On metrics for comparing nondominated sets

Evolutionary multiobjective optimization (EMO) boasts a proliferation of algorithms and benchmark problems. We need principled ways to compare the performance of different EMO algorithms, but this is complicated by the fact that the result of an EMO run is not a single scalar value, but a collection of vectors forming a nondominated set. Various metrics for nondominated sets have been suggested. We compare several, using the framework of ´outperformance relations´ (Hansen and Jaszkiewicz, 1998). This enables us to criticize and contrast a variety of published metrics, leading to some recommendations on which seem most useful in practice