[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

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

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  8. Birgin E.G., Martínez J.M., Raydan M.: Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim. 10, 1196–1211 (2000)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. Dolan E., Moré J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201–213 (2002)

    Article  Google Scholar 

  12. Feo T., Resende M.: A probabilistic heuristic for a computationally difficult set covering problem. Oper. Res. Lett. 8, 67–71 (1989)

    Article  Google Scholar 

  13. Feo T., Resende M.: Greedy randomized adaptive search procedures. J. Glob. Optim. 6, 109–133 (1995)

    Article  Google Scholar 

  14. Floudas C.A.: Deterministic Global Optimization: Theory, Methods, and Applications. Kluwer, Dordrecht (2000)

    Google Scholar 

  15. Hirsch, M., Pardalos, P., Resende, M.: Speeding up Continuous GRASP. Eur. J. Oper. Res. (2007)

  16. Hirsch M., Meneses C., Pardalos P., Resende M.: Global optimization by continuous GRASP. Optim. Lett. 1, 201–212 (2007)

    Article  Google Scholar 

  17. Horst R., Pardalos P., Thoai N.: Introduction to Global Optimization, Nonconvex Optimization and its Applications, vol. 3. Kluwer, Dordrecht (1995)

    Google Scholar 

  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)

    Article  Google Scholar 

  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. Levy A.V., Montalvo A.: The tunneling algorithm for the global minimization of functions. SIAM J. Sci. Comput. 6, 15–29 (1985)

    Article  Google Scholar 

  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)

  22. Locatelli M., Schoen F.: Random linkage: a family of acceptance/rejection algorithms for global optimization. Math. Prog. 85, 379–396 (1999)

    Article  Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil

    Ernesto G. Birgin & Erico M. Gozzi

  2. Algorithms and Optimization Research Department, AT&T Labs Research, Florham Park, NJ, USA

    Mauricio G. C. Resende

  3. Department of Computer Science, Federal University of Lavras, Lavras, Brazil

    Ricardo M. A. Silva

Authors
  1. Ernesto G. Birgin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erico M. Gozzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mauricio G. C. Resende
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ricardo M. A. Silva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mauricio G. C. Resende.

Additional information

This research was done while Ricardo M. A. Silva was a visiting post-doctoral scholar at AT&T Labs Research. His work was partially funded by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil.

About this article

Cite this article

Birgin, E.G., Gozzi, E.M., Resende, M.G.C. et al. Continuous GRASP with a local active-set method for bound-constrained global optimization. J Glob Optim 48, 289–310 (2010). https://doi.org/10.1007/s10898-009-9494-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-009-9494-z

Keywords

Search

Navigation