Multi-round surrogate-based optimization for benchmark aerodynamic design problems

Two benchmark problems provided by AIAA aerodynamic design optimization discussion group (ADODG) is performed using an in-house surrogate-based optimizer called “SurroOpt”. One is drag minimization of the NACA 0012 in transonic inviscid flow and the other is drag minimization of the RAE 2822 in transonic viscous flow. A so-called “multiround optimization strategy” is used to find the global optimal solution. In each round, surrogate models are constructed both for the objective function and constraints, and the infill-sampling criteria of maximizing constrained expected improvement (EI) is adopted to refine the models. Especially, the design space in each round is adjusted on the basis of the optimal airfoil of previous round. In addition, not only the optimal airfoil, but also a part of samples of previous round are also taken as initial samples of the next round to speed up the process of the optimization. The airfoils are parameterized by the class-shape function transformation (CST) method and an in-house CFD code called “PMNS2D” is used to solve the compressible Euler and Reynolds-averaged Navier-Stokes equations. The results show that the design space has great influence on the result of the optimization and the drag coefficients of airfoils are reduced dramatically via transforming the design space. This multi-round optimization strategy turns out to be efficient and suitable for surrogate-based optimization. The optimizations based on different dimensions of design space are also studied. For the NACA0012 case, as the dimension increases, the result of optimization improves until a limit value is reached, while more computational costs are required; however, the result indicates that the RAE2822 case is insensitive to the dimensions. The results have been compared with that of the gradient-based method, which shows that better results can be obtained by surrogate-based optimization.