Optimized radial basis function metamodel for expensive engineering design optimization

At the aim of alleviating the computational burden of complicated engineering optimization problems, metamodels have been widely employed to approximate the expensive blackbox functions. Among the popular metamodeling methods RBF metamodel well balances the global approximation accuracy, computational cost and implementation difficulty. However, the approximation accuracy of RBF metamodel is heavily influenced by the width factors of kernel functions, which are hard to determine and actually depend on the numerical behavior of expensive functions and distribution of samples. The main contribution of this paper is to propose an optimized RBF (ORBF) metamodel for the purpose of improving the global approximation capability with an affordable extra computational cost. Several numerical problems are used to compare the global approximation performance of the proposed ORBF metamodeling methods to determine the promising optimization approach. And the proposed ORBF is also adopted in adaptive metamodel-based optimization method. Two numerical benchmark examples and an I-beam optimization design are used to validate the adaptive metamodel-based optimization method using ORBF metamodel. It is demonstrated that ORBF metamodeling is beneficial to improving the optimization efficiency and global convergence capability for expensive engineering optimization problems.