Comparing constraint programming and mathematical programming approaches to discrete optimisation—the change problem

Abstract

This paper is aimed at researchers and practitioners in Operational Research who are interested in the new field of Constraint Programming/Constraint Logic Programming. Due to differing terminology and problem representation they might have found it difficult to access the field. The paper focuses on discrete optimisation problems. The first part lists frequently used terms in Constraint Programming (CP), contrasting them with their counterparts in Mathematical Programming (MP). The second part explains some of the most important concepts and techniques in more detail by comparing the CP and MP implementations of a small example problem, the ‘Change Problem’. It includes an overview of the respective results. In conclusion a more generalised comparison of CP and MP techniques is given.