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

Author

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  • 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
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    References listed on IDEAS

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    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.
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