Alternative Kriging-HDMR optimization method with expected improvement sampling strategy

The purpose of study is to overcome the error estimation of standard deviation derived from Expected improvement (EI) criterion. Compared with other popular methods, a quantitative model assessment and analysis tool, termed high-dimensional model representation (HDMR), is suggested to be integrated with an EI-assisted sampling strategy.

To predict standard deviation directly, Kriging is imported. Furthermore, to compensate for the underestimation of error in the Kriging predictor, a Pareto frontier (PF)-EI (PFEI) criterion is also suggested. Compared with other surrogate-assisted optimization methods, the distinctive characteristic of HDMR is to disclose the correlations among component functions. If only low correlation terms are considered, the number of function evaluations for HDMR grows only polynomially with the number of input variables and correlative terms.

To validate the suggested method, various nonlinear and high-dimensional mathematical functions are tested. The results show the suggested method is potential for solving complicated real engineering problems.

In this study, the authors hope to integrate superiorities of PFEI and HDMR to improve optimization performance.