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 Summary

Fields

Modifier and Type	Field	Description
protected double	offset

Constructor Summary

Constructors

Constructor	Description
Hypervolume(double offset)	Constructs a Hypervolume.

Method Summary

Modifier and Type	Method	Description
protected double	calculateHypervolume(List<double[]> front, int nObjectives)	Implements the hypervolume calculations as proposed by Zitzler, E., and Thiele, L.
protected Map<Individual,Double>	calculateHypervolumeContribution2D(List<Individual> individuals, double offset)	Calculates the hypervolume contribution for two dimensions.
protected Map<Individual,Double>	calculateHypervolumeContributionN(List<Individual> individuals, double offset)	Calculates the hypervolume contribution for n dimensions.
protected boolean	dominates(double[] p1, double[] p2, int nObjectives)
protected List<double[]>	filterNondominatedSet(List<double[]> front, int nObjectives)
Map<Individual,Double>	getDensityValues(Collection<Individual> individuals)	Returns the density values for a collection on Individuals.
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.
protected List<double[]>	getMinValues(List<Individual> individuals)	Transforms the non-dominated individuals to a front where each objective is to be minimized.
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.
protected List<double[]>	normalize(List<double[]> front)	Normalizes a front of non-dominated solutions to values between 0 and 1.
protected List<double[]>	reduceNondominatedSet(List<double[]> front, int objective, double threshold)
protected double	surfaceUnchangedTo(List<double[]> front, int objective)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

offset

protected final double offset

Constructor Detail

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 Detail

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)