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Exploiting derivative-free local searches in DIRECT-type algorithms for global optimization

Author

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  • G. Liuzzi

    (Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti”, CNR)

  • S. Lucidi

    (“Sapienza” Università di Roma)

  • V. Piccialli

    (Università degli Studi di Roma “Tor Vergata”)

Abstract

In this paper we consider bound constrained global optimization problems where first-order derivatives of the objective function can be neither computed nor approximated explicitly. For the solution of such problems the DIRECT algorithm has been proposed which has a good ability to locate promising regions of the feasible domain and convergence properties based on the generation of a dense set of points over the feasible domain. However, the efficiency of DIRECT deteriorates as the dimension and the ill-conditioning of the objective function increase. To overcome these limits, we propose DIRECT-type algorithms enriched by the efficient use of derivative-free local searches combined with nonlinear transformations of the feasible domain and, possibly, of the objective function. We report extensive numerical results both on test problems from the literature and on an application in structural proteomics.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:65:y:2016:i:2:d:10.1007_s10589-015-9741-9
    DOI: 10.1007/s10589-015-9741-9
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    References listed on IDEAS

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    1. 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.
    2. Remigijus Paulavičius & Yaroslav Sergeyev & Dmitri Kvasov & Julius Žilinskas, 2014. "Globally-biased Disimpl algorithm for expensive global optimization," Journal of Global Optimization, Springer, vol. 59(2), pages 545-567, July.
    3. Qunfeng Liu & Jinping Zeng, 2015. "Global optimization by multilevel partition," Journal of Global Optimization, Springer, vol. 61(1), pages 47-69, January.
    4. Qunfeng Liu & Wanyou Cheng, 2014. "A modified DIRECT algorithm with bilevel partition," Journal of Global Optimization, Springer, vol. 60(3), pages 483-499, November.
    5. Remigijus Paulavičius & Julius Žilinskas, 2014. "Simplicial Lipschitz optimization without the Lipschitz constant," Journal of Global Optimization, Springer, vol. 59(1), pages 23-40, May.
    6. D. Serafino & G. Liuzzi & V. Piccialli & F. Riccio & G. Toraldo, 2011. "A Modified DIviding RECTangles Algorithm for a Problem in Astrophysics," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 175-190, October.
    7. 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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    Citations

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    Cited by:

    1. Donald R. Jones & Joaquim R. R. A. Martins, 2021. "The DIRECT algorithm: 25 years Later," Journal of Global Optimization, Springer, vol. 79(3), pages 521-566, March.
    2. Nazih-Eddine Belkacem & Lakhdar Chiter & Mohammed Louaked, 2024. "A Novel Approach to Enhance DIRECT -Type Algorithms for Hyper-Rectangle Identification," Mathematics, MDPI, vol. 12(2), pages 1-24, January.
    3. Siti Nor Habibah Binti Hassan & Tomohiro Niimi & Nobuo Yamashita, 2019. "Augmented Lagrangian Method with Alternating Constraints for Nonlinear Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 883-904, June.
    4. Linas Stripinis & Remigijus Paulavičius, 2023. "Novel Algorithm for Linearly Constrained Derivative Free Global Optimization of Lipschitz Functions," Mathematics, MDPI, vol. 11(13), pages 1-19, June.
    5. 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.
    6. Matteo Lapucci & Tommaso Levato & Marco Sciandrone, 2021. "Convergent Inexact Penalty Decomposition Methods for Cardinality-Constrained Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 473-496, February.
    7. E. F. Campana & M. Diez & G. Liuzzi & S. Lucidi & R. Pellegrini & V. Piccialli & F. Rinaldi & A. Serani, 2018. "A multi-objective DIRECT algorithm for ship hull optimization," Computational Optimization and Applications, Springer, vol. 71(1), pages 53-72, September.
    8. Stripinis, Linas & Žilinskas, Julius & Casado, Leocadio G. & Paulavičius, Remigijus, 2021. "On MATLAB experience in accelerating DIRECT-GLce algorithm for constrained global optimization through dynamic data structures and parallelization," Applied Mathematics and Computation, Elsevier, vol. 390(C).

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