Multimodal multiobjective optimization algorithm with fine-grained special crowding distance and dual-space selection mechanism

Many multimodal multiobjective optimization algorithms strive to solve multimodal multiobjective optimization problems (MMOPs), which have multiple equivalent Pareto optimal solution sets (PSs) in the decision space, and these PSs correspond to the same Pareto front in the objective space. Although these algorithms have the advantage of enhanced search capabilities, there are still various challenges in addressing MMOPs, such as incomplete Pareto optimal sets and unevenly distributed Pareto optimal sets. To address these problems, this paper presents a multimodal multiobjective optimization algorithm with a fine-grained special crowding distance and a dual-space selection mechanism. In the proposed algorithm, a fine-grained special crowding distance (FSCD) is used to measure the comprehensive crowding distances of individuals in the decision and objective spaces. Next, an FSCD-based reproduction strategy is employed to select an exemplar and generate high-quality offspring. Finally, environmental selection based on dual spaces is proposed to improve the convergence of the population without decreasing its diversity. To verify the effectiveness of the proposed algorithm, a series of experiments are carried out on CEC2019 benchmark problems and a path planning optimization problem. The experimental results indicate that the proposed algorithm outperforms its peer competitors.