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Symmetry in Integer Linear Programming

In: 50 Years of Integer Programming 1958-2008

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  • François Margot

    (Tepper School of Business, Carnegie Mellon University)

Abstract

An integer linear program (ILP) is symmetric if its variables can be permuted without changing the structure of the problem. Areas where symmetric ILPs arise range from applied settings (scheduling on identical machines), to combinatorics (code construction), and to statistics (statistical designs construction). Relatively small symmetric ILPs are extremely difficult to solve using branch-and-cut codes oblivious to the symmetry in the problem. This paper reviews techniques developed to take advantage of the symmetry in an ILP during its solution. It also surveys related topics, such as symmetry detection, polyhedral studies of symmetric ILPs, and enumeration of all non isomorphic optimal solutions.

Suggested Citation

  • François Margot, 2010. "Symmetry in Integer Linear Programming," Springer Books, in: Michael Jünger & Thomas M. Liebling & Denis Naddef & George L. Nemhauser & William R. Pulleyblank & (ed.), 50 Years of Integer Programming 1958-2008, chapter 0, pages 647-686, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-68279-0_17
    DOI: 10.1007/978-3-540-68279-0_17
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