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The Data-Correcting Algorithm for the Minimization of Supermodular Functions

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Author Info

  • Boris Goldengorin

    (Department of Econometrics and Operations Research, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands)

  • Gerard Sierksma

    (Department of Econometrics and Operations Research, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands)

  • Gert A. Tijssen

    (Department of Econometrics and Operations Research, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands)

  • Michael Tso

    (Department of Mathematics, University of Manchester, Institute of Science and Technology, UMIST, Manchester, United Kingdom)

Abstract

The Data-Correcting (DC) Algorithm is a recursive branch-and-bound type algorithm, in which the data of a given problem instance are "heuristically corrected" at each branching in such a way that the new instance will be as close as possible to polynomially solvable and the result satisfies a prescribed accuracy (the difference between optimal and current solution). In this paper the DC algorithm is applied to determining exact or approximate global minima of supermodular functions. The working of the algorithm is illustrated by an instance of the Simple Plant Location (SPL) Problem. Computational results, obtained for the Quadratic Cost Partition Problem (QCP), show that the DC algorithm outperforms a branch-and-cut algorithm, not only for sparse graphs but also for nonsparse graphs (with density more than 40%), often with speeds 100 times faster.

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File URL: http://dx.doi.org/10.1287/mnsc.45.11.1539
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 45 (1999)
Issue (Month): 11 (November)
Pages: 1539-1551

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Handle: RePEc:inm:ormnsc:v:45:y:1999:i:11:p:1539-1551

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Related research

Keywords: data-correcting algorithm; supermodular function; global minimum;

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Citations

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Cited by:
  1. Barros, Lilian & Riley, Michael, 2001. "A combinatorial approach to level of repair analysis," European Journal of Operational Research, Elsevier, vol. 129(2), pages 242-251, March.
  2. Goldengorin, Boris & Tijssen, Gert A. & Tso, Michael, 1999. "The maximization of submodular functions : old and new proofs for the correctness of the dichotomy algorithm," Research Report 99A17, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
  3. Goldengorin, Boris & Ghosh, Diptesh & Sierksma, Gerard, 2001. "Branch and peg algorithms for the simple plant location problem," Research Report 01A14, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
  4. Cui, Tingting & Ouyang, Yanfeng & Shen, Zuo-Jun Max J, 2010. "Reliable Facility Location Design under the Risk of Disruptions," University of California Transportation Center, Working Papers qt5sh2c7pw, University of California Transportation Center.
  5. Goldengorin, Boris & Vink, Marius de, 1999. "Solving large instances of the quadratic cost of partition problem on dense graphs by data correcting algorithms," Research Report 99A50, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
  6. Ghosh, Diptesh & Sierksma, Gerard & Goldengorin, Boris & AlMohammad, Bader F., 2000. "Equivalent instances of the simple plant location problem," Research Report 00A54, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
  7. Goldengorin, Boris, 2001. "Solving the simple plant location problem using a data correcting approach," Research Report 01A53, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
  8. Goldengorin, Boris & Ghosh, Diptesh, 2004. "A Multilevel Search Algorithm for the Maximization of Submodular Functions," Research Report 04A20, University of Groningen, Research Institute SOM (Systems, Organisations and Management).

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