  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.
