Efficient surrogate-based aerodynamic optimization with parameter-free adaptive penalty function

Complex constraints must be addressed in the aerodynamic optimizations. Distinct constraints not only influence the optimization outcomes but also significantly influence the optimization method's efficacy. This paper investigates the impact of reference points on optimization design results using the constrained efficient global optimization method (EGO) and suggests a mechanism for selecting reference points that takes constraints into account. Afterwards, for the problem of constraint processing, the constrained expected improvement (EI) method and the penalty function method are compared and found that the penalty function method can find a feasible solution that satisfies the constraints more quickly. However, in this process, the penalty factor has a great influence on the optimization efficiency, and inappropriate penalty factors will damage the optimization efficiency. Drawing on the aforementioned evaluation, this study suggests a constrained EGO technique utilizing an adaptive penalty function that is free of parameters. By normalizing the target value and the constraint value, the feasible solution with the smallest target value or the infeasible solution closest to the feasible region is selected as the reference point. The penalty factor is adaptively adjusted, so that the algorithm can search for the ideal solution sufficiently. This approach can significantly increase the optimization efficiency, as shown by the constrained test functions and airfoil design challenges. © 2024 Beijing University of Aeronautics and Astronautics (BUAA). All rights reserved.