Optimal Allocation of Surgery Blocks to Operating Rooms Under Uncertainty
Operations Research
Operating Room Pooling and Parallel Surgery Processing Under Uncertainty
INFORMS Journal on Computing
Branch-cut-and-propagate for the maximum k-colorable subgraph problem with symmetry
CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Solving large Steiner Triple Covering Problems
Operations Research Letters
Three Ideas for the Quadratic Assignment Problem
Operations Research
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Using symmetry to optimize over the sherali-adams relaxation
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Network reduction in the Transmission-Constrained Unit Commitment problem
Computers and Industrial Engineering
Operating Room Pooling and Parallel Surgery Processing Under Uncertainty
INFORMS Journal on Computing
Efficient symmetry breaking formulations for the job grouping problem
Computers and Operations Research
Statistical relational data integration for information extraction
RW'13 Proceedings of the 9th international conference on Reasoning Web: semantic technologies for intelligent data access
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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 that 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 that 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 integer programming 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 pruning and significantly better than a state-of-the-art commercial solver on symmetric integer programs.