IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v174y2017i3d10.1007_s10957-016-1042-7.html
   My bibliography  Save this article

Theoretical and Practical Convergence of a Self-Adaptive Penalty Algorithm for Constrained Global Optimization

Author

Listed:
  • M. Fernanda P. Costa

    (University of Minho)

  • Rogério B. Francisco

    (Polytechnic of Porto)

  • Ana Maria A. C. Rocha

    (University of Minho)

  • Edite M. G. P. Fernandes

    (University of Minho)

Abstract

This paper proposes a self-adaptive penalty function and presents a penalty-based algorithm for solving nonsmooth and nonconvex constrained optimization problems. We prove that the general constrained optimization problem is equivalent to a bound constrained problem in the sense that they have the same global solutions. The global minimizer of the penalty function subject to a set of bound constraints may be obtained by a population-based meta-heuristic. Further, a hybrid self-adaptive penalty firefly algorithm, with a local intensification search, is designed, and its convergence analysis is established. The numerical experiments and a comparison with other penalty-based approaches show the effectiveness of the new self-adaptive penalty algorithm in solving constrained global optimization problems.

Suggested Citation

  • M. Fernanda P. Costa & Rogério B. Francisco & Ana Maria A. C. Rocha & Edite M. G. P. Fernandes, 2017. "Theoretical and Practical Convergence of a Self-Adaptive Penalty Algorithm for Constrained Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 875-893, September.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:3:d:10.1007_s10957-016-1042-7
    DOI: 10.1007/s10957-016-1042-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-016-1042-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-016-1042-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. M. Ali & W. Zhu, 2013. "A penalty function-based differential evolution algorithm for constrained global optimization," Computational Optimization and Applications, Springer, vol. 54(3), pages 707-739, April.
    2. Ngaam J Cheung & Xue-Ming Ding & Hong-Bin Shen, 2014. "Adaptive Firefly Algorithm: Parameter Analysis and its Application," PLOS ONE, Public Library of Science, vol. 9(11), pages 1-12, November.
    3. Ngaam J. Cheung & Xue-Ming Ding & Hong-Bin Shen, 2016. "A Non-homogeneous Firefly Algorithm and Its Convergence Analysis," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 616-628, August.
    4. 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.
    5. Anthony V. Fiacco & Garth P. McCormick, 1966. "Extensions of SUMT for Nonlinear Programming: Equality Constraints and Extrapolation," Management Science, INFORMS, vol. 12(11), pages 816-828, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ana Maria A. C. Rocha & M. Fernanda P. Costa & Edite M. G. P. Fernandes, 2017. "On a smoothed penalty-based algorithm for global optimization," Journal of Global Optimization, Springer, vol. 69(3), pages 561-585, November.
    2. 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.
    3. M. Joseane F. G. Macêdo & Elizabeth W. Karas & M. Fernanda P. Costa & Ana Maria A. C. Rocha, 2020. "Filter-based stochastic algorithm for global optimization," Journal of Global Optimization, Springer, vol. 77(4), pages 777-805, August.
    4. Yulong Xu & Jian-an Fang & Wu Zhu & Xiaopeng Wang & Lingdong Zhao, 2015. "Differential evolution using a superior–inferior crossover scheme," Computational Optimization and Applications, Springer, vol. 61(1), pages 243-274, May.
    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. Fahd A. Alturki & Emad Mahrous Awwad, 2021. "Sizing and Cost Minimization of Standalone Hybrid WT/PV/Biomass/Pump-Hydro Storage-Based Energy Systems," Energies, MDPI, vol. 14(2), pages 1-20, January.
    7. 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.
    8. Stephen G. Nash, 1998. "SUMT (Revisited)," Operations Research, INFORMS, vol. 46(6), pages 763-775, December.
    9. Ubaldo M. García-Palomares, 2020. "Non-monotone derivative-free algorithm for solving optimization models with linear constraints: extensions for solving nonlinearly constrained models via exact penalty methods," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 599-625, October.
    10. Ngaam J. Cheung & Xue-Ming Ding & Hong-Bin Shen, 2016. "A Non-homogeneous Firefly Algorithm and Its Convergence Analysis," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 616-628, August.
    11. Geng Lin & Wenxing Zhu & M. Montaz Ali, 2016. "An effective discrete dynamic convexized method for solving the winner determination problem," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 563-593, August.
    12. 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.
    13. Liu, Jianjun & Wu, Changzhi & Wu, Guoning & Wang, Xiangyu, 2015. "A novel differential search algorithm and applications for structure design," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 246-269.
    14. Anurag Jayswal & Sarita Choudhury, 2016. "An Exact Minimax Penalty Function Method and Saddle Point Criteria for Nonsmooth Convex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 179-199, April.
    15. Hao Liu & Yue Wang & Liangping Tu & Guiyan Ding & Yuhan Hu, 2019. "A modified particle swarm optimization for large-scale numerical optimizations and engineering design problems," Journal of Intelligent Manufacturing, Springer, vol. 30(6), pages 2407-2433, August.
    16. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:174:y:2017:i:3:d:10.1007_s10957-016-1042-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.