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Preliminary research

Before implementing CONDOR, several kinds of optimizer have been tested. The following table describe them:
Available
Optimization
algorithms
Derivatives
required
Type of
optimum
constraints Number of
design

variables
Type of
design

variables
Noise
Pattern Search
(Discrete Rosenbrock's
method, simplex,
PDS,...)
no local box Large continuous Small
Finite-differences
Gradient-Based
Approach (FSQP,
Lancelot,NPSOL,...)
yes local Non-linear medium continuous
Nearly
no noise
Genetic Algorithm

no global box small mixed Small
Gradient-Based
Approach using
Interpolation
techniques (CONDOR,
UOBYQA, DFO)
no local Non-linear medium continous Small

The pattern search and the genetic algorithm were rejected because numerical results on simple test functions demonstrated that they were too slow (They require many function evaluations). Furthermore, we can only have box constraints with these kinds of algorithms. This is insufficient for the method project where we have box, linear and non-linear constraints. The finite-difference gradient-based approach (more precisely: the FSQP algorithm) was used. The gradient was computed in parallel in a cluster of computers. Unfortunately, this approach is very sensitive to the noise, as already discussed in Section 7.4. The final, most appropriate solution, is CONDOR.
next up previous contents
Next: Preliminary numerical results Up: The METHOD project Previous: Parametrization of the shape   Contents
Frank Vanden Berghen 2004-04-19