A radial basis function surrogate model assisted evolutionary algorithm for high-dimensional expensive optimization problems

Abstract

Evolutionary algorithms require large number of function evaluations to locate the global optimum, making it computationally prohibitive on dealing with expensive problems. Surrogate-based optimization methods have shown promising ability on accelerating the convergence speed. However, it is still a challenging work for surrogate-assisted methods to deal with high-dimensional expensive problems because it is hard to approximate the objective function in high-dimensional space. In this paper, a novel radial basis function surrogate model assisted evolutionary algorithm for high-dimensional expensive optimization problems (RSAEH) is proposed. Specifically, the proposed algorithm consists of local search part and surrogate-guided prescreening part. In the local search part, the local surrogate is built by radial basis function with the most promising training sample points, and the optima (or near-optima) is located by optimizer to conduct exact function evaluation. In the surrogate-guided prescreening part, the current best sample point is refined by using sequential quadratic programming, thus guide the mutation direction by using differential evolution operator, and promising offspring prescreened by surrogate model are evaluated using exact function evaluation. To validate the effectiveness of the proposed algorithm, it is tested on benchmark problems with dimension ranging from 30 to 100, as well as a real-world oil reservoir production optimization problem. The proposed algorithm achieved best optimization results on 16 benchmark functions among 21 benchmark function sets in comparison with other algorithms. The performance of RSAEH is competitive especially on 100-D benchmark functions. In addition, RSAEH also showed promising performance on a real-world oil reservoir production optimization problem with 160 variables, in comparison with several state-of-the-art algorithms.