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In this paper, we focus on developing efficient sensitivity analysis methodsfor a computationally expensive objective function $f(x)$ in the case that theminimization of it has just been performed. Here "computationally expensive"means that each of its evaluation takes significant amount of time, andtherefore our main goal to use a small number of function evaluations of $f(x)$to further infer the sensitivity information of these different parameters.Correspondingly, we consider the optimization procedure as an adaptiveexperimental design and re-use its available function evaluations as theinitial design points to establish a surrogate model $s(x)$ (or called responsesurface). The sensitivity analysis is performed on $s(x)$, which is an lieu of$f(x)$. Furthermore, we propose a new local multivariate sensitivity measure,for example, around the optimal solution, for high dimensional problems. Then acorresponding "objective-oriented experimental design" is proposed in order tomake the generated surrogate $s(x)$ better suitable for the accuratecalculation of the proposed specific local sensitivity quantities. In addition,we demonstrate the better performance of the Gaussian radial basis functioninterpolator over Kriging in our cases, which are of relatively highdimensionality and few experimental design points. Numerical experimentsdemonstrate that the optimization procedure and the "objective-orientedexperimental design" behavior much better than the classical Latin HypercubeDesign. In addition, the performance of Kriging is not as good as Gaussian RBF,especially in the case of high dimensional problems.

Sensitivity Analysis for Computationally Expensive Models using Optimization and Objective-oriented Surrogate Approximations