Generalized resolution and cutting planes
Annals of Operations Research
An efficient algorithm for the minimum capacity cut problem
Mathematical Programming: Series A and B
The precedence-constrained asymmetric traveling salesman polytope
Mathematical Programming: Series A and B
A polyhedral approach to the asymmetric traveling salesman problem
Management Science
Constraint satisfaction methods for generating valid cuts
Advances in computational and stochastic optimization, logic programming, and heuristic search
Solving TSP with time windows with constraints
Proceedings of the 1999 international conference on Logic programming
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Tight Cooperation and Its Application in Piecewise Linear Optimization
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Branch and Infer: a Unifying Framework for Integer and Finite Domain Constraint Programming
INFORMS Journal on Computing
Network Flow Problems in Constraint Programming
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Coupling Variable Fixing Algorithms for the Automatic Recording Problem
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Simple and Fast: Improving a Branch-And-Bound Algorithm for Maximum Clique
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A totally unimodular description of the consistent value polytope for binary constraint programming
CPAIOR'06 Proceedings of the Third international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
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In recent years, a growing number of attempts have been performed in order to integrate well known Operations Research( OR) techniques in Constraint Programming (CP) tools. The aim of the integration is to maintain the modelling facilities of the CP paradigm, while improving its performances by exploiting effective OR techniques. In our previous work, we proposed the use of optimization constraints [9], embedding a linear relaxation of the constraint itself and performing pruning on the basis of costs. In particular, domain values can be removed whenever it can be shown that their assignment will necessarily lead to solutions worse than the best solution found. In this setting, the use of cutting planes in global constraints allows to tighten the relaxation so as to infer more accurate bounds on the problem. We propose different ways of using cutting-planes in optimization constraints achieving different levels of tightness of the integration and pruning power. Even if the proposed technique is general, we use as testing application the Travelling Salesman Problem (TSPs) and its time constrained variant. Computational results compare different relaxations in terms of pruning achieved and computational complexity.