Efficient hierarchical surrogate-assisted differential evolution for high-dimensional expensive optimization

Abstract

Surrogate-assisted evolutionary algorithms have gained increasingly attention due to the promising search capabilities for solving computationally expensive optimization problems. However, when dealing with high-dimensional expensive optimization problems, the effectiveness of surrogate-assisted algorithms deteriorates drastically. In this paper, a novel and efficient hierarchical surrogate-assisted differential evolution (EHSDE) algorithm is proposed towards high-dimensional expensive optimization problems. To balance the exploration and exploitation during the optimization process, EHSDE utilizes a hierarchical framework. In the first phase, the best and the most uncertain offspring are identified respectively. The best offspring is prescreened by a global surrogate model which is built by using a radial basis function network with all the sample points, while the most uncertain offspring is built by the Euclidean distance between offspring and existing sample points. Subsequently, two local surrogate models, which are built by using the most promising sample points and the sample points surrounding the current best solution respectively, are utilized to accelerate the convergence speed. Moreover, experimental studies are conducted on the benchmark functions from 20D to 100D and on an oil reservoir production optimization problem. The results show that the proposed method is effective and efficient for most benchmark functions and for the production optimization problem compared with other state-of-the-art algorithms.