Some convergence-based M-ary cardinal metrics for comparing performances of multi-objective optimizers

There is still a big question to the community of multi-objective optimization: how to compare effectively the performances of multi-objective stochastic optimizers? The existing metrics suffer from different drawbacks to address this question. In this article, three convergence-based M-ary cardinal metrics are proposed, based on different forms of dominance relations between two solutions, for comparing performances of two optimizers from their multiple runs. The metrics are first tested on some benchmark instances whose performances are already known, and then their outcomes for some other instances are compared with those of three existing metrics.