Author(s)

J. Martinez-Frutos & P. Marti-Montrull

Abstract

Multi-objective robust optimization (MORO) is a highly demanding computational task because of the direct nesting of the uncertainty quantification within optimization. This work presents an approach based on Kriging models to efficiently include the uncertainty quantification in the optimization procedures. In the proposed approach the metamodels appear both at optimization level as well as at uncertainty quantification level. The proposed methodology allows us to: (1) assess the robustness of each design using a reduced number of simulator runs, as compared with conventional approach procedures; and (2) to decouple the uncertainty quantification of the optimization, allowing us to solve the problem with a lower computational cost compared to the nested approach. A benchmark problem has been considered using different approaches in order to compare their relative merits. The results show that the proposed method has potential to obtain solutions with reasonable accuracy and a considerably lower number of function calls than required by conventional methods. Keywords: efficient multi-objective robust optimization, evolutionary algorithms, Kriging models. 1 Introduction In structural engineering, the designer often has to deal with problems that involve conflicting objectives and sources of uncertainty in diverse structural parameters, such as geometric imperfections, material properties or applied loads. The set of optimal solutions obtained using conventional deterministic methods can be very sensitive to perturbations in design variables, leading to a deterioration of the optimal structural performance or even to a set of infeasible designs. Hence, it is desirable to obtain a set of optimal solutions which are less sensitive to variations

Keywords

efficient multi-objective robust optimization, evolutionary algorithms,Kriging models.