Region Division and Merging-Based Multiobjective Optimization for Multimodal Problems

Recently, considerable research efforts have been directed toward multimodal optimization problems in consumer electronics. Given the existence of multiple equally significant solutions applicable to diverse scenarios, simultaneously locating these optima is essential. Utilizing multiobjective optimization presents a promising avenue for addressing such problems, provided an effective transformation from multimodal optimization to multiobjective optimization is established. To this end, this study proposes an enhanced tri-objective transformation framework based on a specifically designed region division and merging strategy. Three objective functions are constructed by incorporating objective conflict and niching principles, thus enabling multiobjective optimization techniques to efficiently locate multiple optimal solutions. Simultaneously, the proposed region division and merging strategy facilitates the transformation process. Initially, the decision space is partitioned into numerous small tiles during the region division phase. Subsequently, these tiles are progressively merged layer by layer during the merging phase, eventually restoring the original decision space. Consequently, the given optimization problem is decomposed into a series of simplified tri-objective optimization subproblems, facilitating a smooth transition from exploration of potential regions to exploitation of promising candidate solutions. Experiments conducted on 20 benchmark multimodal optimization problems demonstrate that the proposed method achieves superior performance compared to 14 state-of-the-art algorithms in terms of simultaneously identifying multiple optimal solutions.