A study on polynomial regression and Gaussian process global surrogate model in hierarchical surrogate-assisted evolutionary algorithm

This paper presents a study on hierarchical surrogate-assisted evolutionary algorithm (HSAEA) using different global surrogate models for solving computationally expensive optimization problems. In particular, we consider the use of Gaussian process (GP) and polynomial regression (PR) methods for approximating the global fitness landscape in the surrogate-assisted evolutionary search. The global surrogate model serves to pre-screen the EA population for promising individuals. Subsequently, these potential individuals undergo a local search in the form of Lamarckian learning using online local surrogate models. Numerical results are presented on two multimodal benchmark test functions. The results obtained show that both PR-HSAEA and GP-HSAEA converge to good designs on a limited computational budget. Further, our study also shows that the GP model is suitable for global surrogate modeling in HSAEA if the evaluation function is very expensive in computations. On moderately expensive problems, the PR method may serve to generate better efficiency than using GP.