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Volker Kaibel (kaibelovgu.de) Abstract: The topic of this paper are integer programming models in which a subset of 0/1variables encode a partitioning of a set of objects into disjoint subsets. Such models can be surprisingly hard to solve by branchandcut algorithms if the permutation of the subsets of the partition is irrelevant. This kind of symmetry unnecessarily blows up the branchandcut tree. We present a general tool, called orbitopal fixing, for enhancing the capabilities of branchandcut algorithms in solving this kind of symmetric integer programming models. We devise a linear time algorithm that, applied at each node of the branchandcut 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. Keywords: symmetry breaking, variable fixing, orbitopes Category 1: Integer Programming (01 Programming ) Category 2: Combinatorial Optimization (Branch and Cut Algorithms ) Category 3: Combinatorial Optimization (Polyhedra ) Citation: Report, Zuse Institute Berlin, November 2006 Download: [PDF] Entry Submitted: 11/17/2006 Modify/Update this entry  
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