MOEA Framework 2.12
API Specification

Package org.moeaframework.core.indicator

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


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


  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.

MOEA Framework 2.12
API Specification

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