Study of hybrid radial basis function for design optimization problems

Radial basis function (RBF) surrogate model has been widely applied in engineering design optimization problems. Ensemble of RBF (ERBF) combines individual RBF together linearly by using weighted factors to improve approximation behavior of surrogate models. In this paper, a new RBF ensemble method referred as hybrid radial basis function (HRBF) is proposed. Different from the conventional ERBF methods, HRBF determines the weighted factors through solving an optimal quadratic programming problem. Several methods to solve the optimal quadratic programming problem are investigated. Standard numerical test functions are utilized to assess the performances of various ERBFs. The results show that the proposed HRBF can significantly improve the modeling efficiency compared with the conventional ERBF methods. Moreover, the approximation accuracy of HRBF is also slightly improved. Finally, a satellite multidisciplinary design optimization problem is used to illustrate the effectiveness of HRBF in solving real-world engineering design optimization problem.