By Bohm J.
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Saraswat and P. , Principles and Practice of Constraint Programming: The Newport Papers, MIT Press (Cambridge, MA, 1995) 267-288. N. Hooker and H. Yan. A relaxation for the cumulative constraint. In P. Van Hentenryck, editor, Proceedings of the Eighth International Conference on Principles and Practice of Constraint Programming (CP), LNCS 2470, 686–690. Springer-Verlag, 2002.  ILOG S. A. The CPLEX mixed integer linear programming and barrier optimizer. com/products/cplex/.  V. Jain and I.
Indeed, propagation will permit to drop from decision variable domains values leading to unfeasible solutions. We perform propagation using the following filtering algorithms, that are detailed in Baptiste et al. . Precedence Constraints. Each node of the search tree corresponds to a partial selection in the disjunctive graph G = (V, U, E), where U is the set of conjunctive arcs and disjunctive arcs for which a direction has been chosen. Consistency is 42 Christian Artigues et al. Fig. 3. Disjunctive constraints ensured at the bounds of the domains of variables using constraints where is the weight of the arc in the graph.
G. Benders ) that solve parts of the problem with different techniques [10,14, 19, 21, 24, 33]; allowing different models/solvers to exchange information ; using linear programming to reduce the domains of variables or to fix them to certain values [4, 11, 32]; automatic reformulation of global constraints as systems of linear inequalities ; continuous relaxations of global constraints and disjunctions of linear systems [1, 14, 18, 22, 28, 36, 37, 38]; understanding the generation of cutting planes as a form of logical inference [6, 7]; strengthening the problem formulation by embedding the generation of valid cutting planes into CP constraints ; maintaining the continuous relaxation of a constraint updated when the domains of its variables change ; and using global constraints as a key component in the intersection of CP and OR .