Integrating Benders Decomposition Within Constraint Programming

Benders decomposition [1] is a solving strategy based on the separation of the variables of the problem. It is often introduced as a basis for models and techniques using the complementary strengths of constraint programming and optimization techniques. Hybridization schemes have appeared recently and provided interesting computational results [4, 5, 7, 8]. They have been extended [2, 3, 6] to take into account other kinds of sub-problems and not only the classical linear programming ones. However, decomposition has never been proposed to our knowledge in a generic constraint programming approach. This paper discusses the way a decomposition framework could be embedded in a constraint solver, taking advantage of structures for a non expert user. We explore the possibility of deriving logic Benders cuts using an explanation-based framework for CP and describe Benders decomposition as a nogood recording strategy. We propose a tool implemented at the top of an explained constraint solver that could offer such a systematic decomposition framework.