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Improving an exact approach for solving separable integer quadratic knapsack problems

Author

Listed:
  • Federico Della Croce

    (Politecnico di Torino)

  • Dominique Quadri

    (Université d’Avignon)

Abstract

We consider the specially structured (pure) integer Quadratic Multi-Knapsack Problem (QMKP) tackled in the paper “Exact solution methods to solve large scale integer quadratic knapsack problems” by D. Quadri, E. Soutif and P. Tolla (2009), recently appeared on this journal, where the problem is solved by transforming it into an equivalent 0–1 linearized Multi-Knapsack Problem (MKP). We show that, by taking advantage of the structure of the transformed (MKP), it is possible to derive an effective variable fixing procedure leading to an improved branch-and-bound approach. This procedure reduces dramatically the resulting linear problem size inducing an impressive improvement in the performances of the related branch and bound approach when compared to the results of the approach proposed by D. Quadri, E. Soutif and P. Tolla.

Suggested Citation

  • Federico Della Croce & Dominique Quadri, 2012. "Improving an exact approach for solving separable integer quadratic knapsack problems," Journal of Combinatorial Optimization, Springer, vol. 23(1), pages 21-28, January.
    • Handle: RePEc:spr:jcomop:v:23:y:2012:i:1:d:10.1007_s10878-010-9337-3
    DOI: 10.1007/s10878-010-9337-3
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    References listed on IDEAS

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    1. Korner, Frank, 1990. "On the numerical realization of the exact penalty method for quadratic programming algorithms," European Journal of Operational Research, Elsevier, vol. 46(3), pages 404-408, June.
    2. 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.
    3. Duan Li & Xiaoling Sun, 2006. "Nonlinear Integer Programming," International Series in Operations Research and Management Science, Springer, number 978-0-387-32995-6, September.
    4. Bruce Faaland, 1974. "An Integer Programming Algorithm for Portfolio Selection," Management Science, INFORMS, vol. 20(10), pages 1376-1384, June.
    5. Fred Glover, 1975. "Improved Linear Integer Programming Formulations of Nonlinear Integer Problems," Management Science, INFORMS, vol. 22(4), pages 455-460, December.
    6. 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.
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