source: branches/HeuristicLab.Problems.MultiObjectiveTestFunctions/HeuristicLab.Problems.MultiObjectiveTestFunctions/3.3/Calculators/HyperVolume.cs @ 13672

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#endregion
using System;
using System.Collections.Generic;
using System.Linq;

namespace HeuristicLab.Problems.MultiObjectiveTestFunctions {

  public class Hypervolume {

    /// <summary>
    /// The Hyprevolume-metric is defined as the Hypervolume enclosed between a given reference point,
    /// that is fixed for every evaluation function and the evaluated front.
    /// 
    /// Example:
    /// r is the reference Point at (1|1)  and every Point p is part of the evaluated front
    /// The filled Area labled HV is the 2 diensional Hypervolume enclosed by this front. 
    /// 
    /// (0|1)                (1|1)
    ///   +      +-------------r
    ///   |      |###### HV ###|
    ///   |      p------+######|
    ///   |             p+#####|
    ///   |              |#####|
    ///   |              p-+###|
    ///   |                p---+
    ///   |                 
    ///   +--------------------1
    /// (0|0)                (1|0)
    /// 
    ///  Please note that in this example both dimensions are minimized. The reference Point need to be dominated by EVERY point in the evaluated front 
    /// 
    /// </summary>
    public static double Calculate(IEnumerable<double[]> front, double[] reference, bool[] maximization) {
      if (front == null) throw new ArgumentException("Fronts must not be null");
      //TODO what to do if set contains dominated points
      double[][] set = front.ToArray();   //Still no Good
      if (set.Length == 0) throw new ArgumentException("Fronts must not be empty");
      Array.Sort<double[]>(set, Utilities.getDimensionComparer(0, maximization[0]));
      double[] last = set[set.Length - 1];
      CheckConsistency(last, 0, reference, maximization);
      CheckConsistency(last, 1, reference, maximization);

      double sum = 0;
      for (int i = 0; i < set.Length - 1; i++) {
        CheckConsistency(set[i], 1, reference, maximization);
        sum += Math.Abs((set[i][0] - set[i + 1][0])) * Math.Abs((set[i][1] - reference[1]));
      }

      sum += Math.Abs(reference[0] - last[0]) * Math.Abs(reference[1] - last[1]);
      return sum;
    }

    private static void CheckConsistency(double[] point, int dim, double[] reference, bool[] maximization) {
      if (!maximization[dim] && point[dim] > reference[dim]) throw new ArgumentException("Reference Point must be dominated by all points of the front");
      if (maximization[dim] && point[dim] < reference[dim]) throw new ArgumentException("Reference Point must be dominated by all points of the front");
      if (point.Length != 2) throw new ArgumentException("Only 2-dimensional cases are supported yet");
    }
  }
}