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

Charles Audet, Edward Hallé-Hannan () and Sébastien Le Digabel ()
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Charles Audet: Polytechnique Montréal
Edward Hallé-Hannan: Polytechnique Montréal
Sébastien Le Digabel: Polytechnique Montréal

SN Operations Research Forum, 2023, vol. 4, issue 1, 1-37

Abstract: 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.

Keywords: Blackbox optimization; Derivative-free optimization; Mixed-variable optimization; Categorical variables; Meta variables (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s43069-022-00180-6

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