David Ginsbourger

We present two recently released R packages, DiceKriging and DiceOptim, for the approximation and the optimization of expensive-to-evaluate deterministic functions. Following a self-contained mini tutorial on Kriging-based approximation and optimization, the functionalities of both packages are detailed and demonstrated in two distinct sections. In particular, the versatility of DiceKriging with respect to trend and noise specifications, covariance parameter estimation, as well as conditional and unconditional simulations are illustrated on the basis of several reproducible numerical experiments. We then put to the fore the implementation of sequential and parallel optimization strategies relying on the expected improvement criterion on the occasion of DiceOptim’s presentation. An appendix is dedicated to complementary mathematical and computational details.

This paper addresses the issue of designing experiments for a metamodel that needs to be accurate for a certain level of the response value. Such a situation is common in constrained optimization and reliability analysis. Here, we propose an adaptive strategy to build designs of experiments that is based on an explicit trade-off between reduction in global uncertainty and exploration of regions of interest. A modified version of the classical integrated mean square error criterion is used that weights the prediction variance with the expected proximity to the target level of response. The method is illustrated by two simple examples. It is shown that a substantial reduction in error can be achieved in the target regions with reasonable loss of global accuracy. The method is finally applied to a reliability analysis problem; it is found that the adaptive designs significantly outperform classical space-filling designs.