Advertisement

Journal of Global Optimization

, Volume 48, Issue 2, pp 289–310 | Cite as

Continuous GRASP with a local active-set method for bound-constrained global optimization

  • Ernesto G. Birgin
  • Erico M. Gozzi
  • Mauricio G. C. Resende
  • Ricardo M. A. Silva
Article

Abstract

Global optimization seeks a minimum or maximum of a multimodal function over a discrete or continuous domain. In this paper, we propose a hybrid heuristic—based on the CGRASP and GENCAN methods—for finding approximate solutions for continuous global optimization problems subject to box constraints. Experimental results illustrate the relative effectiveness of CGRASP–GENCAN on a set of benchmark multimodal test functions.

Keywords

Global optimization Stochastic methods Active-set methods Heuristic CGRASP GENCAN 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Akrotirianakis I., Floudas C.: Computational experience with a new class of convex underestimators: box-constrained NLP problems. J. Glob. Optim. 29, 249–264 (2004)CrossRefGoogle Scholar
  2. 2.
    Andreani R., Martínez J.M., Salvatierra M., Yano F.: Global order-value optimization by means of a multistart harmonic oscillator tunneling strategy. In: Liberti, L, Maculan, N (eds) Global Optimization: From Theory to Implementation, pp. 379–404. Springer, New York (2006)Google Scholar
  3. 3.
    Andreani R., Birgin E.G., Martínez J.M., Schuverdt M.L.: On augmented Lagrangian methods with general lower-level constraints. SIAM J. Optim. 18, 1286–1309 (2007)CrossRefGoogle Scholar
  4. 4.
    Andreani R., Birgin E.G., Martínez J.M., Schuverdt M.L.: Augmented Lagrangian methods under the constant positive linear dependence constraint qualification. Math. Program. 111, 5–32 (2008)CrossRefGoogle Scholar
  5. 5.
    Birgin E.G., Martínez J.M.: A box constrained optimization algorithm with negative curvature directions and spectral projected gradients. Computing [Suppl] 15, 49–60 (2001)Google Scholar
  6. 6.
    Birgin E.G., Martínez J.M.: Large-scale active-set box-constrained optimization method with spectral projected gradients. Comput. Optim. Appl. 23, 101–125 (2002)CrossRefGoogle Scholar
  7. 7.
    Birgin E.G., Martínez J.M.: Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization. Comput. Optim. Appl. 39, 1–16 (2008)CrossRefGoogle Scholar
  8. 8.
    Birgin E.G., Martínez J.M., Raydan M.: Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim. 10, 1196–1211 (2000)CrossRefGoogle Scholar
  9. 9.
    Birgin E.G., Martínez J.M., Raydan M.: Algorithm 813: SPG—Software for convex-constrained optimization. ACM Trans. Math. Softw. 27, 340–349 (2001)CrossRefGoogle Scholar
  10. 10.
    Birgin, E.G., Floudas, C.A., Martínez, J.M.: Global minimization using an augmented lagrangian method with variable lower-level constraints. Mathematical Programming Published online 20 January 2009 (2009). doi: 10.1007/s10107-009-0264-y
  11. 11.
    Dolan E., Moré J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201–213 (2002)CrossRefGoogle Scholar
  12. 12.
    Feo T., Resende M.: A probabilistic heuristic for a computationally difficult set covering problem. Oper. Res. Lett. 8, 67–71 (1989)CrossRefGoogle Scholar
  13. 13.
    Feo T., Resende M.: Greedy randomized adaptive search procedures. J. Glob. Optim. 6, 109–133 (1995)CrossRefGoogle Scholar
  14. 14.
    Floudas C.A.: Deterministic Global Optimization: Theory, Methods, and Applications. Kluwer, Dordrecht (2000)Google Scholar
  15. 15.
    Hirsch, M., Pardalos, P., Resende, M.: Speeding up Continuous GRASP. Eur. J. Oper. Res. (2007)Google Scholar
  16. 16.
    Hirsch M., Meneses C., Pardalos P., Resende M.: Global optimization by continuous GRASP. Optim. Lett. 1, 201–212 (2007)CrossRefGoogle Scholar
  17. 17.
    Horst R., Pardalos P., Thoai N.: Introduction to Global Optimization, Nonconvex Optimization and its Applications, vol. 3. Kluwer, Dordrecht (1995)Google Scholar
  18. 18.
    Krejic N., Martínez J.M., Mello M.P., Pilotta E.A.: Validation of an augmented Lagrangian algorithm with a Gauss–Newton Hessian approximation using a set of hard-spheres problems. Comput. Optim. Appl. 16, 247–263 (2000)CrossRefGoogle Scholar
  19. 19.
    Levy A.V., Gomez S.: The tunneling method applied to global optimization. In: Bogus, P. (eds) Numerical Optimization, pp. 213–244. SIAM, Philadelphia (1985)Google Scholar
  20. 20.
    Levy A.V., Montalvo A.: The tunneling algorithm for the global minimization of functions. SIAM J. Sci. Comput. 6, 15–29 (1985)CrossRefGoogle Scholar
  21. 21.
    Locatelli, M., Schoen, F.: Numerical experience with random linkage algorithms for global optimisation. Tech. Rep. 15-98, Dip. di Sistemi e Informatica, Università di Firenze, Italy (1998)Google Scholar
  22. 22.
    Locatelli M., Schoen F.: Random linkage: a family of acceptance/rejection algorithms for global optimization. Math. Prog. 85, 379–396 (1999)CrossRefGoogle Scholar
  23. 23.
    Martínez J.M.: BOX-QUACAN and the implementation of augmented Lagrangian algorithms for minimization with inequality constraints. Comput. Appl. Math. 19, 31–56 (2000)Google Scholar

Copyright information

© AT&T Intellectual Property 2009

Authors and Affiliations

  • Ernesto G. Birgin
    • 1
  • Erico M. Gozzi
    • 1
  • Mauricio G. C. Resende
    • 2
  • Ricardo M. A. Silva
    • 3
  1. 1.Instituto de Matemática e EstatísticaUniversidade de São PauloSão PauloBrazil
  2. 2.Algorithms and Optimization Research DepartmentAT&T Labs ResearchFlorham ParkUSA
  3. 3.Department of Computer ScienceFederal University of LavrasLavrasBrazil

Personalised recommendations