Optimization and Computational Fluid Dynamics - Department of ...

5 Efficient Deterministic Approaches for Aerodynamic Shape Optimization 129
drag
drag
(a)
step
(b)
Fig. 5.6 Optimization history of FD and AD for (a) Hicks-Henne and (b) cosine functions
parameterization
tune the stepsize for each parameter separately, which means selecting n
stepsizes hi for every approximation in (5.33). With this possibility, a more
accurate result might be achieved for the original airfoil, but based on the
fact that this tuning cannot be done for every optimization step due to the
high computational effort, it might cause worse optimization results at the
end. Therefore, a stepsize of 10 −3 has been used for all gradient computations
within the optimizations for both parameterizations.
In Fig. 5.6, the optimization history for both parameterizations can be
seen. In case of the Hicks-Henne functions parameterization, the optimization
step