A Hierarchical Decision-Space Modeling and Local–Global Surrogate Coevolutionary Algorithm for Expensive Multiobjective Optimization

Abstract

Expensive multiobjective optimization requires a diverse Pareto approximation under a severely limited evaluation budget. Existing surrogate-assisted algorithms often treat decision variables homogeneously and rely on either global or local models, causing inaccurate regional prediction or premature search concentration. This paper proposes HDS-LGSC, a hierarchical decision-space modeling and local–global surrogate coevolutionary algorithm. A lightweight graph-attention encoder learns variable interactions and partitions variables into global-dominant, locally coupled, and weakly related groups. A global radial-basis-function ensemble and local Gaussian processes guide cooperating populations, while an adaptive infill criterion combines hypervolume improvement, uncertainty, and decision-space novelty. Experiments on four benchmarks and a building energy-efficiency case demonstrate lower IGD, higher hypervolume, improved scalability, and robust prediction. Ablation results verify the complementary contributions of hierarchical modeling, dual surrogates, and composite infill selection.