Abstract
Integer programming (IP) is one of the most successful approaches for combinatorial optimization problems. Many IP solvers make use of the linear relaxation, which removes the integrality requirement on the variables. The relaxed problem can then be solved using linear programming (LP), a very efficient optimization paradigm. Constraint programming (CP) can solve a much wider variety of problems, since it does not require the problem to be expressed in terms of linear equations. The cost of this versatility is that in CP there is no easy way to automatically derive a good bound on the objective. This paper presents an approach based on ideas from Lagrangian decomposition (LD) that establishes a general bounding scheme for any CP. We provide an implementation for optimization problems that can be formulated with knapsack and regular constraints, and we give comparisons with pure CP approaches. Our results clearly demonstrate the benefits of our approach on these problems.
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Hà, M.H., Quimper, CG., Rousseau, LM. (2015). General Bounding Mechanism for Constraint Programs. In: Pesant, G. (eds) Principles and Practice of Constraint Programming. CP 2015. Lecture Notes in Computer Science(), vol 9255. Springer, Cham. https://doi.org/10.1007/978-3-319-23219-5_12
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DOI: https://doi.org/10.1007/978-3-319-23219-5_12
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