On Metrics for Comparing Non Dominated Sets

Evolutionary multi objective optimisation EMO now boasts a proliferation of algorithms and bench mark problems We need principled ways to compare the performance of di erent EMO algorithms but this is com plicated by the fact that the result of an EMO run is not a single scalar value but a collection of vectors forming a non dominated set Various metrics for non dominated sets have been suggested Here we compare several using the framework of outperformance relations Hansen and Jaszkiewicz This enables us to criticise and contrast a variety of published metrics leading to some recommenda tions on which seem most useful in practice