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Mathematical Programming

, Volume 98, Issue 1–3, pp 3–21 | Cite as

Exploiting orbits in symmetric ILP

  • François Margot
Article

Abstract.

This paper describes components of a branch-and-cut algorithm for solving integer linear programs having a large symmetry group. It describes an isomorphism pruning algorithm and variable setting procedures using orbits of the symmetry group. Pruning and orbit computations are performed by backtracking procedures using a Schreier-Sims table for representing the symmetry group. Applications to hard set covering problems, generation of covering designs and error correcting codes are given.

Keywords

Branch-and-cut Isomorphism pruning Symmetry 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KentuckyLexington

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