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A General Mathematical Framework for Constrained Mixed-variable Blackbox Optimization Problems with Meta and Categorical Variables

Author

Listed:
  • Charles Audet

    (Polytechnique Montréal)

  • Edward Hallé-Hannan

    (Polytechnique Montréal)

  • Sébastien Le Digabel

    (Polytechnique Montréal)

Abstract

A mathematical framework for modelling constrained mixed-variable optimization problems is presented in a blackbox optimization context. The framework introduces a new notation and allows solution strategies. The notation framework allows meta and categorical variables to be explicitly and efficiently modelled, which facilitates the solution of such problems. The new term meta variables is used to describe variables that influence which variables are included or excluded: meta variables may affect the number of variables and constraints. The flexibility of the solution strategies supports the main blackbox mixed-variable optimization approaches: direct search methods and surrogate-based methods (Bayesian optimization). The notation system and solution strategies are illustrated through an example of a hyperparameter optimization problem from the machine learning community.

Suggested Citation

  • Charles Audet & Edward Hallé-Hannan & Sébastien Le Digabel, 2023. "A General Mathematical Framework for Constrained Mixed-variable Blackbox Optimization Problems with Meta and Categorical Variables," SN Operations Research Forum, Springer, vol. 4(1), pages 1-37, March.
    • Handle: RePEc:spr:snopef:v:4:y:2023:i:1:d:10.1007_s43069-022-00180-6
    DOI: 10.1007/s43069-022-00180-6
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    References listed on IDEAS

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    1. 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.
    2. Charles Audet & Christophe Tribes, 2018. "Mesh-based Nelder–Mead algorithm for inequality constrained optimization," Computational Optimization and Applications, Springer, vol. 71(2), pages 331-352, November.
    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.
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