A benchmark study on the efficiency of unconstrained optimization algorithms in 2D-aerodynamic shape design. Issue 1 (1st January 2017) - Vorspel, L.; Schramm, M.; Stoevesandt, B.; Brunold, L.; Bünner, M.
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.