Multimodal multi-objective optimization algorithm based on hierarchical environment selection strategy.

The article proposes an optimization algorithm using a hierarchical environment selection strategyto solve the deficiencies of current multimodal multi-objective optimization algorithms in obtaining the completeness and convergence of Pareto optimal Sets (PSs). Firstly, the algorithm in this article is framed by a differential evolutionary algorithm (DE) and uses a special crowding distance to design a neighborhood-based individual variation strategy, which also ensures the diversity, and then special crowding distance is used to help populations with non-dominated sorting. In the stage of environmental selection, a strategy of hierarchical selection of individuals was designed, which selects sorted non-dominant ranked individual layer by layer according to the ratio, which allows potential individuals tobe explored. Finally, in the stage of evolution of individuals, the convergence and diversity of populations were investigated, anddifferent mutation strategies were selectedaccording to the characteristics of individuals. DE reproduction strategies are used for iteration, preventing individuals from avoiding premature convergence and ensuring the algorithm's searchability. These strategies help the algorithm to obtain more diverse and uniformly distributed PSs and Pareto Front (PF). The algorithm of this article compares with several other excellent algorithms on 13 test problems, and the test results show that all the algorithms of this article exhibit superior performance.