Most multimodal multi-objective evolutionary algorithms (MMEAs) aim to find all global Pareto optimal sets (PSs) for a multimodal multi-objective optimization problem (MMOP). However, in real-world problems, decision makers (DMs) may be also interested in local PSs. Also, searching for both global and local PSs is more general in view of dealing with MMOPs, which can be seen as a generalized MMOP. In addition, the state-of-the-art MMEAs exhibit poor convergence on high-dimension MMOPs. To address the above two issues, in this study, a novel coevolutionary framework termed CoMMEA for multimodal multi-objective optimization is proposed to better obtain both global and local PSs, and simultaneously, to improve the convergence performance in dealing with high-dimension MMOPs. Specifically, the CoMMEA introduces two archives to the search process, and coevolves them simultaneously through effective knowledge transfer. The convergence archive assists the CoMMEA to quickly approaching the Pareto optimal front (PF). The knowledge of the converged solutions is then transferred to the diversity archive which utilizes the local convergence indicator and the $\epsilon$-dominance-based method to obtain global and local PSs effectively. Experimental results show that CoMMEA is competitive compared to seven state-of-the-art MMEAs on fifty-four complex MMOPs.
翻译:多数多式联运多目标演进算法(MMAEAs)旨在寻找所有全球多模式多目标优化问题的全球最佳套件(PS),然而,在现实世界的问题中,决策者(DMs)也可能对当地PS感兴趣。此外,在与MMOS打交道时,寻找全球和地方的PS也比较普遍,这可以被看作是一个普遍的MMOP。此外,最先进的MMEAs在高度分散的MMOPs上没有很好地趋同。为了解决上述两个问题,在本研究中,提议了一个称为MMMOE的新的变革框架,称为MOME的多式联运多目标优化共同框架,以更好地获得全球和地方PSs。同时,在与高分散的MMOPs打交道时,寻求全球和当地的PSS。具体地说,CMMEA为搜索进程提供了两个档案,同时通过有效的知识转让来发展这些档案。趋同档案有助于COMEA迅速接近Pareto最佳前沿(PFE)。随后,建议一个名为COMA的趋同式解决办法的知识被有效地转移到了当地五金-MMMMMMMA指标。