Research On Response Surface Method Based On Multivariate Adaptive Regression Spline

Response surface methods have become the mainstream method in solving simulation optimization problems. The efficiency of traditional optimization methods is low in achieving the optimum design though multiple variables. In order to reduce optimization interaction times during the simulation process, response surface methods have come into being. For the purpose of improving the efficiency of design optimization of complex models especially in high dimensional cases, an improved method based on multivariate adaptive regression spline (MARS) is presented in this paper.MARS is a regression method with strong ability to generalize specifically for high-dimensional data. MARS uses the tensor product of the splines as basis functions, which targets on minimizing the lost of fit. The basis functions are determined by the training data automatically. However, MARS has some limitations comparing with the popular response surface methods for its higher time complexity and lower model accuracy. So improving the efficiency and accuracy of MARS is necessary. The main work of this paper is as follows:Firstly, some popular response surface methods and the advantages of MARS are introduced in this paper. Besides, several other spline-based response surface methods were also analyzed.Secondly, the modeling process of MARS is deeply researched in detail, and an Improved MARS based on one linear search methods is proposed. The improved method guarantees the precision of MARS, but greatly reducing the model construction time.Thirdly, an incremental method based on MARS is put forward. The incremental MARS ensures that if new data are added in the variable space, the model does not need to be re-build; the new data are just used to update the model. The experimental tests prove the incremental methods could significantly reduce the reconstruction time.Finally, both Improved MARS and Incremental MARS are realized on the MATLAB platform.