Multi-modal multi-objective optimization problems (MMOPs) are particularly challenging due to the difficulty of identifying multiple equivalent Pareto optimal solutions that are similar in the objective space but differ significantly in the decision space. While some evolutionary algorithms perform well on MMOPs, they struggle with large-scale MMOPs, especially those with sparse optimal solutions, due to the curse of dimensionality. These algorithms not only face challenges in converging to Pareto optimal solutions but also in assessing population diversity in a high-dimensional decision space. To remedy these issues, this paper proposes a cooperative multi-population evolutionary algorithm for large-scale MMOPs with sparse optimal solutions. The proposed algorithm balances solutions’ optimality in the objective space and diversity in the decision space by evolving two categories of subpopulations. The first category of subpopulations groups decision variables to efficiently converge to specific Pareto optimal solutions. The second category explores the global search space to discover potential equivalent Pareto optimal solutions, preserving solutions’ diversity in the decision space. These two categories collaborate by exchanging information, enabling dynamic management of subpopulations to allocate computational resources evenly across equivalent Pareto optimal solutions. Experimental results on benchmark problems and real-world applications demonstrate that the proposed algorithm has significant advantages over state-of-the-art evolutionary algorithms.
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