On the influence of optimization algorithm and initial design on wing aerodynamic shape optimization

Abstract Aerodynamic shape optimization is a useful tool in wing design, but the impact of the choice of optimization algorithm and the multimodality of the design space in wing design optimization is still poorly understood. To address this, we benchmark both gradient-based and gradient-free optimization algorithms for computational fluid dynamics based aerodynamic shape optimization problems based on the Common Research Model wing geometry. The aerodynamic model solves the Reynolds-averaged Navier–Stokes equations with a Spalart–Allmaras turbulence model. The drag coefficient is minimized subject to lift, pitching moment, and geometry constraints, with up to 720 shape variables and 11 twist variables for two mesh sizes. We benchmark six gradient-based and three gradient-free algorithms by comparing both the accuracy of the optima and the computational cost. Most of the optimizers reach similar optima, but the gradient-based methods converge to more accurate solutions at a much lower computational cost. Since multimodality and nonsmoothness of the design space are common arguments for the use of gradient-free methods, we investigate these issues by solving the same optimization problem starting from a series of randomly generated initial geometries, as well as a wing based on the NACA 0012 airfoil with zero twist and constant thickness-to-chord ratio. All the optimizations consistently converge to practically identical results, where the differences in drag are within 0.05%, and the shapes and pressure distributions are very similar. Our overall conclusion is that the design space for wing design optimization with a fixed planform is largely convex, with a very small flat region that is multimodal because of numerical errors. However, this region is so small, and the differences in drag so minor, that the design space can be considered unimodal for all practical purposes.