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Polyhedral Methods for the QAP

  • Chapter
Nonlinear Assignment Problems

Part of the book series: Combinatorial Optimization ((COOP,volume 7))

Abstract

For many combinatorial optimization problems investigations of associated polyhedra have led to enormous successes with respect to both theoretical insights into the structures of the problems as well as to their algorithmic solvability. Among these problems are quite prominent NP-hard ones, like, e.g., the traveling salesman problem, the stable set problem, or the maximum cut problem. In this chapter we overview the polyhedral work that has been done on the quadratic assignment problem (QAP). Our treatment includes a brief introduction to the methods of polyhedral combinatorics in general, descriptions of the most important polyhedral results that are known about the QAP, explanations of the techniques that are used to prove such results, and a discussion of the practical results obtained by cutting plane algorithms that exploit the polyhedral knowledge. We close by some remarks on the perspectives of this kind of approach to the QAP.

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Sekr. 7-1, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Volker Kaibel

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  1. Volker Kaibel
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Editor information

Editors and Affiliations

  1. University of Florida, USA

    Panos M. Pardalos

  2. Princeton University, USA

    Leonidas S. Pitsoulis

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© 2000 Springer Science+Business Media Dordrecht

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Kaibel, V. (2000). Polyhedral Methods for the QAP. In: Pardalos, P.M., Pitsoulis, L.S. (eds) Nonlinear Assignment Problems. Combinatorial Optimization, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3155-2_6

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  • DOI: https://doi.org/10.1007/978-1-4757-3155-2_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4841-0

  • Online ISBN: 978-1-4757-3155-2

  • eBook Packages: Springer Book Archive

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