Robustness criterion for kriging based optimization

International audienceWithin the context of robust shape optimization, the computational estimation cost of physical models is usually reduced throughout the use of a response surface [R. Troian et al., 2016]. A procedure that requires the estimation of moment 1 and 2 is then set up for the robust optimization [J.Martínez-Frutos et al., 2016]. Optimization procedure as well as pareto front partitioning have been deeply studied in the literature. However, research work dealing with criteria to estimate the robustness of each solution at each iteration is still under consideration. The function, the first and second derivatives are computed by the majority of industrial code. We propose a robust optimization procedure based on the prediction of the function and its derivatives predicted by a kriging with a matern 5/2 covariance kernel. The modeling of the second derivative and consequently the prediction of the curvature are possible with this kernel.In this context we propose to consider the norm one of the hessian matrix calculated in each point of the conception space as the robustness criterion. This norm is used as the replacement of the moment 2 usually employed. A classical criterion of Expected Improvement (EI, [Jones et al., 2002] and [Villemonteix et al., 2009] is calculated with the conditional expected value and variance. A pareto front of the robust solutions (minimization of EI and robustness criteria) is generated by a genetic algorithm, in our case the famous NSGA-II [K. Deb et al., 2002]. This algorithm is able to provide a pareto front in an reasonable computing time