Ensemble of neighborhood search operators for decomposition-based multi-objective evolutionary optimization

Decomposition-based multi-objective evolutionary algorithms (MOEA/Ds) have gained significant attention for their effectiveness in addressing multi-objective optimization problems (MOPs). These algorithms operate by decomposing the target MOP into a series of single-objective subproblems, which are then solved collaboratively. A critical component of MOEA/D is the concept of neighborhood, with the neighborhood search operator playing a pivotal role in driving the evolutionary process. However, most existing MOEA/D variants employ a fixed neighborhood search operator throughout the evolution, which tends to prioritize neighborhood exploration at the expense of subproblem exploitation. To mitigate this limitation, we propose an ensemble framework for neighborhood search operators designed to achieve an appropriate balance between exploration and exploitation. This framework integrates three distinct methods: the evolutionary operators from the genetic algorithm (GA), the covariance matrix adaptation evolution strategy (CMA-ES), and the Nelder–Mead simplex (NMS) method. During the initial phase, both GA and CMA-ES are utilized concurrently to optimize the subproblems. The robust exploration capabilities of GA are synergistically combined with CMA-ES to adaptively fine-tune the balance between exploration and exploitation. In the subsequent phase, the NMS method, renowned for its exceptional local search capabilities, is further employed to enhance neighborhood exploitation, thereby accelerating convergence. Extensive experiments conducted on twelve benchmark problems with varying numbers of objectives and five real-world problems demonstrate the superior performance of the proposed algorithm compared to eight state-of-the-art algorithms.