Sequential Radial Basis Function-Based Optimization Method Using Virtual Sample Generation

Abstract

To further reduce the computational expense of metamodel-based design optimization (MBDO), a novel sequential radial basis function (RBF)-based optimization method using virtual sample generation (SRBF-VSG) is proposed. Different from the conventional MBDO methods with pure expensive samples, SRBF-VSG employs the virtual sample generation mechanism to improve the optimization efficiency. In the proposed method, a least squares support vector machine (LS-SVM) classifier is trained based on expensive real samples considering the objective and constraint violation. The classifier is used to determine virtual points without evaluating any expensive simulations. The virtual samples are then generated by combining these virtual points and their Kriging responses. Expensive real samples and cheap virtual samples are used to refine the objective RBF metamodel for efficient space exploration. Several numerical benchmarks are tested to demonstrate the optimization capability of SRBF-VSG. The comparison results indicate that SRBF-VSG generally outperforms the competitive MBDO methods in terms of global convergence, efficiency, and robustness, which illustrates the effectiveness of virtual sample generation. Finally, SRBF-VSG is applied to an airfoil aerodynamic optimization problem and a small Earth observation satellite multidisciplinary design optimization problem to demonstrate its practicality for solving real-world optimization problems.