Boosting Decision-Space Diversity in Multi-Objective Optimization unsing Nichcing-CMA and Aggregation

Two solutions that occupy (almost) the same space in the objective space may have pre-images in the decision space that are essentially different. For a decision maker it can be interesting to know both pre-images in such cases. However, most Pareto optimization algorithms focus on diversity in the objective space only and thus will likely obtain only one solution. In this paper we propose a method aiming for approximation sets that possess a high diversity in objective space as well as decision space. The method integrates aggregation of the two spaces into an existing CMA-niching framework to yield a multi-objective algorithm. Based on a study on synthetic multimodal problems we discuss the aggregation and niching concept and assess the performance of the new approach. We conclude that considering the aggregated space by itself is not sufficient for attaining high diversity in the decision space, but it is rather a bridge for niching to multi-objective optimization.