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A lagrangian heuristic for set‐covering problems

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  • J. E. Beasley

Abstract

In this article we present a heuristic algorithm for non‐unicost set‐covering problems based upon Lagrangian relaxation and subgradient optimization. Computational results, based upon problems involving up to 1000 rows and 10000 columns, indicate that this heuristic produces better‐quality results than a number of other heuristics.

Suggested Citation

  • J. E. Beasley, 1990. "A lagrangian heuristic for set‐covering problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(1), pages 151-164, February.
    • Handle: RePEc:wly:navres:v:37:y:1990:i:1:p:151-164
    DOI: 10.1002/1520-6750(199002)37:13.0.CO;2-2
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    1. Francis J. Vasko, 1984. "An efficient heuristic for large set covering problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(1), pages 163-171, March.
    2. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    3. Beasley, J. E., 1987. "An algorithm for set covering problem," European Journal of Operational Research, Elsevier, vol. 31(1), pages 85-93, July.
    4. Marshall L. Fisher, 1985. "An Applications Oriented Guide to Lagrangian Relaxation," Interfaces, INFORMS, vol. 15(2), pages 10-21, April.
    5. Baker, Edward & Fisher, Michael, 1981. "Computational results for very large air crew scheduling problems," Omega, Elsevier, vol. 9(6), pages 613-618.
    6. Francis J. Vasko & George R. Wilson, 1986. "Hybrid heuristics for minimum cardinality set covering problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(2), pages 241-249, May.
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    Cited by:

    1. Amadeu A. Coco & Andréa Cynthia Santos & Thiago F. Noronha, 2022. "Robust min-max regret covering problems," Computational Optimization and Applications, Springer, vol. 83(1), pages 111-141, September.
    2. Patrizia Beraldi & Andrzej Ruszczyński, 2002. "The Probabilistic Set-Covering Problem," Operations Research, INFORMS, vol. 50(6), pages 956-967, December.
    3. Olli Bräysy & Michel Gendreau, 2005. "Vehicle Routing Problem with Time Windows, Part II: Metaheuristics," Transportation Science, INFORMS, vol. 39(1), pages 119-139, February.
    4. Renata Mansini & Roberto Zanotti, 2020. "A Core-Based Exact Algorithm for the Multidimensional Multiple Choice Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1061-1079, October.
    5. Sven de Vries & Rakesh V. Vohra, 2003. "Combinatorial Auctions: A Survey," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 284-309, August.
    6. Wang, Yiyuan & Pan, Shiwei & Al-Shihabi, Sameh & Zhou, Junping & Yang, Nan & Yin, Minghao, 2021. "An improved configuration checking-based algorithm for the unicost set covering problem," European Journal of Operational Research, Elsevier, vol. 294(2), pages 476-491.
    7. 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.
    8. Kroon, L.G. & Fischetti, M., 2000. "Crew Scheduling for Netherlands Railways: "destination: customer"," ERIM Report Series Research in Management ERS-2000-56-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    9. Lu Yang & Leishan Zhou & Hanxiao Zhou & Chang Han & Wenqiang Zhao, 2023. "A Lagrangian Method for Calculation of Passing Capacity on a Railway Hub Station," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    10. M. Almiñana & J. Pastor, 1994. "Two new heuristics for the location set covering problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 2(2), pages 315-328, December.
    11. Sven de Vries & Rakesh Vohra, 2000. "Combinatorial Auctions: A Survey," Discussion Papers 1296, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. P N Ram Kumar & T T Narendran, 2011. "On the usage of Lagrangean Relaxation for the convoy movement problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 722-728, April.
    13. Olli Bräysy & Michel Gendreau, 2002. "Tabu Search heuristics for the Vehicle Routing Problem with Time Windows," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 211-237, December.
    14. Vié, Marie-Sklaerder & Zufferey, Nicolas & Cordeau, Jean-François, 2019. "Solving the Wire-Harness Design Problem at a European car manufacturer," European Journal of Operational Research, Elsevier, vol. 272(2), pages 712-724.
    15. Gérard Cornuéjols & Miroslav Karamanov & Yanjun Li, 2006. "Early Estimates of the Size of Branch-and-Bound Trees," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 86-96, February.

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