Markov Blanket-guided variable analysis with learnable activation mapping for large-scale many-objective optimization

Large-scale many-objective optimization problems (LSMaOPs) are challenging due to the high dimensionality of the decision space and complex nonlinear relationships between decision variables and objectives. Existing decision variable analysis methods often rely on auxiliary function evaluations and typically classify variables only as convergence- or diversity-related, overlooking redundant or weakly influential variables. In addition, objective-to-decision space mappings used to reduce effective dimensionality are commonly linear or based on fixed nonlinear transformations, limiting adaptability across diverse problem landscapes. To address these limitations, this paper proposes MBLEA, a novel evolutionary algorithm featuring two complementary innovations. First, a Markov Blanket-guided decision variable analysis (MBDVA) exploits conditional independence analysis to dynamically partition decision variables into convergence-related, diversity-related, and non-intrinsic groups without requiring auxiliary function evaluations. Second, a meta-learning mechanism adapts the nonlinear transformations in the objective-to-decision space mapping online by optimizing its activation-function parameters, improving adaptability across diverse problem landscapes. Experimental results on large-scale many-objective benchmark problems and a deep reinforcement learning policy optimization task demonstrate that MBLEA achieves superior optimization performance, convergence behavior, and computational efficiency compared with state-of-the-art algorithms.