This paper presents an algorithmic extension of Powell’s UOBYQA algorithm (”Unconstrained Optimization BY Quadratical Approximation”). We start by summarizing the original algorithm of Powell and by presenting it in a more comprehensible form. Thereafter, we report comparative numerical results between UOBYQA, DFO and a parallel, constrained extension of UOBYQA that will be called in the paper CONDOR (”COnstrained, Non-linear, Direct, parallel Optimization using trust Region method for high-computing load function”). The experimental results are very encouraging and validate the approach. They open wide possibilities in the field of noisy and high-computing-load objective functions optimization (from two minutes to several days) like, for instance, industrial shape optimization based on CFD (Computation Fluid Dynamic) codes or PDE (partial differential equations) solvers. Finally, we present a new, free, easily comprehensible and fully stand-alone implementation in C++ of the parallel algorithm.
Citation
Technical report TR/IRIDIA/2004-11, august 2004, IRIDIA laboratory, Free University of Brussel (ULB), august 2004