Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
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Management Science
Packing and partitioning orbitopes
Mathematical Programming: Series A and B
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
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Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Automatic Generation of Symmetry-Breaking Constraints
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
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CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Quantified linear programs: a computational study
ESA'11 Proceedings of the 19th European conference on Algorithms
The maximum k-colorable subgraph problem and orbitopes
Discrete Optimization
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We introduce orbital branching, an effective branching method for integer programs containing a great deal of symmetry. The method is based on computing groups of variables that are equivalent with respect to the symmetry remaining in the problem after branching, including symmetry which is not present at the root node. These groups of equivalent variables, called orbits, are used to create a valid partitioning of the feasible region which significantly reduces the effects of symmetry while still allowing a flexible branching rule. We also show how to exploit the symmetries present in the problem to fix variables throughout the branch-and-bound tree. Orbital branching can easily be incorporated into standard IP software. Through an empirical study on a test suite of symmetric integer programs, the question as to the most effective orbit on which to base the branching decision is investigated. The resulting method is shown to be quite competitive with a similar method known as isomorphism pruningand significantly better than a state-of-the-art commercial solver on symmetric integer programs.