Comparative study of HDMRs and other popular metamodeling techniques for high dimensional problems

The efficiency of optimization for the high dimensional problem has been improved by the metamodeling techniques in multidisciplinary in the past decades. In this study, comparative studies are implemented for high dimensional problems on the accuracy of four popular metamodeling methods, Kriging (KRG), radial basis function (RBF), least square support vector regression (LSSVR) and cut-high dimensional model representation (cut-HDMR) methods. Besides, HDMR methods with different basis functions are considered, including KRG-HDMR, RBF-HDMR and SVR-HDMR. Four factors that might influence the quality of metamodeling methods involving parameter interaction of problems, sample sizes, noise level and sampling strategies are considered. The results show that the LSSVR with Gaussian kernel, using Latin hypercube sampling (LHS) strategy, constructs more accurate metamodels than the KRG. The RBF with Gaussian basis function performs poor in the group. Generally, cut-HDMR methods perform much better than the other metamodeling methods when handling the function with weak parameter interaction, but not better when handling the function with strong parameter interaction.