A distance correlation-based Kriging modeling method for high-dimensional problems

Abstract

By using the kriging modeling method, the design efficiency of computationally expensive optimization problems is greatly improved. However, as the dimension of the problem increases, the time for constructing a kriging model increases significantly. It is unaffordable for limited computing resources, especially for the cases where the kriging model needs to be constructed frequently. To address this challenge, an efficient kriging modeling method which utilizes a new spatial correlation function, is developed in this article. More specifically, for the characteristics of optimized hyper-parameters, distance correlation (DIC) is used to estimate the relative magnitude of hyper-parameters in the new correlation function. This translates the hyper-parameter tuning process into a one-dimensional optimization problem, which greatly improves the modeling efficiency. Then the corrector step is used to further exploit the hyper-parameters space. The proposed method is validated through nine representative numerical benchmarks from 10-D to 60-D and an engineering problem with 35 variables. Results show that when compared with the conventional kriging, the modeling time of the proposed method is dramatically reduced. For the problems with more than 30 variables, the proposed method can obtain a more accurate kriging model. Besides, the proposed method is compared with another state-of-the-art high-dimensional Kriging modeling method, called KPLS+K. Results show that the proposed method has higher modeling accuracy for most problems, while the modeling time of the two methods is comparable. It can be conclusive that the proposed method is very promising and can be used to significantly improve the efficiency for approximating high-dimensional expensive problems.