Exploring a Promising Region and Enhancing Decision Space Diversity for Multimodal Multi-Objective Optimization

During the past decade, research efforts have been gradually directed to the widely existing yet less noticed multimodal multi-objective optimization problems (MMOPs) in the multi-objective optimization community. Recently, researchers have begun to investigate enhancing the decision space diversity and preserving valuable dominated solutions to overcome the shortage caused by a preference for objective space convergence. However, many existing methods still have limitations, such as giving unduly high priorities to convergence and insufficient ability to enhance decision space diversity. To overcome these shortcomings, this article aims to explore a promising region (PR) and enhance the decision space diversity for handling MMOPs. Unlike traditional methods, we propose the use of non-dominated solutions to determine a limited region in the PR in the decision space, where the Pareto sets (PSs) are included, and explore this region to assist in solving MMOPs. Furthermore, we develop a novel neighbor distance measure that is more suitable for the complex geometry of PSs in the decision space than the crowding distance. Based on the above methods, we propose a novel dual-population-based coevolutionary algorithm. Experimental studies on three benchmark test suites demonstrates that our proposed methods can achieve promising performance and versatility on different MMOPs. The effectiveness of the proposed neighbor distance has also been justified through comparisons with crowding distance methods.