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Improving an exact approach for solving separable integer quadratic knapsack problems

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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.

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References

  • Bretthauer K, Shetty B (2002) The nonlinear knapsack problem—algorithms and applications. Eur J Oper Res 138(3):459–472

    Article  MATH  MathSciNet  Google Scholar 

  • Chu PC, Beasley JE (1998) A genetic algorithm for the multidimensional knapsack problem. J Heuristics 4:63–86

    Article  MATH  Google Scholar 

  • Djerdjour M, Mathur K, Salkin H (1988) A Surrogate-based algorithm for the general quadratic multidimensional knapsack. Oper Res Lett 7(5):253–257

    Article  MATH  MathSciNet  Google Scholar 

  • Faaland B (1974) An integer programming algorithm for portfolio selection. Manag Sci 20(10):1376–1384

    Article  MATH  MathSciNet  Google Scholar 

  • Glover F (1975) Improved linear integer programming formulations of nonlinear integer problems. Manag Sci 22(4):455–460

    Article  MathSciNet  Google Scholar 

  • Korner F (1985) Integer quadratic programming. Eur J Oper Res 19(2):268–273

    Article  MathSciNet  Google Scholar 

  • Korner F (1990) On the numerical realization of the exact penalty method for quadratic programming algorithms. Eur J Oper Res 46(3):404–408

    Article  MathSciNet  Google Scholar 

  • Li D, Sun XL (2006) Nonlinear integer programming. Springer, Berlin

    MATH  Google Scholar 

  • Li D, Wang J, Sun XL (2007) Computing exact solution to nonlinear integer programming: Convergent Lagrangian and objective level cut method. J Glob Optim 39(1):127–154

    Article  MATH  MathSciNet  Google Scholar 

  • Mathur K, Salkin H (1983) A branch and bound algorithm for a class of nonlinear knapsack problems. Oper Res Lett 2(4):155–160

    Article  MATH  MathSciNet  Google Scholar 

  • Quadri D, Soutif E, Tolla P (2009) Exact solution methods to solve large scale integer quadratic knapsack problems. J Comb Optim 17:157–167

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. DAI, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, Italy

    Federico Della Croce

  2. LIA, Université d’Avignon, 84911, Cedex 9, Avignon, France

    Dominique Quadri

Authors
  1. Federico Della Croce
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  2. Dominique Quadri
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Correspondence to Federico Della Croce.

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Della Croce, F., Quadri, D. Improving an exact approach for solving separable integer quadratic knapsack problems. J Comb Optim 23, 21–28 (2012). https://doi.org/10.1007/s10878-010-9337-3

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  • DOI: https://doi.org/10.1007/s10878-010-9337-3

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