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Analysis of multi-objective Kriging-based methods for constrained global optimization

Abstract

Metamodeling, i.e., building surrogate models to expensive black-box functions, is an interesting way to reduce the computational burden for optimization purpose. Kriging is a popular metamodel based on Gaussian process theory, whose statistical properties have been exploited to build efficient global optimization algorithms. Single and multi-objective extensions have been proposed to deal with constrained optimization when the constraints are also evaluated numerically. This paper first compares these methods on a representative analytical benchmark. A new multi-objective approach is then proposed to also take into account the prediction accuracy of the constraints. A numerical evaluation is provided on the same analytical benchmark and a realistic aerospace case study.

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Acknowledgments

The authors are indebted to Sébastien Defoort (ONERA) for the definition of the booster benchmark model.

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Correspondence to Julien Marzat.

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Durantin, C., Marzat, J. & Balesdent, M. Analysis of multi-objective Kriging-based methods for constrained global optimization. Comput Optim Appl 63, 903–926 (2016). https://doi.org/10.1007/s10589-015-9789-6

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  • DOI: https://doi.org/10.1007/s10589-015-9789-6

Keywords

  • Black-box functions
  • Constrained global optimization
  • Kriging
  • Multi-objective optimization