Weighted Indicator-Based Evolutionary Algorithm for Multimodal Multiobjective Optimization

Multimodal multiobjective problems (MMOPs) arise frequently in the real world, in which multiple Pareto-optimal solution (PS) sets correspond to the same point on the Pareto front. Traditional multiobjective evolutionary algorithms (MOEAs) show poor performance in solving MMOPs due to a lack of diversity maintenance in the decision space. Thus, recently, many multimodal MOEAs (MMEAs) have been proposed. However, for most existing MMEAs, the convergence performance in the objective space does not meet expectations. In addition, many of them cannot always obtain all equivalent Pareto solution sets. To address these issues, this study proposes an MMEA based on a weighted indicator, termed MMEA-WI. The algorithm integrates the diversity information of solutions in the decision space into an objective space performance indicator to maintain the diversity in the decision space and introduces a convergence archive to ensure a more effective approximation of the Pareto-optimal front (PF). These strategies can readily be applied to other indicator-based MOEAs. The experimental results show that MMEA-WI outperforms some state-of-the-art MMEAs on the chosen benchmark problems in terms of the inverted generational distance (IGD) and IGD in the decision space (IGDX) metrics.