A heterogeneous population co-evolutionary algorithm for sparse large-scale multi-objective optimization problems

Abstract Sparse large-scale multi-objective optimization problems (sparse LSMOPs) are highly challenging due to the curse of dimensionality and the inherent sparsity of Pareto optimal solutions. Although co-evolutionary algorithms demonstrate significant potential, existing methods are frequently constrained by static resource allocation and undifferentiated variable grouping strategies. These limitations induce a severe mismatch between computational budgets and evolutionary states, making it difficult to effectively eliminate redundant noise variables while activating critical ones. To bridge these gaps, this paper proposes a heterogeneous population co-evolutionary algorithm (HPCEA) tailored for sparse LSMOPs. First, an adaptive population division strategy is introduced to dynamically adjust the scales of convergence and diversity sub-populations based on real-time evolutionary states, facilitating the on-demand allocation of computational resources. Second, a heterogeneous variable grouping strategy is designed: a correlation grouping approach captures structural correlation patterns in sparse space within the convergence sub-population, whereas a structural grouping approach unearths potential sparse patterns for the diversity sub-population. Finally, guided by these distinct architectures and sparse importance scores, heterogeneous genetic operators precisely manipulate variables to balance rapid convergence and broad exploration. Extensive experiments against six state-of-the-art algorithms across eight benchmark suites and three real-world scenarios demonstrate HPCEA’s superiority.