Correction: A Parametric Study of Multimodality in Aerodynamic Shape Optimization of Wings

Abstract

A parametric study of multimodality in wing optimization is undertaken utilizing a gradient-based multistart method. The lift-constrained drag minimization of a wing is performed using between 17 and 33 initial geometries in subsonic and transonic viscous flows with varying degrees of freedom and under a variety of constraints. In nearly every examined case, including the ADODG CRM case, multimodality of some degree is found. The cross-sectional optimization of a wing is found to be unimodal to somewhat multimodal in both subsonic and transonic flows, depending on which degrees of freedom are permitted. Permitting large-scale planform deformations and non-planar geometries is shown to produce clear and significant multimodality in all examined cases. Requiring straight leading and trailing edges can significantly reduce, but not fully eliminate, multimodality. Other examined constraints, such as linear taper, linear twist, minimum thickness, and minimum pitching moment are shown to have lesser e↵ects on multimodality. Multimodality is ultimately found to be an inherent characteristic of most wing optimization design spaces, and it is concluded that gradient-based optimization based on a single initial geometry may not be su cient to ensure global optimality even in tightly constrained practical problems.