D-SOMA: A Dynamic Self-Organizing Map-Assisted Multi-Objective Evolutionary Algorithm with Adaptive Subregion Characterization

Multi-objective evolutionary optimization faces significant challenges due to guidance mismatch under complex Pareto-front geometries. This paper proposes a dynamic self-organizing map-assisted evolutionary algorithm (D-SOMA), a manifold-aware framework that harmonizes knowledge-informed priors with unsupervised objective-space characterization. Specifically, a knowledge-informed guided resampling strategy is formulated to bridge stochastic initialization and targeted exploitation. By distilling spatial distribution priors from the decision-variable boundaries of early-stage elite solutions, it establishes a high-quality starting population biased towards promising regions. To capture the intrinsic geometry of the evolving population, a self-organizing map (SOM)-based adaptive subregion characterization strategy leverages the topological preservation of self-organizing maps to extract latent modeling parameters. This strategy adaptively determines subregion centers and influence radii, enabling a data-driven partitioning that respects the underlying manifold structure. Furthermore, a density-driven phase-responsive scale adjustment strategy is introduced. By synthesizing spatial density feedback and temporal evolutionary trajectories, it dynamically modulates the characterization granularity K, thereby maintaining a rigorous balance between geometric modeling fidelity and computational overhead. Extensive experiments on 50 benchmark problems from the DTLZ, WFG, MaF and RWMOP suites demonstrate that D-SOMA is statistically superior to seven state-of-the-art algorithms, exhibiting robust convergence and superior diversity across diverse problem landscapes.