A global method for mixed categorical optimization with catalogs

In this article, we propose an algorithmic framework for globally solving mixed problems with continuous variables and categorical variables whose properties are available from a catalog. It supports catalogs of arbitrary size and properties of arbitrary dimension, and does not require any modeling effort from the user. Our tree search approach, similar to spatial branch and bound methods, performs an exhaustive exploration of the range of the properties of the categorical variables ; branching, constraint programming and catalog lookup phases alternate to discard inconsistent values. A novel catalog-based contractor guarantees consistency between the categorical properties and the existing catalog items. This results in an intuitive generic approach that is exact and easy to implement. We demonstrate the validity of the approach on a numerical example in which a categorical variable is described by a two-dimensional property space.