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。该方法支持任意大小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算子（或过滤算子）保证了分类属性与现有目录项之间的一致性。由此形成了一种直观且通用的方法，该方法精确、严谨（对舍入误差具有鲁棒性），并且可以轻松集成到现成的、交替进行分支与约束传播的区间连续求解器中。我们通过一个数值问题验证了该方法的有效性，该问题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