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Subsections

Improvements

Unconstrained case

The algorithm is still limited to search space of dimension lower than 50 ($ n<50$). This limitation has two origin: Other improvements are possible:


Constrained case

The home-made QP is not very performant and could be upgraded.
Currently, we are using an SQP approach to handle non-linear constraints. It could be interesting to use a penalty-function approach.
When the model is invalid, we have to sample the objective function at a point of the space which will increase substantially the quality of the model. This point is calculated using Equation 3.38:

$\displaystyle \max_{d} \{ \vert P_j(\boldsymbol{x}_{(k)}+d)\vert : \Vert d \Vert \leq \rho \}$ (12.1)

The method to solve this equation is described in Chapter 5. This method does not take into account the constraints. As a result, CONDOR may ask for some evaluations of the objective function in the infeasible space. The infeasibility is never excessive (it's limited by $ \rho $: see equation 12.1 ) but can sometime be a problem. A major improvement is to include some appropriate techniques to have a fully feasible-only algorithm.
Sometimes the evaluation of the objective function fails. This phenomenon is usual in the field of shape design optimization by CFD code. It simply means that the CFD code has not converged. This is referred in the literature as ``virtual constraints'' [CGT98]. In this case, a simple strategy is to reduce the Trust Region radius $ \Delta$ and continue normally the optimization process. This strategy has been implemented and tested on some small examples and shows good results. However, It is still in development and tuning phase. It is the subject of current, ongoing research.

next up previous contents
Next: Some advice on how Up: Conclusions Previous: About the code   Contents
Frank Vanden Berghen 2004-04-19