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Exact solution method to solve large scale integer quadratic multidimensional knapsack problems

Author

Listed:
  • D. Quadri

    (Université Paris-Dauphine)

  • E. Soutif

    (Conservatoire des Arts et Métiers)

  • P. Tolla

    (Université Paris-Dauphine)

Abstract

In this paper we develop a branch-and-bound algorithm for solving a particular integer quadratic multi-knapsack problem. The problem we study is defined as the maximization of a concave separable quadratic objective function over a convex set of linear constraints and bounded integer variables. Our exact solution method is based on the computation of an upper bound and also includes pre-procedure techniques in order to reduce the problem size before starting the branch-and-bound process. We lead a numerical comparison between our method and three other existing algorithms. The approach we propose outperforms other procedures for large-scaled instances (up to 2000 variables and constraints).

Suggested Citation

  • D. Quadri & E. Soutif & P. Tolla, 2009. "Exact solution method to solve large scale integer quadratic multidimensional knapsack problems," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 157-167, February.
    • Handle: RePEc:spr:jcomop:v:17:y:2009:i:2:d:10.1007_s10878-007-9105-1
    DOI: 10.1007/s10878-007-9105-1
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    References listed on IDEAS

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    1. W. David Pisinger & Anders Bo Rasmussen & Rune Sandvik, 2007. "Solution of Large Quadratic Knapsack Problems Through Aggressive Reduction," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 280-290, May.
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    7. Bretthauer, Kurt M. & Shetty, Bala, 2002. "The nonlinear knapsack problem - algorithms and applications," European Journal of Operational Research, Elsevier, vol. 138(3), pages 459-472, May.
    8. 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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    Cited by:

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