Robustness kriging-based optimization

In the context of robust shape optimization, the estimation cost of some physical models is reduced 10 by the use of a response surface. The multi objective methodology for robust optimization that requires the partitioning of the Pareto front (minimization of the function and the robustness criterion) has already been developed. However, the efficient estimation of the robustness criterion in the context of time-consuming simulation has not been much explored. We propose a robust optimization procedure based on the prediction of the function and its derivatives by a kriging. The 15 usual moment 2 is replaced by an approximated version using Taylor theorem. A Pareto front of the robust solutions is generated by a genetic algorithm named NSGA-II. This algorithm gives a Pareto front in an reasonable time of calculation. We detail seven relevant strategies and compare them for the same budget in two test functions (2D and 6D). In each case, we compare the results when the derivatives are observed and not.

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