In the multimodal multi-objective optimization problems (MMOPs), there exists more than one Pareto optimal solutions in the decision space corresponding to the same location on the Pareto front in the objective space. To solve the MMOPs, the designed algorithm is supposed to converge to the accurate and well-distributed Pareto front, and at the same time to search for the multiple Pareto optimal solutions in the decision space. This paper presents a new cluster based particle swarm optimization algorithm (PSO) with leader updating mechanism and ring-topology for solving MMOPs. Multiple subpopulations are formed by a new decision variable clustering method with the aim of searching for the multiple Pareto optima solutions and maintaining the diversity. Global-best PSO is employed for independent evolution of subpopulations, while local-best PSO with ring topology is used to enhance the information interaction among subpopulations. Seamlessly integrated, the proposed algorithm provides a good balance between exploration and exploitation. In addition, leader updating strategy is introduced to identify the best leaders in PSO. The performance of the proposed algorithm is compared with six state-of-the-art designs over 11 multimodal multi-objective optimization test functions. Experimental results demonstrate the effectiveness of the proposed algorithm.

中文翻译：

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一种基于集群的 PSO，具有领导者更新机制和环拓扑，用于多模态多目标优化

在多模态多目标优化问题（MMOP）中，决策空间中存在多个帕累托最优解，对应于目标空间中帕累托前沿上的同一位置。为了求解MMOP，设计的算法应该收敛到准确且分布均匀的Pareto前沿，同时在决策空间中搜索多个Pareto最优解。本文提出了一种新的基于集群的粒子群优化算法（PSO），具有领导者更新机制和环形拓扑，用于求解 MMOP。通过一种新的决策变量聚类方法形成多个子群，其目的是搜索多个帕累托最优解并保持多样性。全局最佳PSO用于子种群的独立进化，而具有环形拓扑的局部最佳PSO用于增强子种群之间的信息交互。所提出的算法无缝集成，在探索和利用之间提供了良好的平衡。此外，还引入了领导者更新策略来识别 PSO 中最好的领导者。将所提出算法的性能与 11 个多模态多目标优化测试函数的 6 个最先进的设计进行了比较。实验结果证明了该算法的有效性。