Diversity Metrics in Multi-objective Optimization: Review and Perspective

In literature, many diversity metrics have been proposed to evaluate the optimization results of multi-objective problems. However, it has been proved that there exists no unary quality measure that is able to indicate whether an approximation A is better than an approximation B, even when we consider a finite combination of unary measure. In this paper, we review several popular diversity metrics and give each one a counterexample to show their failures. To make diversity metrics more theoretic and systematic, three possible novel ways are proposed to improve the quality of diversity metrics, including combination of metrics, at-least-one-solution metric and metrics based on distribution test.