Robust optimization: a kriging-based multi-objective optimization approach

In the robust shape optimization context, the evaluation cost of numerical models is reduced by the use of a response surface. Multi-objective methodologies for robust optimization that consist in simultaneously minimizing the expectation and variance of a function have already been developed to answer to this question. However, efficient estimation in the framework of time-consuming simulation has not been completely explored. In this paper, a robust optimization procedure based on Taylor expansion, kriging prediction and a genetic NSGA-II algorithm is proposed. The two objectives are the Taylor expansion of expectation and variance. The kriging technique is chosen to surrogate the function and its derivatives. Afterwards, NSGA-II is performed on kriging response surfaces or kriging expected improvements to construct a Pareto front. One point or a batch of points is chosen carefully to enrich the learning set of the model. When the budget is reached the non-dominated points provide designs that make compromises between optimization and robustness. Seven relevant strategies based on this main procedure are detailed and compared in two test functions (2D and 6D). In each case, the results are compared when the derivatives are observed and when they are not. The procedure is also applied to an industrial case study where the objective is to optimize the shape of a motor fan.