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Global optimization of expensive black box problems with a known lower bound

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  • Andrea Cassioli

  • Fabio Schoen

Abstract

In this paper we propose an algorithm for the global optimization of computationally expensive black–box functions. For this class of problems, no information, like e.g. the gradient, can be obtained and function evaluation is highly expensive. In many applications, however, a lower bound on the objective function is known; in this situation we derive a modified version of the algorithm introduced in Gutmann (J Glob Optim 19:201–227, 2001 ). Using this information produces a significant improvement in the quality of the resulting method, with only a small increase in the computational cost. Extensive computational results are provided which support this statement. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Andrea Cassioli & Fabio Schoen, 2013. "Global optimization of expensive black box problems with a known lower bound," Journal of Global Optimization, Springer, vol. 57(1), pages 177-190, September.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:1:p:177-190
    DOI: 10.1007/s10898-011-9834-7
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    References listed on IDEAS

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    1. Jiaqiao Hu & Michael C. Fu & Steven I. Marcus, 2007. "A Model Reference Adaptive Search Method for Global Optimization," Operations Research, INFORMS, vol. 55(3), pages 549-568, June.
    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. 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.
    4. Rommel Regis & Christine Shoemaker, 2005. "Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions," Journal of Global Optimization, Springer, vol. 31(1), pages 153-171, January.
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    Cited by:

    1. Danny D’Agostino, 2026. "An efficient global optimization algorithm with adaptive estimates of the local Lipschitz constants," Journal of Global Optimization, Springer, vol. 94(3), pages 635-666, March.
    2. Yaohui Li & Yizhong Wu & Jianjun Zhao & Liping Chen, 2017. "A Kriging-based constrained global optimization algorithm for expensive black-box functions with infeasible initial points," Journal of Global Optimization, Springer, vol. 67(1), pages 343-366, January.
    3. 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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