source: trunk/sources/HeuristicLab.Encodings.PermutationEncoding/3.3/Crossovers/MaximalPreservativeCrossover.cs @ 4068

#region License Information
/* HeuristicLab
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#endregion

using System;
using HeuristicLab.Core;
using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;

namespace HeuristicLab.Encodings.PermutationEncoding {
  /// <summary>An operator which performs the maximal preservative crossover on two permutations.</summary>
  /// <remarks>
  /// Performs a crossover between two permuation arrays by preserving a large number of edges in both parents.
  /// The operator also maintains the position in the arrays to some extent.
  /// It is implemented as described in Mühlenbein, H. 1991. Evolution in time and space - the parallel genetic algorithm. FOUNDATIONS OF GENETIC ALGORITHMS, pp. 316-337. Morgan Kaufmann.<br /><br />
  /// The length of the segment copied from the first parent to the offspring is uniformly distributed in the interval [3;N/3) with N = length of the permutation.
  /// This recommendation is mentioned in Pohlheim, H. 1999. Evolutionäre Algorithmen: Verfahren, Operatoren und Hinweise für die Praxis, p. 44, Springer.
  /// If the length of the permutation is smaller than 15, the size of the segment is always equal to 3.
  /// </remarks>
  [Item("MaximalPreservativeCrossover", "An operator which performs the maximal preservative crossover on two permutations. It is implemented as described in Mühlenbein, H. 1991. Evolution in time and space - the parallel genetic algorithm. FOUNDATIONS OF GENETIC ALGORITHMS, pp. 316-337. Morgan Kaufmann.")]
  [StorableClass]
  public class MaximalPreservativeCrossover : PermutationCrossover {
    /// <summary>
    /// Performs the maximal preservative crossover on <paramref name="parent1"/> and <paramref name="parent2"/>
    /// by preserving a large number of edges in both parents.
    /// </summary>
    /// <exception cref="ArgumentException">Thrown when <paramref name="parent1"/> and <paramref name="parent2"/> are not of equal length or when the permutations are shorter than 4 elements.</exception>
    /// <exception cref="InvalidOperationException">Thrown if the numbers in the permutation elements are not in the range [0;N) with N = length of the permutation.</exception>
    /// <remarks>
    /// First one segment is copied from the first parent to the offspring in the same position.
    /// Then the tour is completed by adding the next number from the second parent if such an edge exists,
    /// or from the first parent, or from the next number of the second parent.
    /// The last case results in an unwanted mutation.
    /// </remarks>
    /// <param name="random">A random number generator.</param>
    /// <param name="parent1">The first parent permutation to cross.</param>
    /// <param name="parent2">The second parent permutation to cross.</param>
    /// <returns>The new permutation resulting from the crossover.</returns>
    public static Permutation Apply(IRandom random, Permutation parent1, Permutation parent2) {
      if (parent1.Length != parent2.Length) throw new ArgumentException("MaximalPreservativeCrossover: The parent permutations are of unequal length.");
      if (parent1.Length < 4) throw new ArgumentException("MaximalPreservativeCrossover: The parent permutation must be at least of size 4.");
      int length = parent1.Length;
      int[] result = new int[length];
      bool[] numberCopied = new bool[length];
      int breakPoint1, breakPoint2, subsegmentLength, index;

      subsegmentLength = random.Next(3, Math.Max(length / 3, 4)); // as mentioned in Pohlheim, H. Evolutionäre Algorithmen: Verfahren, Operatoren und Hinweise für die Praxis, 1999, p.44, Springer.
      breakPoint1 = random.Next(length);
      breakPoint2 = breakPoint1 + subsegmentLength;
      if (breakPoint2 >= length) breakPoint2 -= length;

      // copy string between position [breakPoint1, breakPoint2) from parent1 to the offspring
      index = breakPoint1;
      do {
        result[index] = parent1[index];
        numberCopied[result[index]] = true;
        index++;
        if (index >= length) index -= length;
      } while (index != breakPoint2);

      // calculate inverse permutation (number -> index) to help finding the follower of a given number
      int[] invParent1 = new int[length];
      int[] invParent2 = new int[length];
      try {
        for (int i = 0; i < length; i++) {
          invParent1[parent1[i]] = i;
          invParent2[parent2[i]] = i;
        }
      }
      catch (IndexOutOfRangeException) {
        throw new InvalidOperationException("MaximalPreservativeCrossover: The permutation must consist of numbers in the interval [0;N) with N = length of the permutation.");
      }

      int prevIndex = ((index > 0) ? (index - 1) : (length - 1));
      do {
        // look for the follower of the last number in parent2
        int p2Follower = GetFollower(parent2, invParent2[result[prevIndex]]);
        if (!numberCopied[p2Follower]) {
          result[index] = p2Follower;
        } else {
          // if that follower has already been added, look for the follower of the last number in parent1
          int p1Follower = GetFollower(parent1, invParent1[result[prevIndex]]);
          if (!numberCopied[p1Follower]) {
            result[index] = p1Follower;
          } else {
            // if that has also been added, look for the next not already added number in parent2
            int tempIndex = index;
            for (int i = 0; i < parent2.Length; i++) {
              if (!numberCopied[parent2[tempIndex]]) {
                result[index] = parent2[tempIndex];
                break;
              }
              tempIndex++;
              if (tempIndex >= parent2.Length) tempIndex = 0;
            }
          }
        }
        numberCopied[result[index]] = true;
        prevIndex = index;
        index++;
        if (index >= length) index -= length;
      } while (index != breakPoint1);

      return new Permutation(parent1.PermutationType, result);
    }

    private static int GetFollower(Permutation parent, int index) {
      if (index + 1 == parent.Length)
        return parent[0];
      return parent[index + 1];
    }

    /// <summary>
    /// Checks number of parents and calls <see cref="Apply(IRandom, Permutation, Permutation)"/>.
    /// </summary>
    /// <exception cref="InvalidOperationException">Thrown if there are not exactly two permutations in <paramref name="parents"/>.</exception>
    /// <param name="random">A random number generator.</param>
    /// <param name="parents">An array containing the two permutations that should be crossed.</param>
    /// <returns>The newly created permutation, resulting from the crossover operation.</returns>
    protected override Permutation Cross(IRandom random, ItemArray<Permutation> parents) {
      if (parents.Length != 2) throw new InvalidOperationException("MaximalPreservativeCrossover: Number of parents is not equal to 2.");
      return Apply(random, parents[0], parents[1]);
    }
  }
}