942
eng
reportzib
0
2006-11-17
2006-11-17
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Orbitopal Fixing
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 permutation 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 this kind of 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 permutations. The method relies on certain polyhedra, called orbitopes, which have been investigated in (Kaibel and Pfetsch (2006)). However, it does 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.
06-48
942
urn:nbn:de:0297-zib-9422
Appeared in: Proc. of the 12th Integer Programming and Combinatorial Optimization Conference (IPCO) M. Fischetti and D. Williamson (eds.), LNCS 4513, Springer-Verlag, 74-88
Volker Kaibel
Matthias Peinhardt
Marc Pfetsch
ZIB-Report
06-48
eng
uncontrolled
symmetry breaking
eng
uncontrolled
variable fixing
eng
uncontrolled
orbitopes
Informatik, Informationswissenschaft, allgemeine Werke
Special polytopes (linear programming, centrally symmetric, etc.)
Integer programming
Polyhedral combinatorics, branch-and-bound, branch-and-cut
ZIB Allgemein
MATHEON-B12:IPSym
https://opus4.kobv.de/opus4-zib/files/942/ZR_06_48.pdf
https://opus4.kobv.de/opus4-zib/files/942/ZR-06-48.pdf
https://opus4.kobv.de/opus4-zib/files/942/ZR_06_48.ps
https://opus4.kobv.de/opus4-zib/files/942/ZR-06-48.ps