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A Decomposition Method for Quadratic Zero-One Programming

Author

Listed:
  • Pierre Chardaire

    (School of Information Systems, University of East Anglia, Norwich NR4 7TJ, United Kingdom)

  • Alain Sutter

    (France-Télécom, CNET, 38-40 rue du général Leclerc, F 92131 Issy Les Moulineaux, France)

Abstract

This paper proposes a decomposition method to compute a lower bound for unconstrained quadratic zero-one minimization. First, we show that any quadratic function can be expressed as a sum of particular quadratic functions whose minima can be computed by a simple branch and bound algorithm. Then, assuming some hypothesis, we prove that, among all possible decompositions, the best one can be found by a Lagrangian decomposition method. Moreover, we show that our algorithm gives at least the roof dual bound and should give better results in practice. Eventually, computational results and comparison with Pardalos and Rodgers' algorithm demonstrate the efficiency of our method for medium size problems (up to 100 variables).

Suggested Citation

  • Pierre Chardaire & Alain Sutter, 1995. "A Decomposition Method for Quadratic Zero-One Programming," Management Science, INFORMS, vol. 41(4), pages 704-712, April.
    • Handle: RePEc:inm:ormnsc:v:41:y:1995:i:4:p:704-712
    DOI: 10.1287/mnsc.41.4.704
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    Citations

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    Cited by:

    1. Lodi, Andrea & Allemand, Kim & Liebling, Thomas M., 1999. "An evolutionary heuristic for quadratic 0-1 programming," European Journal of Operational Research, Elsevier, vol. 119(3), pages 662-670, December.
    2. Fred Glover & Gary A. Kochenberger & Bahram Alidaee, 1998. "Adaptive Memory Tabu Search for Binary Quadratic Programs," Management Science, INFORMS, vol. 44(3), pages 336-345, March.
    3. Serigne Gueye & Philippe Michelon, 2005. "“Miniaturized” Linearizations for Quadratic 0/1 Problems," Annals of Operations Research, Springer, vol. 140(1), pages 235-261, November.
    4. Billionnet, Alain & Faye, Alain & Soutif, Eric, 1999. "A new upper bound for the 0-1 quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 112(3), pages 664-672, February.
    5. Gili Rosenberg & Mohammad Vazifeh & Brad Woods & Eldad Haber, 2016. "Building an iterative heuristic solver for a quantum annealer," Computational Optimization and Applications, Springer, vol. 65(3), pages 845-869, December.
    6. 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).
    7. repec:dgr:rugsom:99a50 is not listed on IDEAS
    8. Neng Fan & Panos Pardalos, 2010. "Linear and quadratic programming approaches for the general graph partitioning problem," Journal of Global Optimization, Springer, vol. 48(1), pages 57-71, September.
    9. Billionnet, Alain & Soutif, Eric, 2004. "An exact method based on Lagrangian decomposition for the 0-1 quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 157(3), pages 565-575, September.

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