An efficient geometric constraint handling method for surrogate-based aerodynamic shape optimization

Handling a large number of geometric constraints brings a big challenge to the surrogate-based aerodynamic shape optimization (ASO) driven by computational fluid dynamics (CFD). It is not feasible to calculate the geometric constraint functions directly during the sub-optimization of a surrogate-based optimization, as the geometric constraint functions are to be evaluated thousands of times for each updating cycle and the total cost of a number of cycles can be prohibitive. This article proposes an efficient method of handling geometric constraints within the framework of a surrogate-based optimization to address this problem. The core idea is to use the Kreisselmeier-Steinhauser (KS) method to aggregate all geometric constraints into one that can be approximated by a cheap surrogate model, in order to avoid the large computational cost associated with tremendous calculation of geometric constraint values. The proposed method is verified by an analytical test case. Then, the proposed method is demonstrated and compared with the methods of building surrogate models of all geometric constraints and calculating all geometric constraints directly during each sub-optimization by drag minimizations of NACA0012 air foil and ONERA M6 wing in transonic flows. To investigate the ability of the proposed method for handling various geometric constraints, drag minimization of CRM wing in viscous transonic flow driven by CFD is performed. Results show that the proposed method can dramatically improve the optimization efficiency of ASO with the number of geometric constraints ranging from 15 to 1429 and the number of types of geometric constraints up to 3, which offers great potential for handling a larger number and more types of geometric constraints.