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A mathematical framework for modelling constrained mixed-variableoptimization problems is presented in a blackbox optimization context. Theframework introduces a new notation and allows solution strategies. Thenotation framework allows meta and categorical variables to be explicitly andefficiently modelled, which facilitates the solution of such problems. The newterm meta variables is used to describe variables that influence whichvariables are acting or nonacting: meta variables may affect the number ofvariables and constraints. The flexibility of the solution strategies supportsthe main blackbox mixed-variable optimization approaches: direct search methodsand surrogate-based methods (Bayesian optimization). The notation system andsolution strategies are illustrated through an example of a hyperparameteroptimization problem from the machine learning community.

A general mathematical framework for constrained mixed-variable blackbox optimization problems with meta and categorical variables