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An Adapted Step Size Algorithm for a 0-1 Biknapsack Lagrangean Dual

Author

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  • Babacar Thiongane
  • Anass Nagih
  • Gérard Plateau

Abstract

This paper deals with a new algorithm for a 0-1 bidimensional knapsack Lagrangean dual which relaxes one of the two constraints. Classical iterative algorithms generate a sequence of multipliers which converges to an optimal one. In this way, these methods generate a sequence of 0-1 one-dimensional knapsack instances. Generally, the procedure for solving each instance is considered as a black box. We propose to design a new iterative scheme in which the computation of the step size takes into account the algorithmic efficiency of each instance. Our adapted step size iterative algorithm is compared favorably with several other algorithms for the 0-1 biknapsack Lagrangean dual over difficult instances for CPLEX 7.0. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • Babacar Thiongane & Anass Nagih & Gérard Plateau, 2005. "An Adapted Step Size Algorithm for a 0-1 Biknapsack Lagrangean Dual," Annals of Operations Research, Springer, vol. 139(1), pages 353-373, October.
    • Handle: RePEc:spr:annopr:v:139:y:2005:i:1:p:353-373:10.1007/s10479-005-3454-x
    DOI: 10.1007/s10479-005-3454-x
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    References listed on IDEAS

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    1. Loukakis, E. & Muhlemann, A. P., 1984. "Parameterisation algorithms for the integer linear programs in binary variables," European Journal of Operational Research, Elsevier, vol. 17(1), pages 104-115, July.
    2. A. M. Geoffrion & R. Nauss, 1977. "Exceptional Paper--Parametric and Postoptimality Analysis in Integer Linear Programming," Management Science, INFORMS, vol. 23(5), pages 453-466, January.
    3. Jenkins, Larry, 1987. "Parametric-objective integer programming using knapsack facets and Gomory cutting planes," European Journal of Operational Research, Elsevier, vol. 31(1), pages 102-109, July.
    4. Freville, Arnaud & Plateau, Gerard, 1993. "An exact search for the solution of the surrogate dual of the 0-1 bidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 68(3), pages 413-421, August.
    5. Linus Schrage & Laurence Wolsey, 1985. "Sensitivity Analysis for Branch and Bound Integer Programming," Operations Research, INFORMS, vol. 33(5), pages 1008-1023, October.
    6. Christopher J. Piper & Andris A. Zoltners, 1976. "Some Easy Postoptimality Analysis for Zero-One Programming," Management Science, INFORMS, vol. 22(7), pages 759-765, March.
    7. Crema, Alejandro, 2002. "The multiparametric 0-1-integer linear programming problem: A unified approach," European Journal of Operational Research, Elsevier, vol. 139(3), pages 511-520, June.
    8. Gary M. Roodman, 1974. "Postoptimality analysis in integer programming by implicit enumeration: The mixed integer case," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 21(4), pages 595-607, December.
    9. Desrochers, Martin & Soumis, Francois, 1988. "A reoptimization algorithm for the shortest path problem with time windows," European Journal of Operational Research, Elsevier, vol. 35(2), pages 242-254, May.
    10. Egon Balas & Eitan Zemel, 1980. "An Algorithm for Large Zero-One Knapsack Problems," Operations Research, INFORMS, vol. 28(5), pages 1130-1154, October.
    11. Crema, Alejandro, 2000. "An algorithm for the multiparametric 0-1-integer linear programming problem relative to the objective function," European Journal of Operational Research, Elsevier, vol. 125(1), pages 18-24, August.
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