Interval constraint programming for globally solving catalog-based categorical optimization

TL;DR

This paper introduces an interval constraint programming approach for solving catalog-based categorical optimization problems, supporting arbitrary catalog sizes and properties without user modeling, ensuring robustness and ease of implementation.

Contribution

It presents a novel catalog-based contractor that guarantees consistency and can be integrated into existing interval solvers, providing an exact and robust solution method.

Findings

Validated on a numerical example with a 2D property space

Open-source Julia implementation available

Demonstrates robustness to roundoff errors

Abstract

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