Package org.moeaframework.core.indicator

Collection of unary quality indicators for comparing the quality of non-dominated approximation sets.

See:
Description

Interface Summary

RIndicator.UtilityFunction

Interface for defining utility functions.

Class Summary

AdditiveEpsilonIndicator	Additive ε-indicator for minimization problems.
Contribution	Measures the contribution of the approximation set to the reference set.
GenerationalDistance	Generational distance indicator.
Hypervolume	Hypervolume indicator.
IndicatorUtils	Collection of methods shared by indicators.
InvertedGenerationalDistance	Inverted generational distance indicator.
MaximumParetoFrontError	Maximum Pareto front error metric.
NormalizedIndicator	Abstract class for indicators that require normalized approximation and reference sets.
Normalizer	Normalizes populations so that all objectives reside in the range [0, 1].
QualityIndicator	Evaluates multiple indicators while avoiding repetitive computations.
R1Indicator	Computes the R1 indicator.
R2Indicator	Computes the R2 indicator.
R3Indicator	Computes the R3 indicator.
RIndicator	Abstract class for implementing R indicator functions.
RIndicator.ChebychevUtility	Chebychev (also referred to as Tchebycheff) utility function.
RIndicator.LinearWeightedSumUtility	Utility computed as the sum of the weighted objective values.
Spacing	Spacing metric.

Package org.moeaframework.core.indicator Description

Collection of unary quality indicators for comparing the quality of non-dominated approximation sets. The table below shows the supported indicators and key properties. Pareto compliant implies that better indicator values correspond to approximation sets that are preferred by weak Pareto dominance.

Indicator	Pareto Compliant	Reference Set Required	Normalized	Target
Hypervolume	Yes	Yes	Yes	Maximize → 1
GenerationalDistance	No	Yes	Yes	Minimize → 0
InvertedGenerationalDistance	No	Yes	Yes	Minimize → 0
AdditiveEpsilonIndicator	Yes	No	Yes	Minimize → 0
MaximumParetoFrontError	No	Yes	Yes	Minimize → 0
Spacing	No	No	No	Minimize → 0
Contribution	Yes	Yes	No	Maximize → 1
R2Indicator	No	Yes	Yes	Minimize → -1

References:

1. Knowles, J. and D. Corne. "On Metrics for Comparing Non-Dominated Sets." Proceedings of the 2002 Congress on Evolutionary Computation, pp. 711-716, 2002.
2. Coello Coello, C.A. et al. "Evolutionary Algorithms for Solving Multi-Objective Problems." 2nd Edition, Springer, 2007.