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Note--A Computational Survey of Methods for the Set Covering Problem

Author

Listed:
  • Nicos Christofides

    (Imperial College of Science and Technology, England)

  • S. Korman

    (Imperial College of Science and Technology, England)

Abstract

This paper is a survey of available methods for the solution of the Set Covering Problem. The prime objective has been to establish the computational efficiency and relative merits of the various algorithms that have been proposed. To this end five methods have been programmed and tested on the same set of 33 test problems some of which can be found in the literature and the rest of which were randomly generated. Some of the methods examined have--as far as the authors are aware--never been previously tested, and in some cases some surprising results have been noted. In addition, one type of tree search method has been studied in some greater detail and new techniques involving multiple dominance tests, and the calculation of a better lower bound have been suggested to limit the search. This resulting algorithm was found to be better than the original one by orders of magnitude in both computation times and numbers of tree-nodes generated, and has proved to be the most efficient of the methods tested.

Suggested Citation

  • Nicos Christofides & S. Korman, 1975. "Note--A Computational Survey of Methods for the Set Covering Problem," Management Science, INFORMS, vol. 21(5), pages 591-599, January.
    • Handle: RePEc:inm:ormnsc:v:21:y:1975:i:5:p:591-599
    DOI: 10.1287/mnsc.21.5.591
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    Cited by:

    1. Giovanni Felici & Sokol Ndreca & Aldo Procacci & Benedetto Scoppola, 2016. "A-priori upper bounds for the set covering problem," Annals of Operations Research, Springer, vol. 238(1), pages 229-241, March.
    2. Jee Eun Kang & Will Recker, 2015. "Strategic Hydrogen Refueling Station Locations with Scheduling and Routing Considerations of Individual Vehicles," Transportation Science, INFORMS, vol. 49(4), pages 767-783, November.
    3. E Rappos & E B Thompson, 2008. "An integer programming approach to optimize Housing Benefit data retrieval," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(2), pages 182-185, February.
    4. Caruso, C. & Colorni, A. & Aloi, L., 2003. "Dominant, an algorithm for the p-center problem," European Journal of Operational Research, Elsevier, vol. 149(1), pages 53-64, August.
    5. Giovanni Felici & Sokol Ndreca & Aldo Procacci & Benedetto Scoppola, 2016. "A-priori upper bounds for the set covering problem," Annals of Operations Research, Springer, vol. 238(1), pages 229-241, March.
    6. Haddadi, Salim, 1997. "Simple Lagrangian heuristic for the set covering problem," European Journal of Operational Research, Elsevier, vol. 97(1), pages 200-204, February.

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