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Lattice based extended formulations for integer linear equality systems

Author

Listed:
  • AARDAL, Karen
  • WOLSEY, Laurence A.

    (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

Abstract

We study different extended formulations for the set X = {x [belong] Z exp.n | Ax = Ax exp.0} in order to tackle the feasibility problem for the set X+ = X [intersection] Z+ exp.n . Here the goal is not to find an improved polyhedral relaxation of conv(X+), but rather to reformulate in such a way that the new variables introduced provide good branching directions, and in certain circumstances permit one to deduce rapidly that the instance is infeasible. For the case that A has one row a we analyze the reformulations in more detail. In particular, we determine the integer width of the extended formulations in the direction of the last coordinate, and derive a lower bound on the Frobenius number of a. We also suggest how a decomposition of the vector a can be obtained that will provide a useful extended formulation. Our theoretical results are accompanied by a small computational study.

Suggested Citation

  • AARDAL, Karen & WOLSEY, Laurence A., 2007. "Lattice based extended formulations for integer linear equality systems," LIDAM Discussion Papers CORE 2007017, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2007017
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2007.html
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