<scp>M2M</scp> ‐ <scp>GD</scp> : Integrating Gradient Guidance and Diffusion Mechanisms in Decomposition‐Based Multi‐Objective Optimization

ABSTRACT The multi‐objective to multi‐objective (M2M) decomposition strategy can effectively maintain population diversity in evolutionary multi‐objective optimization by handling the decomposed subproblems in parallel within geometric partitioned objective space. However, existing approaches are hindered by the slow convergence from random evolutionary operators and a lack of collaboration between subproblems when handling complex Pareto front (PF) shapes. To address this issue, this paper proposes the M2M‐GD, a novel algorithm that comprehensively improves the M2M framework with three different strategies. First, we incorporate a gradient guidance mechanism that utilizes directional information to expedite convergence. Second, we devise a gradient diffusion strategy that enables knowledge transfer among subproblems through a dynamically updated matrix, promoting synergistic collaboration. Coupled with adaptive parameter control, these innovations collectively provide a more realistic convergence guarantee for the proposed M2M‐GD. Empirical results on MOEADM2M, DTLZ and WFG benchmark problems confirm that M2M‐GD achieves superior performance in both convergence and diversity compared to existing state‐of‐the‐art algorithms.