Package org.opt4j.optimizer.ea

Class Hypervolume

java.lang.Object
org.opt4j.optimizer.ea.Hypervolume
All Implemented Interfaces:
FrontDensityIndicator
public class Hypervolume extends Object implements FrontDensityIndicator
The Hypervolume is a FrontDensityIndicator based on determination of the hypervolume contribution. The calculation is based on a normalization between 0 and 1 in each dimension and a transformation to a maximization problem. Additionally an offset values (default 1) is added to each dimension.
See Also:
  • SMSModule
  • "Zitzler, E., and Thiele, L. (1998): Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study. Parallel Problem Solving from Nature (PPSN-V), 292-301."

  • Field Details

    • offset

      protected final double offset

  • Constructor Details

    • Hypervolume

      @Inject public Hypervolume(double offset)
      Constructs a Hypervolume.
      Parameters:
      offset - the offset that is added to each dimension before the hypervolume is calculated

  • Method Details

    • getDensityValues

      public Map<Individual,Double> getDensityValues(Collection<Individual> individuals)
      Description copied from interface: FrontDensityIndicator
      Returns the density values for a collection on Individuals.
      Specified by:
      getDensityValues in interface FrontDensityIndicator
      Parameters:
      individuals - the individuals
      Returns:
      a map of each individual to its density value

    • getDensityValues

      protected Map<Individual,Double> getDensityValues(Collection<Individual> individuals, double offset)
      Calculates the density values for a front of non-dominated individuals based on the contribution of the hypervolume. A special approach for two dimension exists as well as a general approach for n dimensions.
      Parameters:
      individuals - the individuals
      offset - the offset
      Returns:
      the map of density values

    • calculateHypervolumeContributionN

      protected Map<Individual,Double> calculateHypervolumeContributionN(List<Individual> individuals, double offset)
      Calculates the hypervolume contribution for n dimensions.
      Parameters:
      individuals - the individuals
      offset - the offset
      Returns:
      the map of density values

    • calculateHypervolumeContribution2D

      protected Map<Individual,Double> calculateHypervolumeContribution2D(List<Individual> individuals, double offset)
      Calculates the hypervolume contribution for two dimensions.
      Parameters:
      individuals - the individuals
      offset - the offset
      Returns:
      the map of density values

    • getMinValues

      protected List<double[]> getMinValues(List<Individual> individuals)
      Transforms the non-dominated individuals to a front where each objective is to be minimized.
      Parameters:
      individuals - the individuals
      Returns:
      the front of vectors that is minimized

    • normalize

      protected List<double[]> normalize(List<double[]> front)
      Normalizes a front of non-dominated solutions to values between 0 and 1.
      Parameters:
      front - the front of non-dominated solutions
      Returns:
      the normalized front

    • invert

      protected List<double[]> invert(List<double[]> front, double offset)
      Inverts (from a minimization to a maximization problem) a front of solutions and adds an offset value to each dimension.
      Parameters:
      front - the front of non-dominated solutions
      offset - the offset
      Returns:
      the inverted front

    • calculateHypervolume

      protected double calculateHypervolume(List<double[]> front, int nObjectives)
      Implements the hypervolume calculations as proposed by Zitzler, E., and Thiele, L. (1998). All points have positive values in all dimensions and the hypervolume is calculated from 0.
      Parameters:
      front - the front of non-dominated solutions
      nObjectives - the number of objectives
      Returns:
      the hypervolume

    • filterNondominatedSet

      protected List<double[]> filterNondominatedSet(List<double[]> front, int nObjectives)

    • dominates

      protected boolean dominates(double[] p1, double[] p2, int nObjectives)

    • surfaceUnchangedTo

      protected double surfaceUnchangedTo(List<double[]> front, int objective)

    • reduceNondominatedSet

      protected List<double[]> reduceNondominatedSet(List<double[]> front, int objective, double threshold)