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Implicit cover inequalities

Author

Listed:
  • Agostinho Agra

    (University of Aveiro)

  • Cristina Requejo

    (University of Aveiro)

  • Eulália Santos

    (ISLA-Higher Institute of Leiria)

Abstract

In this paper we consider combinatorial optimization problems whose feasible sets are simultaneously restricted by a binary knapsack constraint and a cardinality constraint imposing the exact number of selected variables. In particular, such sets arise when the feasible set corresponds to the bases of a matroid with a side knapsack constraint, for instance the weighted spanning tree problem and the multiple choice knapsack problem. We introduce the family of implicit cover inequalities which generalize the well-known cover inequalities for such feasible sets and discuss the lifting of the implicit cover inequalities. A computational study for the weighted spanning tree problem is reported.

Suggested Citation

  • Agostinho Agra & Cristina Requejo & Eulália Santos, 2016. "Implicit cover inequalities," Journal of Combinatorial Optimization, Springer, vol. 31(3), pages 1111-1129, April.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:3:d:10.1007_s10878-014-9812-3
    DOI: 10.1007/s10878-014-9812-3
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    References listed on IDEAS

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    6. Amado, Ligia & Barcia, Paulo, 1996. "New polynomial bounds for matroidal knapsacks," European Journal of Operational Research, Elsevier, vol. 95(1), pages 201-210, November.
    7. Kaparis, Konstantinos & Letchford, Adam N., 2008. "Local and global lifted cover inequalities for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 186(1), pages 91-103, April.
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    Cited by:

    1. Cristina Requejo & Eulália Santos, 2020. "Efficient lower and upper bounds for the weight-constrained minimum spanning tree problem using simple Lagrangian based algorithms," Operational Research, Springer, vol. 20(4), pages 2467-2495, December.

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