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Filter-based stochastic algorithm for global optimization

Author

Listed:
  • M. Joseane F. G. Macêdo

    (Federal Rural University of Semi-Árido)

  • Elizabeth W. Karas

    (Federal University of Paraná)

  • M. Fernanda P. Costa

    (University of Minho)

  • Ana Maria A. C. Rocha

    (University of Minho)

Abstract

We propose the general Filter-based Stochastic Algorithm (FbSA) for the global optimization of nonconvex and nonsmooth constrained problems. Under certain conditions on the probability distributions that generate the sample points, almost sure convergence is proved. In order to optimize problems with computationally expensive black-box objective functions, we develop the FbSA-RBF algorithm based on the general FbSA and assisted by Radial Basis Function (RBF) surrogate models to approximate the objective function. At each iteration, the resulting algorithm constructs/updates a surrogate model of the objective function and generates trial points using a dynamic coordinate search strategy similar to the one used in the Dynamically Dimensioned Search method. To identify a promising best trial point, a non-dominance concept based on the values of the surrogate model and the constraint violation at the trial points is used. Theoretical results concerning the sufficient conditions for the almost surely convergence of the algorithm are presented. Preliminary numerical experiments show that the FbSA-RBF is competitive when compared with other known methods in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:77:y:2020:i:4:d:10.1007_s10898-020-00917-9
    DOI: 10.1007/s10898-020-00917-9
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    References listed on IDEAS

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    1. 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.
    2. Regis, Rommel G. & Shoemaker, Christine A., 2007. "Parallel radial basis function methods for the global optimization of expensive functions," European Journal of Operational Research, Elsevier, vol. 182(2), pages 514-535, October.
    3. Y. Petalas & K. Parsopoulos & M. Vrahatis, 2007. "Memetic particle swarm optimization," Annals of Operations Research, Springer, vol. 156(1), pages 99-127, December.
    4. 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.
    5. M. Gonçalves & J. Melo & L. Prudente, 2015. "Augmented Lagrangian methods for nonlinear programming with possible infeasibility," Journal of Global Optimization, Springer, vol. 63(2), pages 297-318, October.
    6. Rommel G. Regis & Christine A. Shoemaker, 2007. "A Stochastic Radial Basis Function Method for the Global Optimization of Expensive Functions," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 497-509, November.
    7. Regis, Rommel G., 2010. "Convergence guarantees for generalized adaptive stochastic search methods for continuous global optimization," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1187-1202, December.
    8. 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.
    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.
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