2024

IEEE Transactions on Evolutionary Computation

Journal year: 2024 | Journal volume: in press

scientific article

english

EN Quality indicators play an essential role in evolutionary multiobjective optimization (EMO). Most likely the most often used quality indicator in EMO is hypervolume, due to its strict monotonicity with respect to the dominance relation. However, hypervolume is not free of some weak points. For example, a number of recent papers pointed out its high sensitivity to the specification of the reference point. Furthermore, hypervolume is based on fully geometric reasoning which may lead to some undesired results. Thus, it is worth to consider also other quality indicators. In this paper we prove that another well-known R2 quality indicator is also strictly monotonic with respect to the dominance relation when calculated exactly and the reference point strongly dominates any solution in the evaluated set. Furthermore, we adapt the Improved Quick Hypervolume algorithm to the exact calculation of R2 indicator. To our knowledge this is the first exact algorithm for R2 calculation with publicly available implementation. In addition, through both theoretical analysis and computational experiments we show that R2 performs consistently for Pareto fronts with different shapes. We discuss also differences of Pareto fronts representations generated by an indicator-based EMO with hypervolume and R2, where the latter tends to generate solutions having a high chance to be preferred by the DM, not necessarily uniformly distributed in geometric sense. All of these results, make R2 a sound alternative or a complement to hypervolume in EMO.

07.08.2024

10.1109/TEVC.2024.3440571

https://ieeexplore.ieee.org/document/10630708

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