Global Optimization of Multimodal Aerodynamic Optimization Benchmark Case

Abstract

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. An investigation into a multimodal aerodynamic optimization benchmark case using an approximate global optimization approach is presented. A new benchmark case of the AIAA Aerodynamic Design Optimization Discussion Group that involves the drag minimization of a rectangular NACA0012 wing subject to lift and root bending moment, as well as other geometric constraints, that is currently believed to be multimodal has been suggested. In this paper, optimization of that case using a constrained populationbased global optimization framework is presented, with three independent runs of the optimizer (each with different starting locations) having been performed. The runs are all coarsely-converged to give approximately converged solutions such that rapid run-times can be achieved and used to demonstrate any pitfalls that may be encountered when using a gradient-based optimizer. All three of the runs converged onto drag values close to the theoretical optimum, however with substantially different final shapes. This likely indicates the presence of a flat optimum region within the design space, where a substantial number of wing shapes are able to obtain the theoretical optimum span loading.

Artificial neural network based wing planform aerodynamic optimization

“…At the same time, there is a drawback in the case of multiple optima, as the first search direction ends when it finds the nearest local minimum to which it leads. Therefore, gradient-based algorithms do not guarantee whether the found minimum is a local or a global minimum (Poole et al , 2017). Overcoming this problem in the current study required starting the algorithm from different starting points to obtain the global minimum (Dababneh et al , 2018).…”

“…Some studies have included the angle of attack in the optimization process, and two studies have considered wing projection (planform) parameters (Lyu and Martins, 2014; Yu et al , 2018). Poole et al based their wing optimization study on the twist angle, angle of attack and thickness and positions of the chord, keeping the airfoil constant, whereas Morris et al ’s study focused on the airfoil, dihedral, sweep angle and tip twist angle (Poole et al , 2017; Morris et al , 2009).…”

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

“…9,10 It has been demonstrated that multimodality can exist in aerodynamic shape optimization problems, 11 and the importance of understanding multimodality in this context is underscored by the recent inclusion of a multimodal problem in the Aerodynamic Design and Optimization Discussion Group (ADODG) test suite at the AIAA Aviation 2017 conference. [12][13][14][15] The objective of this paper is to present a detailed study of the relationship between various problem parameters and multimodality in aerodynamic shape optimization of wings. This includes variations in available degrees of freedom, constraints, as well as Mach number, with particular attention paid to di↵erences ⇤ Ph.D.…”

Global Optimization of Wing Aerodynamic Optimization Case Exhibiting Multimodality

“…Furthermore, recently, aerodynamic topology optimization results have suggested multimodality for a number of supersonic flow problems [32]. Recently, a variety of takes of the optimization of ADODG case 6 have been presented that use a vortex-lattice code for lower fidelity results [33], as well as the requested Euler flow [34,35], and also investigations of the wing in viscous flow [34,36].…”