Surrogate-assisted evolutionary algorithm with hierarchical surrogate technique and adaptive infill strategy

Fitness functions of real-world optimization problems often need to be analyzed by expensive experiments or numerical simulations. Integrating these expensive simulations or experiments directly into optimization algorithms would result in substantial computational costs. Surrogate-assisted evolutionary algorithms (SAEAs) have attracted massive attention recently due to their high efficiency and applicability in solving real world optimization problems. As the dimension of the optimization problem increases, the computational cost of constructing surrogates increases, and the surrogate model's prediction accuracy may be severely degraded. High-dimensional model representation (HDMR) is a promising technique to partition a high dimensional function into low-dimensional component functions. However, HDMR's hierarchical structure limits its applicability in online SAEAs. To address these problems, this paper develops a surrogate-assisted evolutionary algorithm with hierarchical surrogate technique and adaptive infill strategy (SAEA-HAS). In this work, we propose a novel hierarchical surrogate technique, in which a composite surrogate model is constructed by the first-order HDMR model and an error value-based surrogate model, then, using the internal contrastive analysis method, a hierarchical surrogate model (HSM) combining the composite surrogate with the fitness value-based surrogate is established. In addition, an adaptive infill strategy is developed to balance the exploration and exploitation of the surrogate-assisted evolutionary search. Various test functions and an antenna optimization problem are employed to compare SAEA-HAS with several well-known SAEAs. The experimental results validate the effectiveness of SAEA-HAS.