CONDOR

CONDOR, a new parallel, constrained extension of Powell’s UOBYQA algorithm: Experimental results and comparison with the DFO algorithm. This paper presents an algorithmic extension of M. J. D. Powell’s UOBYQA algorithm (Unconstrained Optimization BY Quadratical Approximation) [Math. Program 92, No. 3, 555–582 (2002; Zbl 1014.65050)]. 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 2 min to several days) like, for instance, industrial shape optimization based on computation fluid dynamic codes or partial differential equations solvers. Finally, we present a new, easily comprehensible and fully stand-alone implementation in C++ of the parallel algorithm.


References in zbMATH (referenced in 18 articles , 1 standard article )

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  1. Gumma, E.A.E.; Hashim, M.H.A.; Ali, M.Montaz: A derivative-free algorithm for linearly constrained optimization problems (2014)
  2. Zhang, Zaikun: Sobolev seminorm of quadratic functions with applications to derivative-free optimization (2014)
  3. Ruppert, David; Shoemaker, Christine A.; Wang, Yilun; Li, Yingxing; Bliznyuk, Nikolay: Uncertainty analysis for computationally expensive models with multiple outputs (2012)
  4. Arouxét, Ma.Belén; Echebest, Nélida; Pilotta, Elvio A.: Active-set strategy in Powell’s method for optimization without derivatives (2011)
  5. Snijkers, F.; D’Avino, G.; Maffettone, P.L.; Greco, F.; Hulsen, M.A.; Vermant, J.: Effect of viscoelasticity on the rotation of a sphere in shear flow (2011)
  6. Zhou, Qinghua; Li, Yan; Ha, Minghu: Constructing composite search directions with parameters in quadratic interpolation models (2011)
  7. Denise, A.; Ponty, Y.; Termier, M.: Controlled non-uniform random generation of decomposable structures (2010)
  8. Scheinberg, K.; Toint, Ph.L.: Self-correcting geometry in model-based algorithms for derivative-free unconstrained optimization (2010)
  9. Fasano, Giovanni; Morales, José Luis; Nocedal, Jorge: On the geometry phase in model-based algorithms for derivative-free optimization (2009)
  10. Bagirov, A.M.; Karasözen, B.; Sezer, M.: Discrete gradient method: Derivative-free method for nonsmooth optimization (2008)
  11. Diniz-Ehrhardt, M.A.; Martínez, J.M.; Raydan, M.: A derivative-free nonmonotone line-search technique for unconstrained optimization (2008)
  12. Uğur, Ö.; Karasözen, B.; Schäfer, M.; Yapıcı, K.: Derivative free optimization methods for optimizing stirrer configurations (2008)
  13. Harth, Zerrin; Sun, Hongtao; Schäfer, Michael: Comparison of derivative free Newton-based and evolutionary methods for shape optimization of flow problems (2007)
  14. Karasözen, Bülent: Survey of trust-region derivative free optimization methods (2007)
  15. Regis, Rommel G.; Shoemaker, Christine A.: A stochastic radial basis function method for the global optimization of expensive functions (2007)
  16. Regis, Rommel G.; Shoemaker, Christine A.: Parallel radial basis function methods for the global optimization of expensive functions (2007)
  17. Schäfer, M.; Karasözen, B.; Uğur, Ö.; Yapıcı, K.: Derivative free optimization of stirrer configurations (2006)
  18. Vanden Berghen, Frank; Bersini, Hugues: CONDOR, a new parallel, constrained extension of Powell’s UOBYQA algorithm: Experimental results and comparison with the DFO algorithm (2005)