In this article, we propose an interval constraint programming method for globally solving catalog-based categorical optimization problems. It supports catalogs of arbitrary size and properties of arbitrary dimension, and does not require any modeling effort from the user. A novel catalog-based contractor (or filtering operator) guarantees consistency between the categorical properties and the existing catalog items. This results in an intuitive and generic approach that is exact, rigorous (robust to roundoff errors) and can be easily implemented in an off-the-shelf interval-based continuous solver that interleaves branching and constraint propagation. We demonstrate the validity of the approach on a numerical problem in which a categorical variable is described by a two-dimensional property space. A Julia prototype is available as open-source software under the MIT license at https://github.com/cvanaret/CateGOrical.jl

翻译：本文提出了一种区间约束规划方法，用于全局求解基于目录的分类优化问题。该方法支持任意规模的目录和任意维度的属性，且无需用户进行任何建模工作。一种新颖的基于目录的收缩器（或滤波算子）确保了分类属性与现有目录项之间的一致性。这形成了一种直观且通用的方法，它具有精确性、严格性（对舍入误差鲁棒），且易于在现成的区间连续求解器中实现，该求解器交替进行分支与约束传播。我们通过一个数值问题验证了该方法的有效性，其中分类变量由二维属性空间描述。Julia原型已作为开源软件在MIT许可证下发布，获取地址为：https://github.com/cvanaret/CateGOrical.jl