Constraint Programming Links with Math Programming

Abstract

Although operations research (OR) and constraint programming (CP) have different roots, the links between the two communities have grown stronger in recent years. For solving combinatorial optimization problems, the techniques of CP and OR will become so interdependent that the two research communities could eventually merge. In this article, we first describe CP basic concepts, and then we show different ways of integrating CP and mathematical programming (MP). This article presents a CP perspective: MP is seen as a support to the CP decision process, even if existing approaches from the OR literatures consider a cooperation of CP and MP on an equal basis, but they are out of the scope of this article.

Hybrid optimization of vehicle routing problems

“…Strong objective bounds are necessary for pruning large sections of the search space in hard optimization problems. The linear relaxation bounds in mixed integer programming are generally stronger than the bounds found by propagators in constraint programming because propagators usually have a narrow view of the problem (e.g., Focacci, Lodi and Milano 1999, Hooker 2006, Milano 2010, whereas the constraints in a linear relaxation can directly influence the objective function via elementary row operations. Even though constraint programming lacks strong bounds (e.g., Benchimol et al 2012, Focacci, Lodi and Milano 2002, it excels at finding feasible solutions in satisfaction problems (e.g., Milano 2010), and particularly, in scheduling problems (e.g., Schutt et al 2009Schutt et al , 2010Schutt et al , 2013.…”