Multiparty Multiobjective Optimization for Dynamic Multimodal Optimization Problems

The challenge of dynamic multimodal optimization problems (DMMOPs) lies in tracking multiple global or locally acceptable optimal solutions in environments that change over time. Typically, algorithms address these problems by treating them as static multimodal optimization problems (MMOPs) over short time intervals and employing dynamic response strategies to adapt to environmental changes. This study introduces a novel approach that transforms MMOPs into multiparty multiobjective optimization problems (MPMOPs). Subsequently, we propose a multiparty multiobjective optimization framework, i.e., MPMOP-CMA, to address DMMOPs. The algorithm is structured into four stages. The first three stages occur within a static environment and include the multiparty multiobjective optimization stage, the CMA-ES search stage, and the additional search stage. The fourth stage employs dynamic response strategies to adapt when environmental changes occur. The CEC 2022 DMMOPs benchmark test suite is used to evaluate the proposed algorithm's performance. Comparative analysis with various state-of-the-art algorithms demonstrates that the proposed method exhibits competitive performance.