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International Computing and Combinatorics Conference

COCOON 1999: Computing and Combinatorics pp 339–348Cite as

A Dynamic-Programming Bound for the Quadratic Assignment Problem

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1627))

Abstract

The quadratic assignment problem (QAP) is the NP-complete optimization problem of assigning n facilities to n locations while minimizing certain costs. In practice, proving the optimality of a solution is hard even for moderate problem sizes with n ≈ 20.

We present a new algorithm for solving the QAP. Based on the dynamic-programming paradigm, the algorithm constructs a table of subproblem solutions and uses the solutions of the smaller subproblems for bounding the larger ones. The algorithm can be parallelized, performs well in practice, and has solved the previously unsolved instance NUG25. A comparison between the new dynamic-programming bound (DPB) and the traditionally used Gilmore-Lawler bound (GLB) shows that the DPB is stronger and leads to much smaller search trees than the GLB.

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References

  1. Adrian Brüngger. Solving Hard Combinatorial Optimization Problems in Parallel: Two Case Studies. PhD thesis, ETH Zürich, 1997.

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  2. Adrian Brüngger, Ambros Marzetta, Jens Clausen, and Michael Perregaard. Solving large-scale QAP problems in parallel with the search library ZRAM. Journal of Parallel and Distributed Computing, 50:157–169, 1998. http://wwwjn.inf.ethz.ch/ambros/zram/jpdc_qap.pdf.

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  4. Rainer E. Burkard, Stefan E. Karisch, and Franz Rendl. QAPLIB-a quadratic assignment problem library. Journal of Global Optimization, 10:391–403, 1997. http://serv1.imm.dtu.dk/~sk/qaplib/.

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Author information

Authors and Affiliations

  1. International Computer Science Institute, Berkeley, USA

    Ambros Marzetta

  2. Novartis Pharma AG, Basel, Switzerland

    Adrian Brüngger

Authors
  1. Ambros Marzetta
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  2. Adrian Brüngger
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Editor information

Editors and Affiliations

  1. Department of Information and System Engineering Faculty of Science and Engineering, Chuo University, 1-13-27, Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

    Takano Asano

  2. Department of Information Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Hideki Imai

  3. Academia Sinica, Institute of Information Science, Nankang, Taipei, Taiwan

    D. T. Lee

  4. Department of Computer Science Faculty of Engineering, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma, 376-8515, Japan

    Shin-ichi Nakano

  5. IBM Tokyo Research Laboratory, 1623-14, Shimo-Tsuruma, Yamato Kanagawa, 242-0001, Japan

    Takeshi Tokuyama

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© 1999 Springer-Verlag Berlin Heidelberg

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Marzetta, A., Brüngger, A. (1999). A Dynamic-Programming Bound for the Quadratic Assignment Problem. In: Asano, T., Imai, H., Lee, D.T., Nakano, Si., Tokuyama, T. (eds) Computing and Combinatorics. COCOON 1999. Lecture Notes in Computer Science, vol 1627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48686-0_34

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  • DOI: https://doi.org/10.1007/3-540-48686-0_34

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66200-6

  • Online ISBN: 978-3-540-48686-2

  • eBook Packages: Springer Book Archive

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