Optimization and Computational Fluid Dynamics - Department of ...

160 René A. Van den Braembussche
Fig. 6.8 Convex Pareto front
6.3 Two-level Optimization
The system presented here (Fig. 6.9) is developed at the von Kármán Institute
[13] and makes use of a GA to minimize the OF. A GA requires a large
number of function evaluations. Using an expensive NS solver for all function
evaluations is in most cases, prohibitive in terms of computer effort.
One way to reduce the computational effort is by working on different levels
of sophistication. Fast but approximate prediction methods can be used to
find a near optimum geometry, which is then further verified and refined
by a more accurate but also more expensive analysis. Approximations of
the NS solver and FEA, called meta-functions, are used for the first level
optimization. The more accurate but expensive NS and FEA are used only
to verify the accuracy of the meta-function predictions.
Meta-functions not only need to be fast but must also be accurate. The
GA can only converge to the real optimum if it receives accurate information
about the impact of a geometry change on the performance. Different type
of meta-functions have been proposed. The main problem is the risk that
the discrepancies between the predictions by the meta-function and the NS
results drive the optimizer to a false optimum. Euler and NS solutions on
coarse grids are sometimes proposed as meta-functions. They are fast but
inaccurate and using them for performance predictions may drive the GA to
a non-optimum combination of design parameters. Any further control by an
accurate NS solver will reveal the inherent inaccuracy of the fast calculation
methods but there is no mechanism to correct for it.