Coevolutionary Framework for Generalized Multimodal Multi-Objective Optimization

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 generalized MMOPs. Moreover, most state-of-the-art MMEAs exhibit poor convergence on high-dimension MMOPs and are unable to deal with constrained MMOPs. To address the above issues, we present a novel multimodal multi-objective coevolutionary algorithm (CoMMEA) to better produce 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 approach the Pareto optimal front. 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.