Qu Dan, Xiao Hualin, Chen Huafei, Li Hongyi
College of Mathematics Education, China West Normal University, Nanchong, China.
College of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong, China.
PeerJ Comput Sci. 2024 Mar 14;10:e1839. doi: 10.7717/peerj-cs.1839. eCollection 2024.
Multi-modal multi-objective problems (MMOPs) have gained much attention during the last decade. These problems have two or more global or local Pareto optimal sets (PSs), some of which map to the same Pareto front (PF). This article presents a new affinity propagation clustering (APC) method based on the Multi-modal multi-objective differential evolution (MMODE) algorithm, called MMODE_AP, for the suit of CEC'2020 benchmark functions. First, two adaptive mutation strategies are adopted to balance exploration and exploitation and improve the diversity in the evolution process. Then, the affinity propagation clustering method is adopted to define the crowding degree in decision space (DS) and objective space (OS). Meanwhile, the non-dominated sorting scheme incorporates a particular crowding distance to truncate the population during the environmental selection process, which can obtain well-distributed solutions in both DS and OS. Moreover, the local PF membership of the solution is defined, and a predefined parameter is introduced to maintain of the local PSs and solutions around the global PS. Finally, the proposed algorithm is implemented on the suit of CEC'2020 benchmark functions for comparison with some MMODE algorithms. According to the experimental study results, the proposed MMODE_AP algorithm has about 20 better performance results on benchmark functions compared to its competitors in terms of reciprocal of Pareto sets proximity (rPSP), inverted generational distances (IGD) in the decision (IGDX) and objective (IGDF). The proposed algorithm can efficiently achieve the two goals, i.e., the convergence to the true local and global Pareto fronts along with better distributed Pareto solutions on the Pareto fronts.
多模态多目标问题（MMOPs）在过去十年中受到了广泛关注。这些问题具有两个或更多的全局或局部帕累托最优集（PSs），其中一些映射到相同的帕累托前沿（PF）。本文提出了一种基于多模态多目标差分进化（MMODE）算法的新型亲和传播聚类（APC）方法，称为MMODE_AP，用于CEC'2020基准函数集。首先，采用两种自适应变异策略来平衡探索和利用，并提高进化过程中的多样性。然后，采用亲和传播聚类方法来定义决策空间（DS）和目标空间（OS）中的拥挤程度。同时，非支配排序方案在环境选择过程中纳入了特定的拥挤距离来截断种群，这可以在DS和OS中获得分布良好的解。此外，定义了解的局部PF隶属度，并引入一个预定义参数来维持局部PSs以及全局PS周围的解。最后，在CEC'2020基准函数集上实现了所提出的算法，以便与一些MMODE算法进行比较。根据实验研究结果，在所提出的MMODE_AP算法在帕累托集接近度倒数（rPSP）、决策空间（IGDX）和目标空间（IGDF）中的反向世代距离（IGD）方面，与竞争对手相比，在基准函数上有大约20个更好的性能结果。所提出的算法可以有效地实现两个目标，即收敛到真实的局部和全局帕累托前沿，同时在帕累托前沿上获得分布更好的帕累托解。
