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Filter-based DIRECT method for constrained global optimization

Author

Listed:
  • M. Fernanda P. Costa

    (University of Minho)

  • Ana Maria A. C. Rocha

    (University of Minho)

  • Edite M. G. P. Fernandes

    (Algoritmi Research Centre)

Abstract

This paper presents a DIRECT-type method that uses a filter methodology to assure convergence to a feasible and optimal solution of nonsmooth and nonconvex constrained global optimization problems. The filter methodology aims to give priority to the selection of hyperrectangles with feasible center points, followed by those with infeasible and non-dominated center points and finally by those that have infeasible and dominated center points. The convergence properties of the algorithm are analyzed. Preliminary numerical experiments show that the proposed filter-based DIRECT algorithm gives competitive results when compared with other DIRECT-type methods.

Suggested Citation

  • M. Fernanda P. Costa & Ana Maria A. C. Rocha & Edite M. G. P. Fernandes, 2018. "Filter-based DIRECT method for constrained global optimization," Journal of Global Optimization, Springer, vol. 71(3), pages 517-536, July.
    • Handle: RePEc:spr:jglopt:v:71:y:2018:i:3:d:10.1007_s10898-017-0596-8
    DOI: 10.1007/s10898-017-0596-8
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    References listed on IDEAS

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    1. Chungen Shen & Sven Leyffer & Roger Fletcher, 2012. "A nonmonotone filter method for nonlinear optimization," Computational Optimization and Applications, Springer, vol. 52(3), pages 583-607, July.
    2. Qunfeng Liu & Jinping Zeng & Gang Yang, 2015. "MrDIRECT: a multilevel robust DIRECT algorithm for global optimization problems," Journal of Global Optimization, Springer, vol. 62(2), pages 205-227, June.
    3. C. J. Price & M. Reale & B. L. Robertson, 2016. "Stochastic filter methods for generally constrained global optimization," Journal of Global Optimization, Springer, vol. 65(3), pages 441-456, July.
    4. Giampaolo Liuzzi & Stefano Lucidi & Veronica Piccialli, 2010. "A partition-based global optimization algorithm," Journal of Global Optimization, Springer, vol. 48(1), pages 113-128, September.
    5. G. Di Pillo & G. Liuzzi & S. Lucidi & V. Piccialli & F. Rinaldi, 2016. "A DIRECT-type approach for derivative-free constrained global optimization," Computational Optimization and Applications, Springer, vol. 65(2), pages 361-397, November.
    6. Ernesto Birgin & J. Martínez, 2012. "Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization," Computational Optimization and Applications, Springer, vol. 51(3), pages 941-965, April.
    7. Ana Rocha & M. Costa & Edite Fernandes, 2014. "A filter-based artificial fish swarm algorithm for constrained global optimization: theoretical and practical issues," Journal of Global Optimization, Springer, vol. 60(2), pages 239-263, October.
    8. Qunfeng Liu, 2013. "Linear scaling and the DIRECT algorithm," Journal of Global Optimization, Springer, vol. 56(3), pages 1233-1245, July.
    9. G. Di Pillo & S. Lucidi & F. Rinaldi, 2012. "An approach to constrained global optimization based on exact penalty functions," Journal of Global Optimization, Springer, vol. 54(2), pages 251-260, October.
    10. G. Liuzzi & S. Lucidi & V. Piccialli, 2016. "Exploiting derivative-free local searches in DIRECT-type algorithms for global optimization," Computational Optimization and Applications, Springer, vol. 65(2), pages 449-475, November.
    11. Qunfeng Liu & Jinping Zeng, 2015. "Global optimization by multilevel partition," Journal of Global Optimization, Springer, vol. 61(1), pages 47-69, January.
    12. Qunfeng Liu & Wanyou Cheng, 2014. "A modified DIRECT algorithm with bilevel partition," Journal of Global Optimization, Springer, vol. 60(3), pages 483-499, November.
    13. Gianni Pillo & Stefano Lucidi & Francesco Rinaldi, 2015. "A Derivative-Free Algorithm for Constrained Global Optimization Based on Exact Penalty Functions," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 862-882, March.
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