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A Branch and Bound Algorithm for the Quadratic Assignment Problem using a Lower Bound Based on Linear Programming

  • Chapter
State of the Art in Global Optimization

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 7))

Abstract

In this paper, we study a branch and bound algorithm for the quadratic assignment problem (QAP) that uses a lower bound based on the linear programming (LP) relaxation of a classical integer programming formulation of the QAP. We report on computational experience with the branch and bound algorithm on all QAP test problems of dimension n ≤ 15 of QAPLIB, a standard library of QAP test problems. The linear programming relaxations are solved with an implementation of an interior point algorithm that uses a preconditioned conjugate gradient algorithm to compute directions. The branch and bound algorithm is compared with a similar branch and bound algorithm that uses the Gilmore-Lawler lower bound (GLB) instead of the LP-based bound. The LP-based algorithm examines a small portion of the nodes explored by the GLB-based algorithm. Extensions to the implementation are discussed.

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Author information

Authors and Affiliations

  1. AT&T Bell Laboratories, USA

    K. G. Ramakrishnan

  2. AT&T Bell Laboratories, USA

    Mauricio G. C. Resende

  3. University of Florida, USA

    Panos M. Pardalos

Authors
  1. K. G. Ramakrishnan
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  2. Mauricio G. C. Resende
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  3. Panos M. Pardalos
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Editor information

Editors and Affiliations

  1. Princeton University, USA

    C. A. Floudas

  2. University of Florida, USA

    P. M. Pardalos

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© 1996 Kluwer Academic Publishers

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Ramakrishnan, K.G., Resende, M.G.C., Pardalos, P.M. (1996). A Branch and Bound Algorithm for the Quadratic Assignment Problem using a Lower Bound Based on Linear Programming. In: Floudas, C.A., Pardalos, P.M. (eds) State of the Art in Global Optimization. Nonconvex Optimization and Its Applications, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3437-8_5

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  • DOI: https://doi.org/10.1007/978-1-4613-3437-8_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3439-2

  • Online ISBN: 978-1-4613-3437-8

  • eBook Packages: Springer Book Archive

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