Quasi-sparse response surface constructing accurately and robustly for efficient simulation based optimization. (December 2017) - Li, Pu; Li, Haiyan; Huang, Yunbao; Wang, Kefeng; Xia, Nan
Highlights: An effective quasi-sparse response surface based on a few sampling points is proposed. The regularization of the combination of l1 norm and l2 norm is used to increase the robustness of response surface. Cross-validation is employed to calculate the parameters of response surface. The numerical test results show the approaching performance of quasi-sparse response surface is better than some other test models. Abstract: Response surface method is often employed in simulation based design and optimization for complex products. The sparsity of response surface on the mathematic basis has been explored to accurately represent the variation between design variables and performance response with only a few design points, which is very beneficial to efficient design optimization. Due to the selected basis, it may lead to a large deviation, or under-fitting of the reconstructed response surface since the number of sampling points is often smaller than its sparseness. In this paper, a quasi-sparse response surface is presented to trade-off the sparsity and variation of response surface by introducing coefficient shrinkage regularization and uniformly sampling for the design points, which enables more atoms in the basis included to accurately and robustly reconstruct the surface. The group of basis atoms which are correlated with sampling points instead of the most correlated one are all selected to uniform express the sampling points, and the coefficients of basis atoms are shrunk to improve the prediction performance of the model. Finally, 9 benchmark functions and 1 engineering applications are utilized to demonstrate the significance of the presented approach by comparing with other normally used response surface models, The results shows that the accuracy and robustness of the reconstructed response surface is superior than those of other response surface approaches.