A Three-Level Radial Basis Function Method for Expensive Optimization

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.