The OPL optimization programming language
The OPL optimization programming language
On integrating constraint propagation and linear programming for combinatorial optimization
AAAI '99/IAAI '99 Proceedings of the sixteenth national conference on Artificial intelligence and the eleventh Innovative applications of artificial intelligence conference innovative applications of artificial intelligence
Mixed logical-linear programming
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Mixed Global Constraints and Inference in Hybrid CLP–IP Solvers
Annals of Mathematics and Artificial Intelligence
Logic-Based Methods for Optimization
PPCP '94 Proceedings of the Second International Workshop 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
Cutting Planes in Constraint Programming: A Hybrid Approach
CP '02 Proceedings of the 6th 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
Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems
INFORMS Journal on Computing
Branch-and-cut for combinatorial optimization problems without auxiliary binary variables
The Knowledge Engineering Review
A scheme for unifying optimization and constraint satisfaction methods
The Knowledge Engineering Review
Constraint Programming Contribution to Benders Decomposition: A Case Study
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
On the Sum Constraint: Relaxation and Applications
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
A Relaxation of the Cumulative Constraint
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
A Hybrid Method for the Planning and Scheduling
Constraints
Proceedings of the conference on Design, automation and test in Europe: Proceedings
Computers and Operations Research
EMSOFT '07 Proceedings of the 7th ACM & IEEE international conference on Embedded software
International Journal of Parallel Programming - Special Issue on Multiprocessor-based embedded systems
On the cooperation of the constraint domains ℋ, ℛ, and ℱ in cflp
Theory and Practice of Logic Programming
An Integrated Solver for Optimization Problems
Operations Research
Checking-up on branch-and-check
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
A hybrid algorithm for a class of resource constrained scheduling problems
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
A search-infer-and-relax framework for integrating solution methods
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
CSCLP'05 Proceedings of the 2005 Joint ERCIM/CoLogNET international conference on Constraint Solving and Constraint Logic Programming
Allocation, scheduling and voltage scaling on energy aware MPSoCs
CPAIOR'06 Proceedings of the Third international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Cutting plane algorithms for solving a stochastic edge-partition problem
Discrete Optimization
Coloring Graphs Using Two Colors While Avoiding Monochromatic Cycles
INFORMS Journal on Computing
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We present Branch-and-Check, a hybrid framework integrating Mixed Integer Programming and Constraint Logic Programming, which encapsulates the traditional Benders Decomposition and Branch-and-Bound as special cases. In particular we describe its relation to Benders and the use of nogoods and linear relaxations. We give two examples of how problems can be modelled and solved using Branch-and-Check and present computational results demonstrating more than order-of-magnitude speedup compared to previous approaches. We also mention important future research issues such as hierarchical, dynamic and adjustable linear relaxations.