An Immune-Inspired Approach with Interval Allocation in Solving Multimodal Multi-Objective Optimization Problems with Local Pareto Sets

In practical engineering, multi-objective optimization often encounters situations where multiple Pareto sets (PS) in the decision space correspond to the same Pareto front (PF) in the objective space, known as Multi-Modal Multi-Objective Optimization Problems (MMOP). Locating multiple equivalent global PSs poses a significant challenge in real-world applications, especially considering the existence of local PSs. Effectively identifying and locating both global and local PSs is a major challenge. To tackle this issue, we introduce an immune-inspired reproduction strategy designed to produce more offspring in less crowded, promising regions and regulate the number of offspring in areas that have been thoroughly explored. This approach achieves a balanced trade-off between exploration and exploitation. Furthermore, we present an interval allocation strategy that adaptively assigns fitness levels to each antibody. This strategy ensures a broader survival margin for solutions in their initial stages and progressively amplifies the differences in individual fitness values as the population matures, thus fostering better population convergence. Additionally, we incorporate a multi-population mechanism that precisely manages each subpopulation through the interval allocation strategy, ensuring the preservation of both global and local PSs. Experimental results on 21 test problems, encompassing both global and local PSs, are compared with eight state-of-the-art multimodal multi-objective optimization algorithms. The results demonstrate the effectiveness of our proposed algorithm in simultaneously identifying global Pareto sets and locally high-quality PSs.