Vorspel, Lena and Schramm, Matthias and Stoevesandt, Bernhard and Brunold, Luca and Bünner, Martin (2017) A benchmark study on the efficiency of unconstrained optimization algorithms in 2D-aerodynamic shape design. Cogent Engineering, 4 (1). ISSN 2331-1916

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Abstract

Optimization algorithms are used in various engineering applications to identify optimal shapes. In this work, we benchmark several unconstrained optimization algorithms (Nelder–Mead, Quasi-Newton, steepest descent) under variation of gradient estimation schemes (adjoint equations, finite differences). Flow fields are computed by solving the Reynolds-Averaged Navier–Stokes equations using the open source computational fluid dynamics code OpenFOAM. Design variables vary from N=2 to N=364. The efficiency of the optimization algorithms are benchmarked in terms of: (a) computation time, and (b) applicability and ease of use. Results for lift optimizations are presented for airfoils at a Reynolds number of Re=50,000. As a result, we find for a small number of design variables N≈5 or less, the computational efficiency of all optimization algorithms to be similar, while the ease of use of the Nelder–Mead algorithm makes it a perfect choice for a low number of design variables. For intermediate and large number of design variables, gradient-based algorithms with gradient estimation through the solution of adjoint equations are unbeaten.

Item Type:	Article
Additional Information:	Publiziert mit Hilfe des DFG-geförderten Open Access-Publikationsfonds der Carl von Ossietzky Universität Oldenburg.
Uncontrolled Keywords:	airfoil optimization, airfoil parametrization, computational fluid dynamics, OpenFOAM, gradient-based, gradient-free, adjoint approach, optimization, automatic design
Subjects:	Generalities, computers, information > Computer science, internet
Divisions:	Faculty of Mathematics and Science > Institute of Physics (IfP)
Date Deposited:	28 Sep 2017 13:26
Last Modified:	20 Oct 2017 11:07
URI:	https://oops.uni-oldenburg.de/id/eprint/3354
URN:	urn:nbn:de:gbv:715-oops-34353
DOI:	doi:10.1080/23311916.2017.1354509
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