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Constraint Orbital Branching

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Integer Programming and Combinatorial Optimization (IPCO 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5035))

Abstract

Orbital branching is a method for branching on variables in integer programming that reduces the likelihood of evaluating redundant, isomorphic nodes in the branch-and-bound procedure. In this work, the orbital branching methodology is extended so that the branching disjunction can be based on an arbitrary constraint. Many important families of integer programs are structured such that small instances from the family are embedded in larger instances. This structural information can be exploited to define a group of strong constraints on which to base the orbital branching disjunction. The symmetric nature of the problems is further exploited by enumerating non-isomorphic solutions to instances of the small family and using these solutions to create a collection of typically easy-to-solve integer programs. The solution of each integer program in the collection is equivalent to solving the original large instance. The effectiveness of this methodology is demonstrated by computing the optimal incidence width of Steiner Triple Systems and minimum cardinality covering designs.

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Author information

Authors and Affiliations

  1. Department of Industrial and Systems Engineering, Lehigh University, 200 W. Packer Ave., Bethlehem, PA 18015, USA

    James Ostrowski

  2. Department of Industrial and Systems Engineering, University of Wisconsin-Madison, 1513 University Avenue, Madison, WI 53706, USA

    Jeff Linderoth

  3. Dipartimento di Informatica, Università di L’Aquila, Via Vetoio, I-67010, Coppito (AQ), Italy

    Fabrizio Rossi & Stefano Smriglio

Authors
  1. James Ostrowski
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  2. Jeff Linderoth
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  3. Fabrizio Rossi
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  4. Stefano Smriglio
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Editor information

Andrea Lodi Alessandro Panconesi Giovanni Rinaldi

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© 2008 Springer-Verlag Berlin Heidelberg

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Ostrowski, J., Linderoth, J., Rossi, F., Smriglio, S. (2008). Constraint Orbital Branching. In: Lodi, A., Panconesi, A., Rinaldi, G. (eds) Integer Programming and Combinatorial Optimization. IPCO 2008. Lecture Notes in Computer Science, vol 5035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68891-4_16

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  • DOI: https://doi.org/10.1007/978-3-540-68891-4_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68886-0

  • Online ISBN: 978-3-540-68891-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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