A Three-Level Radial Basis Function Method for Expensive Optimization

• Published in: IEEE transactions on cybernetics Vol. 52; no. 7; pp. 1 - 12
• Main Authors: Li, Genghui, Zhang, Qingfu, Lin, Qiuzhen, Gao, Weifeng
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.07.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Approximation; Clustering; Computational modeling; Data models; Design optimization; Expensive optimization; exploration and exploitation; Iterative methods; Mathematical analysis; Mathematical model; Optimization; Predictive models; Radial basis function; radial basis function model (RBF); Search problems; Searching
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2021.3061420

This article proposes a three-level radial basis function (TLRBF)-assisted optimization algorithm for expensive optimization. It consists of three search procedures at each iteration: 1) the global exploration search is to find a solution by optimizing a global RBF approximation function subject to a distance constraint in the whole search space; 2) the subregion search is to generate a solution by minimizing an RBF approximation function in a subregion determined by fuzzy clustering; and 3) the local exploitation search is to generate a solution by solving a local RBF approximation model in the neighborhood of the current best solution. Compared with some other state-of-the-art algorithms on five commonly used scalable benchmark problems, ten CEC2015 computationally expensive problems, and a real-world airfoil design optimization problem, our proposed algorithm performs well for expensive optimization.