Derivative-free optimization is competitive for aerodynamic design optimization in moderate dimensions

Aerodynamic design optimization is an important problem in aircraft design that depends on the interplay between a numerical optimizer and a flow physics solver. Derivative-based, first- and (quasi)second-order, optimization techniques are the de facto choice, particularly given the availability of the adjoint method and its ability to efficiently compute gradients at the cost of just one solution of the forward problem. However, the implementation of the adjoint method requires careful mathematical treatment, and its sensitivity to changes in mesh quality limits its widespread applicability. Derivative-free approaches are often overlooked for large scale optimization, citing their lack of scalability in higher dimensions and/or the lack of practical interest in globally optimal solutions that they often target. However, breaking free from an adjoint solver can be paradigm-shifting in broadening the applicability of aerodynamic design optimization. We compare derivative-free and derivative-based optimizers on a suite of two- and three-dimensional aerodynamic shape optimization problems with design-space dimensionalities ranging fromO(10) to O(50)shape parameters, including unconstrained and constrained variants of the NACA0012, RAE2822, and ONERAM6 configurations. Our results demonstrate that, for these problems, derivative-free methods are competitive with derivative-based methods and can outperform them in the higher-dimensional cases. Our results demonstrate that derivative-free methods are competitive with derivative-based methods, while outperforming them consistently in the high-dimensional setting. These findings highlight the practical viability of modern derivative-free strategies, offering a promising alternative for aerodynamic design optimization when adjoint-based gradients are unavailable or unreliable.