Index: branches/PerformanceComparison/HeuristicLab.OptimizationExpertSystem.Common/3.3/ProblemCharacteristicAnalysis/QAP/QAPBestDirectedWalk.cs
===================================================================
--- branches/PerformanceComparison/HeuristicLab.OptimizationExpertSystem.Common/3.3/ProblemCharacteristicAnalysis/QAP/QAPBestDirectedWalk.cs	(revision 13861)
+++ branches/PerformanceComparison/HeuristicLab.OptimizationExpertSystem.Common/3.3/ProblemCharacteristicAnalysis/QAP/QAPBestDirectedWalk.cs	(revision 13861)
@@ -0,0 +1,247 @@
+﻿#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;
+    }
+  }
+}
