A Robustness Indicator-Based Dual-Population Evolutionary Algorithm for Multimodal Multiobjective Optimization

In practical scenarios, there may be solutions in the decision space with close objective values but located far apart, a characteristic known as multimodal multiobjective problems (MMOPs). While most multimodal multiobjective evolutionary algorithms (MMEAs) focus on finding global Pareto optimal solution sets (PSs) and local PSs demonstrating satisfactory convergence performance, decision-makers in real-world scenarios are often also interested in local PSs that exhibit strong robustness. In this study, we propose several benchmark functions in which the global and local PSs have varying levels of robustness. Then, we introduce an innovative dual-population evolutionary algorithm, termed GLR-MMEA, designed to simultaneously find both global PSs and local PSs with strong robustness. In GLR-MMEA, the convergence population focuses on identifying global PSs, providing convergence information to the diversity population. Meanwhile, the diversity population manages the detection of both global PSs and local PSs with strong robustness. In the process of updating the diversity population, a robustness indicator is proposed to access the robustness of solutions. Furthermore, a selection mechanism founded on this robustness indicator is applied to identify local PSs with high robustness. The experimental results show that GLR-MMEA performs competitively against other leading MMEAs in working on the selected benchmark functions.