Journal of Global Optimization

, Volume 21, Issue 1, pp 27–37 | Cite as

A Locally-Biased form of the DIRECT Algorithm

  • J.M. Gablonsky
  • C.T. Kelley


In this paper we propose a form of the DIRECT algorithm that is strongly biased toward local search. This form should do well for small problems with a single global minimizer and only a few local minimizers. We motivate our formulation with some results on how the original formulation of the DIRECT algorithm clusters its search near a global minimizer. We report on the performance of our algorithm on a suite of test problems and observe that the algorithm performs particularly well when termination is based on a budget of function evaluations.

DIRECT Locally-biased formulation Local clustering 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baker, C.A., Watson, L.T., Grossman, B., Haftka, R.T. and Mason, W.H. (1999a), Parallel Global Aircraft Configuration Design Space Exploration, (preprint).Google Scholar
  2. 2.
    Baker, C.A., Watson, L.T., Grossman, B., Mason, W.H. Cox, S.E. and Haftka, R.T. (1999b), Study of a Global Design Space Exploration Method for Aerospace Vehicles, (preprint).Google Scholar
  3. 3.
    Carter, R., Gablonsky, J.M., Patrick, A., Kelley, C.T. and Eslinger, O.J. (2000), Algorithm for Noisy Problems in Gas Transmission Pipeline Optimization. Technical Report CRSC-TR00-10, North Carolina State University, Center for Research in Scientific Computation.Google Scholar
  4. 4.
    Carter, R.G. (1998), Pipeline optimization: dynamic programming after 30 years. Proceedings of the Pipeline Simulation Interest Group, Denver Colorado, Paper number PSIG-9803.Google Scholar
  5. 5.
    Carter, R.G. (1999), Private communication.Google Scholar
  6. 6.
    Dennis, J.E. and Torczon, V. (1991), Direct Search Methods on Parallel Machines, SIAM J. Optim. 1: 448-474.Google Scholar
  7. 7.
    Dixon, L. and Szegö, G. (1978), The Global Optimisation Problem: An Introduction, In: L. Dixon and G. Szegö (eds.), Towards Global Optimization 2, Vol. 2, North-Holland Publishing Company, pp. 1-15.Google Scholar
  8. 8.
    Gablonsky, J. (1998), An Implementation of the DIRECT Algorithm. Technical Report CRSCTR98-29, North Carolina State University, Center for Research in Scientific Computation.Google Scholar
  9. 9.
    Gilmore, P. and Kelley, C.T. (1995), An implicit filtering algorithm for optimization of functions with many local minima, SIAM J. Optim. 5: 269-285.Google Scholar
  10. 10.
    Hooke, R. and Jeeves, T.A. (1961), 'Direct search' solution of numerical and statistical problems, Journal of the Association for Computing Machinery 8: 212-229.Google Scholar
  11. 11.
    Huyer, W. and Neumaier, A. (1999), Global optimization by multilevel coordinate search, J. Global Optim. 14(4): 331-355.Google Scholar
  12. 12.
    Janka, E. (1999), Vergleich Stochastischer Verfahren zur Globalen Optimierung. Diplomarbeit, Universität Wien.Google Scholar
  13. 13.
    Jones. D.R. (1999), The DIRECT Global Optimization Algorithm, to appear in the Encyclopedia of Optimization.Google Scholar
  14. 14.
    Jones, D.R., Perttunen, C.C. and Stuckman, B.E. (1993), Lipschitzian Optimization without the Lipschitz Constant, J. Optim. Theory Appl. 79: 157-181.Google Scholar
  15. 15.
    Kelley, C.T. (1999), Iterative Methods for Optimization, No. 18 in Fromtiers in Applied Mathematics. SIAM, Philadelphia.Google Scholar
  16. 16.
    Nelder, J.A. and Mead, R. (1965), A simplex method for function minimization, Comput. J. 7: 308-313.Google Scholar
  17. 17.
    Torczon, V. (1997), On the convergence of pattern search algorithm, SIAM J. Optim. 7: 1-25.Google Scholar
  18. 18.
    Yao, Y. (1989), Dynamic Tunneling Algorithm for Global Optimization, IEEE Transactions on Systems, Man, and Cybernetics 19(5).Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • J.M. Gablonsky
    • 1
  • C.T. Kelley
    • 1
  1. 1.Center for Research in Scientific Computation and Department of MathematicsNorth Carolina State UniversityRaleigh

Personalised recommendations