Large-scale multimodal multiobjective evolutionary optimization based on hybrid hierarchical clustering

Large-scale multimodal multiobjective optimization problems (MMOPs) have different equivalent Pareto optimal solution sets (PSs) for the same Pareto front and contain a great number of decision variables. In particular, when most variables among the Pareto optimal solutions are zero, such problems are termed large-scale MMOPs with sparse Pareto optimal solutions. Due to the multimodal properties of these problems, the curse of dimensionality, and the unknown sparsity of the search space, it is extremely difficult for existing optimizers to solve them. In this study, we propose a multipopulation multimodal evolutionary algorithm based on hybrid hierarchical clustering to solve such problems. The proposed algorithm uses hybrid hierarchical clustering on subpopulations to distinguish the resources of different equivalent PSs and partition them into different subpopulations to achieve efficient cooperative coevolution among multiple subpopulations. Moreover, an adaptive variation method incorporating both local and global guiding information is designed, and an improved environmental selection method based on local guiding information is conducted to improve the convergence in a large search space and introduce diversity to the population. Experimental results verified that the proposed algorithm outperforms the state-of-the-art MOEAs in terms of performance and convergence speed, especially when the number of equivalent PSs is large.