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The compactly supported radial basis function (CS-RBF) is improved and used to design a new response surface model. The model is incorporated into stochastic global optimal methods to develop a fast and efficient global optimal design strategy with the main target to reduce the number of function calls that involve computationally heavy procedures such as, for example, the repetitive usage of finite element analysis which is generally required in solving inverse problems. In order to employ a multistep method to automatically adjust the support of the CS-RBF to realize the "best" tradeoff between computational efficiency and accuracy, a cluster algorithm is proposed to decompose the sample points into a nested sequence of subsets. To validate the proposed algorithm, typical numerical results on two different examples are reported.