Improving discrete model representations via symmetry considerations

Improving discrete model representations via symmetry considerations

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Article ID: iaor20032514
Country: United States
Volume: 47
Issue: 10
Start Page Number: 1396
End Page Number: 1407
Publication Date: Oct 2001
Journal: Management Science
Authors: ,
Abstract:

In this paper, we focus on a useful modeling concept that is frequently ignored while formulating 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.

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