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Filter-based stochastic algorithm for global optimization

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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.

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Acknowledgements

The authors are grateful to the anonymous referees for their fruitful comments and suggestions. The first and second authors were partially supported by Brazilian Funds through CAPES and CNPq by Grants PDSE 99999.009400/2014-01 and 309303/2017-6. The research of the third and fourth authors were partially financed by Portuguese Funds through FCT (Fundação para Ciência e Tecnologia) within the Projects UIDB/00013/2020 and UIDP/00013/2020 of CMAT-UM and UIDB/00319/2020.

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Authors and Affiliations

  1. Department of Exact and Natural Sciences, Federal Rural University of Semi-Árido, Mossoró, Brazil

    M. Joseane F. G. Macêdo

  2. Department of Mathematics, Federal University of Paraná, Curitiba, Brazil

    Elizabeth W. Karas

  3. Centre of Mathematics, University of Minho, Campus de Gualtar, Braga, Portugal

    M. Fernanda P. Costa

  4. ALGORITMI Center, University of Minho, Campus de Gualtar, Braga, Portugal

    Ana Maria A. C. Rocha

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  1. M. Joseane F. G. Macêdo
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  2. Elizabeth W. Karas
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  3. M. Fernanda P. Costa
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  4. Ana Maria A. C. Rocha
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Correspondence to M. Joseane F. G. Macêdo.

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Macêdo, M.J.F.G., Karas, E.W., Costa, M.F.P. et al. Filter-based stochastic algorithm for global optimization. J Glob Optim 77, 777–805 (2020). https://doi.org/10.1007/s10898-020-00917-9

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