Two-Stage Archive Evolutionary Algorithm for Multimodal MultiObjective Optimization

In the real world, there are many multimodal multi-objective problems (MMOPs). In recent years, a large number of multimodal multi-objective evolutionary algorithms (MMOEA) have emerged to address these challenges. However, most of these algorithms mainly focus on converging individuals and overlook diverse individuals. This may lead to individuals with better distribution in the decision space or those who help to make the decision space more better distributed being replaced by individuals with better distribution in the objective space, resulting in poor diversity in the final result of the decision space. In some MOPs, Pareto optimal subsets may have different shapes and positions in the decision space, and ignoring the diversity of the decision space can make it difficult for individuals to uniformly shrink to each Pareto subregion. Therefore, this paper presents an algorithm relying on two-stage archive updates to discover global and local PFs. Regarding this algorithm, a density adaptive approach and a small habitat strategy were also put forward to sustain the diversity and convergence of solutions in both the objective space and decision space. This algorithm was contrasted with seven classical algorithms. An overall comparison of competitive MMOES was conducted based on the performance metrics of the Inverse Generative Distance Alliance (IGDunion).