Journal Article

Multimodality in Aerodynamic Wing Design Optimization


N. P. Bons, X. He, C. A. Mader, and J. R. R. A. Martins


AIAA Journal, 57(3):1004–1018, 2019



The application of gradient-based optimization to wing design could potentially reveal revolutionary new wing concepts. Giving the optimizer the freedom to discover novel wing designs may increase the likelihood of multimodality in the design space. To address this issue, we investigate the existence and possible sources of multimodality in the aerodynamic shape optimization of a rectangular wing. Our test case, specified by the ADODG Case 6, has a high dimensionality design space and a large degree of flexibility within that design space. We study several subproblems of this benchmark test case and analyze the multimodality introduced by each set of variables considering both inviscid and viscous analysis. This methodical approach allows us to isolate a few instances where certain parametrizations create a multimodal design space. However, we demonstrate that these occurrences of multimodality are either due to modeling inaccuracies or can be curbed by the application of practical design constraints. Additionally, we find that the shape of the optimized wing is highly dependent on the interplay between induced and parasite drag, providing more incentive to consider viscous effects in the analysis. As an example, when minimizing drag with respect to chord distribution, there are multiple local minima at low CL , but a single global minimum (the elliptical planform) at high CL . These results will help other researchers to avoid some of the pitfalls that could lead to multimodality in wing optimization.