A Surrogate-Assisted Differential Evolution with fitness-independent parameter adaptation for high-dimensional expensive optimization

Surrogate-assisted evolutionary algorithms (SAEAs) have gained considerable attention owing to their ability of tackling expensive optimization problems (EOPs). The surrogate model can be used to replace real fitness value with approximated one, thus greatly reducing computational cost in expensive function evaluations. However, most existing SAEAs are designed for expensive optimization with low or medium dimensions owing to the curse of dimensionality. To improve the performance for solving high-dimensional expensive optimization problems (HEOPs), a surrogate-assisted Differential Evolution with fitness-independent parameter adaptation (SADE-FI) is proposed in the paper. The SADE-FI algorithm consists of a global surrogate-assisted prescreening strategy (GSA-PS) and a local surrogate-assisted DE with fitness-independent parameter adaptation (LSA-FIDE). The main highlights of the paper can be summarized as follows: First, both global and local surrogates are employed to approximate the fitness value of candidate offspring in GSA-PS and LSA-FIDE, respectively. Second, a fitness-independent parameter adaptation mechanism is firstly incorporated into the framework of surrogate-assisted DE as an efficient parameter adaptation for surrogate-assisted search. Third, both the kernel space determination mechanism and linear population size reduction strategy are implemented to enhance the exploitation capability of LSA-FIDE. To validate the performance of SADE-FI, it was tested on expensive benchmark functions on 30D, 50D, 100D, and 200D, as well as a real-world antenna array design problem. The optimization results were compared with state-of-the-art algorithms, and the results indicate that SADE-FI has a significant performance advantage in solving HEOPs.