
        var end = iter.Current;

        var walk = (bestImprovement ? BestDirectedWalk(qap, start, end) : FirstDirectedWalk(random, qap, start, end)).ToList();
        yield return walk.Select(x => Tuple.Create(x.Item1, (x.Item2 - min) / (max - min))).ToList();
        start = end;
      } // end paths
    }

    private static IEnumerable<Tuple<string, double>> GetCharacteristics(List<List<Tuple<Permutation, double>>> f, List<List<Tuple<Permutation, double>>> f1, List<List<Tuple<Permutation, double>>> f2) {
      var sharpness = f2.Average(x => Area(x));
      var bumpiness = 0.0;
      var flatness = 0.0;
      var downPointing = f1.Where(x => x.Min(y => y.Item2) < 0).ToList();

      var steadiness = 0.0;
      foreach (var path in downPointing) {
        steadiness += ComBelowZero(path);
      }
      if (downPointing.Count > 0) steadiness /= downPointing.Count;

      for (var p = 0; p < f2.Count; p++) {
        if (f2[p].Count <= 2) continue;
        var bump = 0;
        var flat = 0;
        for (var i = 0; i < f2[p].Count - 1; i++) {
          if ((f2[p][i].Item2 > 0 && f2[p][i + 1].Item2 < 0) || (f2[p][i].Item2 < 0 && f2[p][i + 1].Item2 > 0)) {
            bump++;
          } else if (f2[p][i].Item2 == 0) {
            flat++;
          }
        }
        bumpiness += bump / (f2[p].Count - 1.0);
        flatness += flat / (f2[p].Count - 1.0);
      }
      bumpiness /= f2.Count;
      flatness /= f2.Count;
      return new[] {
      Tuple.Create("Sharpness", sharpness),
      Tuple.Create("Bumpiness", bumpiness),
      Tuple.Create("Flatness", flatness),
      Tuple.Create("Steadiness", steadiness)
    };
    }

    public static IEnumerable<Tuple<Permutation, double>> BestDirectedWalk(QuadraticAssignmentProblem qap, Permutation start, Permutation end) {
      var N = qap.Weights.Rows;
      var sol = start;
      var fitness = QAPEvaluator.Apply(sol, qap.Weights, qap.Distances);
      yield return Tuple.Create(sol, fitness);

      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 static IEnumerable<Tuple<Permutation, double>> FirstDirectedWalk(IRandom random, QuadraticAssignmentProblem qap, Permutation start, Permutation end) {
      var N = qap.Weights.Rows;
      var sol = start;
      var fitness = QAPEvaluator.Apply(sol, qap.Weights, qap.Distances);
      yield return Tuple.Create(sol, fitness);

      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 Area(IEnumerable<Tuple<Permutation, double>> path) {
      var iter = path.GetEnumerator();
      if (!iter.MoveNext()) return 0.0;
      var area = 0.0;
      var prev = iter.Current;
      while (iter.MoveNext()) {
        area += TrapezoidArea(prev, iter.Current);
        prev = iter.Current;
      }
      return area;
    }

    private static double TrapezoidArea(Tuple<Permutation, double> a, Tuple<Permutation, double> b) {
      var area = 0.0;
      var dist = Dist(a.Item1, b.Item1);
      if ((a.Item2 <= 0 && b.Item2 <= 0) || (a.Item2 >= 0 && b.Item2 >= 0))
        area += dist * (Math.Abs(a.Item2) + Math.Abs(b.Item2)) / 2.0;
      else {
        var k = (b.Item2 - a.Item2) / dist;
        var d = a.Item2;
        var x = -d / k;
        area += Math.Abs(x * a.Item2 / 2.0);
        area += Math.Abs((dist - x) * b.Item2 / 2.0);
      }
      return area;
    }

    // Center-of-Mass
    private static double ComBelowZero(IEnumerable<Tuple<Permutation, double>> path) {
      var area = 0.0;
      var com = 0.0;
      var nwalkDist = 0.0;
      Tuple<Permutation, double> prev = null;
      var iter = path.GetEnumerator();
      while (iter.MoveNext()) {
        var c = iter.Current;
        if (prev != null) {
          var ndist = Dist(prev.Item1, c.Item1) / (double)c.Item1.Length;
          nwalkDist += ndist;
          if (prev.Item2 < 0 || c.Item2 < 0) {
            var a = TrapezoidArea(prev, c) / (double)c.Item1.Length;
            area += a;
            com += (nwalkDist - (ndist / 2.0)) * a;
          }
        }
        prev = c;
      }
      return com / area;
    }

    private static IEnumerable<Tuple<Permutation, double>> ApproximateDerivative(IEnumerable<Tuple<Permutation, double>> data) {
      Tuple<Permutation, double> prev = null, prev2 = null;
      foreach (var d in data) {
        if (prev == null) {
          prev = d;
          continue;
        }
        if (prev2 == null) {
          prev2 = prev;
          prev = d;
          continue;
        }
        var dist = Dist(prev2.Item1, d.Item1);
        yield return Tuple.Create(prev.Item1, (d.Item2 - prev2.Item2) / (double)dist);
        prev2 = prev;
        prev = d;
      }
    }

    private static double Dist(Permutation a, Permutation b) {
      var dist = 0;
      for (var i = 0; i < a.Length; i++)
        if (a[i] != b[i]) dist++;
      return dist;
    }

    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;
    }

    // permutation must be strictly different in every position
    private static void BiasedShuffle(Permutation p, IRandom random) {
      for (var i = p.Length - 1; i > 0; i--) {
        // Swap element "i" with a random earlier element (excluding itself)
        var swapIndex = random.Next(i);
        var h = p[swapIndex];
        p[swapIndex] = p[i];
        p[i] = h;
      }
    }
  }
}