Clearing-based multimodal multi-objective evolutionary optimization with layer-to-layer strategy

Abstract Equivalent Pareto sets and local Pareto sets in decision space are involved in multimodal multi-objective optimization problems (MMOPs). While popular multimodal multi-objective evolutionary algorithms (MMEAs) devote greater attention to locating equivalent Pareto sets in decision space, resulting in the fact that local Pareto sets are overlooked. To tackle this issue, a clearing-based evolutionary algorithm with layer-to-layer evolution strategy (CEA-LES) is therefore proposed in this paper. A clearing-based niching technique is used in CEA-LES to remove inferior local Pareto optimal solutions, in which the clearing radius dynamically changes with the number of nearest neighbors of each individual. To develop equivalent global Pareto sets and local Pareto sets, a layer-to-layer evolutionary strategy is proposed based on Pareto ranking. Each layer performs mutation selection and reproduction operations with the aid of its closest neighbor layer to produce offspring. Particularly, the whole evolutionary operation is divided into two stages, and the first stage is to select parents using the roulette method and the second stage is using the tournament method. An environmental selection strategy is suggested to maintain diverse solutions and balance the distribution of solutions. The proposed algorithm is performed on CEC 2020 MMOPs benchmark with local Pareto set and Polygon-based MMOPs and is compared with some state-of-the-art MMEAs. Experimental results demonstrate that the proposed algorithm obtains superior performance in comparison to its competing algorithms, and is capable of locating equivalent global Pareto sets and local Pareto sets, simultaneously.