Multimodal multi-objective optimization via multi-operator adaptation and clustering-based environmental selection

Abstract

In real world applications, multimodal multi-objective optimization problems are common, addressing which can offer decision makers multiple choices to accommodate varying scenarios. Many researchers have been focusing on this kind of problem, leading to the development of numerous multimodal multi-objective evolutionary optimization algorithms (MMOEAs). However, most existing MMOEAs employ a fixed operator to generate offspring. For different types of problems, the use of hybrid operators can take advantage of their distinct features in reproduction to produce more valuable individuals. To address this issue, we propose an innovative algorithm that integrates two operators collaboratively and dynamically adjusts the proportion of offspring generated by each operator based on its performance throughout the evolution process evaluated by the survival rate. In addition, to better balance the diversity, the proposed algorithm devises a novel clustering method, which clusters the population in the decision space. Then, individuals within the same cluster with better performance in the objective space are able to survive. We evaluate our algorithm against seven representative MMOEAs on two widely used benchmark problems and real-world problems. The experimental results confirm the superior performance and robustness of our approach on both benchmark and real-world problems.