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.