A cutting plane algorithm for a clustering problem
Mathematical Programming: Series A and B
Facets of the clique partitioning polytope
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
A computational study of graph partitioning
Mathematical Programming: Series A and B
Facets of the k-partition polytope
Discrete Applied Mathematics
Formulations and valid inequalities for the node capacitated graph partitioning problem
Mathematical Programming: Series A and B
The node capacitated graph partitioning problem: a computational study
Mathematical Programming: Series A and B - Special issue on computational integer programming
Packing and partitioning orbitopes
Mathematical Programming: Series A and B
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Symmetric ILP: Coloring and small integers
Discrete Optimization
Cliques and clustering: A combinatorial approach
Operations Research Letters
Operations Research Letters
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
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
Computer Networks: The International Journal of Computer and Telecommunications Networking
The maximum k-colorable subgraph problem and orbitopes
Discrete Optimization
Using symmetry to optimize over the sherali-adams relaxation
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Hi-index | 0.00 |
The topic of this paper are integer programming models in which a subset of 0/1-variables encode a partitioning of a set of objects into disjoint subsets. Such models can be surprisingly hard to solve by branch-and-cut algorithms if the order of the subsets of the partition is irrelevant. This kind of symmetry unnecessarily blows up the branch-and-cut tree.We present a general tool, called orbitopal fixing, for enhancing the capabilities of branch-and-cut algorithms in solving such symmetric integer programming models. We devise a linear time algorithm that, applied at each node of the branch-and-cut tree, removes redundant parts of the tree produced by the above mentioned symmetry. The method relies on certain polyhedra, called orbitopes, which have been investigated in [11]. It does, however, not add inequalities to the model, and thus, it does not increase the difficulty of solving the linear programming relaxations. We demonstrate the computational power of orbitopal fixing at the example of a graph partitioning problem motivated from frequency planning in mobile telecommunication networks.