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Improving Discrete Model Representations via Symmetry Considerations

Author

Listed:
  • Hanif D. Sherali

    (Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061)

  • J. Cole Smith

    (Department of Systems and Industrial Engineering, University of Arizona, P.O. Box 210020, Tucson, Arizona 85721-0020)

Abstract

In this paper, we focus on a useful modeling concept that is frequently ignored while formu lating discrete optimization problems. Very often, there exists a natural symmetry inherent in the problem itself that, if propagated to the model, can hopelessly mire a branch-and-bound solver by burdening it to explore and eliminate such alternative symmetric solutions. We discuss three applications where such a symmetry arises: a telecommunications network design problem, a noise pollution problem, and a machine procurement and operation problem. For each case, we identify the indistinguishable objects in the model that create the problem symmetry and show how imposing certain decision hierarchies within the model significantly enhances its solvability, while using a popular modern-day commercial branch-and-cut software (CPLEX 6.5).

Suggested Citation

  • Hanif D. Sherali & J. Cole Smith, 2001. "Improving Discrete Model Representations via Symmetry Considerations," Management Science, INFORMS, vol. 47(10), pages 1396-1407, October.
    • Handle: RePEc:inm:ormnsc:v:47:y:2001:i:10:p:1396-1407
    DOI: 10.1287/mnsc.47.10.1396.10265
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    References listed on IDEAS

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    1. Alain S. Sutter & François Vanderbeck & Laurence Wolsey, 1998. "Optimal Placement of Add/Drop Multiplexers: Heuristic and Exact Algorithms," Operations Research, INFORMS, vol. 46(5), pages 719-728, October.
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