A high sparse response surface method based on combined bases for complex products optimization. (March 2019) - Li, Pu; Li, Haiyan; Huang, Yunbao; Yang, Senquan; Yang, Haitian; Liu, Yuesheng
Highlights: A high sparse response surface method based on combined bases is proposed. Sparsest solution is relaxed to ℓ p -norm ( p= 1/2) minimum solution. Cross-validation method is proposed to select the initial value. High sparse representation decreases the number of sampling and improves the accuracy of response surface. Abstract: Product optimization requires many times of simulation which is often time-consuming. The sparse response surface, which is constructed over single orthogonal polynomial bases and sparse coefficients from a few samplings, is employed to reduce simulation times. However, it still requires many samplings for response surface of complex products. In this paper, a High Sparse Response Surface (HSRS) method based on combined bases is proposed with the following main contributions: (1) compared with a single base, a base dictionary is combined with a variety of different base functions, and maybe construct sparser response surface by less expressive bases, which reduced the number of sampling and improved the approximation accuracy, (2) ℓ p -norm ( p =1/2) minimum solution, which is calculated by the Conjugate Gradient-FOCal Underdetermined System Solver (CG-FOCUSS) method, is used to approximate the sparest solution through calculating cost and coefficient sparsity trade-off, and (3) cross-validation is employed to select good initial value to obtain approximation optimal solution, which reduces the influence of the initial value on the CG-FOCUSS algorithm result. Finally, HSRS is applied to three benchmark test functions and two engineering problem, and the results are compared with the single base sparse response surface. The results show that (1) about 14.3% to 44.4% sample points can be reduced for HSRS to achieve the same accuracy of single base sparse response surface, (2) the accuracy of HSRS with cross-validation can be increased by about 20.31% to 40.81%.