Modeling the Regular Constraint with Integer Programming

Authors:
Marie-Claude Côté;Bernard Gendron;Louis-Martin Rousseau
Affiliations:
Département de mathématiques appliquées et génie industriel, École Polytechnique de Montréal, Montréal, Canada and Interuniversity Research Center on Enterprise ...;Département d'informatique et de recherche opérationnelle, Université de Montréal, Montréal, Canada and Interuniversity Research Center on Enterprise Networks, Logistics a ...;Département de mathématiques appliquées et génie industriel, École Polytechnique de Montréal, Montréal, Canada and Interuniversity Research Center on Enterprise ...
Venue:
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Year:
2007

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Abstract

Many optimisation problems contain substructures involving constraints on sequences of decision variables. Such constraints can be very complex to express with mixed integer programming (MIP), while in constraint programming (CP), the global constraint regulareasily represents this kind of substructure with deterministic finite automata (DFA). In this paper, we use DFAs and the associated layered graph structure built for the regularconstraint consistency algorithm to develop a MIP version of the constraint. We present computational results on an employee timetabling problem, showing that this new modeling approach can significantly decrease computational times in comparison with a classical MIP formulation.