Package org.moeaframework.core.indicator

package org.moeaframework.core.indicator
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.
List of quality indicators
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.