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Surrogate constraint normalization for the set covering problem

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  • Ablanedo-Rosas, José H.
  • Rego, César

Abstract

The set covering problem (SCP) is central in a wide variety of practical applications for which finding good feasible solutions quickly (often in real-time) is crucial. Surrogate constraint normalization is a classical technique used to derive appropriate weights for surrogate constraint relaxations in mathematical programming. This framework remains the core of the most effective constructive heuristics for the solution of the SCP chiefly represented by the widely-used Chvátal method. This paper introduces a number of normalization rules and demonstrates their superiority to the classical Chvátal rule, especially when solving large scale and real-world instances. Directions for new advances on the creation of more elaborate normalization rules for surrogate heuristics are also provided.

Suggested Citation

  • Ablanedo-Rosas, José H. & Rego, César, 2010. "Surrogate constraint normalization for the set covering problem," European Journal of Operational Research, Elsevier, vol. 205(3), pages 540-551, September.
    • Handle: RePEc:eee:ejores:v:205:y:2010:i:3:p:540-551
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    1. Grossman, Tal & Wool, Avishai, 1997. "Computational experience with approximation algorithms for the set covering problem," European Journal of Operational Research, Elsevier, vol. 101(1), pages 81-92, August.
    2. Alminana, Marcos & Pastor, Jesus T., 1997. "An adaptation of SH heuristic to the location set covering problem," European Journal of Operational Research, Elsevier, vol. 100(3), pages 586-593, August.
    3. Taillard, Eric D. & Waelti, Philippe & Zuber, Jacques, 2008. "Few statistical tests for proportions comparison," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1336-1350, March.
    4. Fred Glover, 1975. "Surrogate Constraint Duality in Mathematical Programming," Operations Research, INFORMS, vol. 23(3), pages 434-451, June.
    5. Lorena, Luiz Antonio N. & Belo Lopes, Fabio, 1994. "A surrogate heuristic for set covering problems," European Journal of Operational Research, Elsevier, vol. 79(1), pages 138-150, November.
    6. Harvey J. Greenberg & William P. Pierskalla, 1970. "Surrogate Mathematical Programming," Operations Research, INFORMS, vol. 18(5), pages 924-939, October.
    7. Fred Glover, 1965. "A Multiphase-Dual Algorithm for the Zero-One Integer Programming Problem," Operations Research, INFORMS, vol. 13(6), pages 879-919, December.
    8. Haddadi, Salim, 1997. "Simple Lagrangian heuristic for the set covering problem," European Journal of Operational Research, Elsevier, vol. 97(1), pages 200-204, February.
    9. Alberto Caprara & Matteo Fischetti & Paolo Toth, 1999. "A Heuristic Method for the Set Covering Problem," Operations Research, INFORMS, vol. 47(5), pages 730-743, October.
    10. Egon Balas & Maria C. Carrera, 1996. "A Dynamic Subgradient-Based Branch-and-Bound Procedure for Set Covering," Operations Research, INFORMS, vol. 44(6), pages 875-890, December.
    11. Marshall L. Fisher & Alexander H. G. Rinnooy Kan, 1988. "The Design, Analysis and Implementation of Heuristics," Management Science, INFORMS, vol. 34(3), pages 263-265, March.
    12. Marshall L. Fisher & Pradeep Kedia, 1990. "Optimal Solution of Set Covering/Partitioning Problems Using Dual Heuristics," Management Science, INFORMS, vol. 36(6), pages 674-688, June.
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