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

TL;DR

This paper benchmarks derivative-free and derivative-based optimization methods for aerodynamic design, showing derivative-free approaches are competitive and scalable in high-dimensional problems.

Contribution

It provides a systematic comparison demonstrating the practical competitiveness and scalability of derivative-free optimization in aerodynamic design tasks.

Findings

Derivative-free methods outperform derivative-based methods in high-dimensional settings.

Modern derivative-free strategies are practical and robust alternatives when adjoint gradients are unreliable.

Benchmarking on canonical aerodynamic bodies confirms the effectiveness of derivative-free optimization.

Abstract

Aerodynamic design optimization is an important problem in aircraft design that depends on the interplay between a numerical optimizer and a high-fidelity 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, implementation of the adjoint method requires careful mathematical treatment, and its sensitivity to changes in mesh quality limits 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 provide a systematic benchmarking of a select sample of widely used derivative-based and derivative-free optimization algorithms on the design optimization of three canonical aerodynamic bodies, namely, the NACA0012 and RAE2822 airfoils, and the ONERAM6 wing. 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 competitiveness of modern derivative-free strategies, offering a scalable and robust alternative for aerodynamic design optimization when adjoint-based gradients are unavailable or unreliable.