Enabling Dual Subpopulations and Clustering for Multimodal Multiobjective Optimization

Multimodal multiobjective optimization problems (MMOPs) present a specific category of multiobjective problems. Unlike conventional multiobjective problems where Pareto opti-mal solutions gather in one or few regions in the decision space, MMOPs aim to find solutions spread across various regions. In particular, these solutions may share similar locations in objective space, making the problem more complex and challenging. Most multiobjective optimization evolutionary algorithms (MOEAs) barely preserve diversity in decision space, whereas multimodal multiobjective optimization evolutionary algorithms (MMOEAs) require additional techniques such as clustering to maintain diversity in the decision space. In this study, we propose a new method that enables two sub populations and a clustering technique for diversity preservation. Furthermore, different clustering methods are compared to investigate their impact on performance. The experimental results show that the proposed method achieves better inverted generational distance in decision space (IGDX), indicating the effectiveness of the diversity preservation approach. In addition, the varying IGDX and inverted generational distance (IGD) obtained from different clustering methods reveal their different strengths in solving MMOPs.