Interval uncertainty can cause uncontrollable variations in the objective and constraint values, which could seriously deteriorate the performance or even change the feasibility of the optimal solutions. Robust optimization is to obtain solutions that are optimal and minimally sensitive to uncertainty. Because large numbers of complex engineering design problems depend on time-consuming simulations, the robust optimization approaches might become computationally intractable. To address this issue, a multi-objective robust optimization approach based on Kriging and support vector machine (MORO-KS) is proposed in this paper. Firstly, the feasible domain of main problem in MORO-KS is iteratively restricted by constraint cuts formed in the subproblem. Secondly, each objective function is approximated by a Kriging model to predict the response value. Thirdly, a Support Vector Machine (SVM) model is constructed to replace all constraint functions classifying design alternatives into two categories: feasible and infeasible. A numerical example and the design optimization of a microaerial vehicle fuselage are adopted to test the proposed MORO-KS approach. Compared with the results obtained from the MORO approach based on Constraint Cuts (MORO-CC), the effectiveness and efficiency of the proposed MORO-KS approach are illustrated.
Estimating Quality of Support Vector Machines Learning under Probabilistic and Interval Uncertainty: Algorithms and Computational Complexity
