Multi-surrogate-assisted stochastic fractal search based on scale-free network for high-dimensional expensive optimization

Abstract

Surrogate-assisted meta-heuristic algorithms (SAMAs) have been increasingly popular in recent years for solving challenging optimization problems. However, the majority of recent studies concentrate on low-dimensional problems. In this paper, a scale-free network based multi-surrogate-assisted stochastic fractal search (SF-MSASFS) algorithm is proposed. Specifically, based on the stochastic fractal search (SFS) algorithm, multiple surrogate models, namely RBF and Kriging models, are used to enhance the robustness of the algorithm. The scale-free network is used to build the topology structure of the SFS algorithm, and the offspring particles are generated by means of the connection relationship between the parent particles. In addition, to further enhance adaptability, an adaptive mechanism is implemented, tailoring three distinct update mechanisms based on their corresponding reward values. Finally, the performance of the proposed algorithm is demonstrated by comparing the proposed algorithm with a number of state-of-the-art SAMAs on several well-known benchmark functions, in particular in solving high-dimensional expensive problems (HEOPs). The results underscore the SF-MSASFS algorithm’s commendable optimization performance. (The MATLAB code can be found at the authors github: https://github.com/xiaodi-Cheng/SF-MSASFS)