IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v37y1990i1p151-164.html
   My bibliography  Save this article

A lagrangian heuristic for set‐covering problems

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(199002)37:13.0.CO;2-2
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(199002)37:13.0.CO;2-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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, 1985. "An Applications Oriented Guide to Lagrangian Relaxation," Interfaces, INFORMS, vol. 15(2), pages 10-21, April.
    3. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    4. Baker, Edward & Fisher, Michael, 1981. "Computational results for very large air crew scheduling problems," Omega, Elsevier, vol. 9(6), pages 613-618.
    5. 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.
    6. Beasley, J. E., 1987. "An algorithm for set covering problem," European Journal of Operational Research, Elsevier, vol. 31(1), pages 85-93, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Patrizia Beraldi & Andrzej Ruszczyński, 2002. "The Probabilistic Set-Covering Problem," Operations Research, INFORMS, vol. 50(6), pages 956-967, December.
    5. Olli Bräysy & Michel Gendreau, 2005. "Vehicle Routing Problem with Time Windows, Part II: Metaheuristics," Transportation Science, INFORMS, vol. 39(1), pages 119-139, February.
    6. 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.
    7. Sven de Vries & Rakesh Vohra, 2000. "Combinatorial Auctions: A Survey," Discussion Papers 1296, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Sven de Vries & Rakesh V. Vohra, 2003. "Combinatorial Auctions: A Survey," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 284-309, August.
    14. 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.
    15. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Beasley, J. E. & Cao, B., 1996. "A tree search algorithm for the crew scheduling problem," European Journal of Operational Research, Elsevier, vol. 94(3), pages 517-526, November.
    2. Torbjörn Larsson & Michael Patriksson, 2006. "Global Optimality Conditions for Discrete and Nonconvex Optimization---With Applications to Lagrangian Heuristics and Column Generation," Operations Research, INFORMS, vol. 54(3), pages 436-453, June.
    3. 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.
    4. Ogbe, Emmanuel & Li, Xiang, 2017. "A new cross decomposition method for stochastic mixed-integer linear programming," European Journal of Operational Research, Elsevier, vol. 256(2), pages 487-499.
    5. Mazzola, Joseph B. & Neebe, Alan W., 1999. "Lagrangian-relaxation-based solution procedures for a multiproduct capacitated facility location problem with choice of facility type," European Journal of Operational Research, Elsevier, vol. 115(2), pages 285-299, June.
    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. Huisman, D. & Jans, R.F. & Peeters, M. & Wagelmans, A.P.M., 2003. "Combining Column Generation and Lagrangian Relaxation," ERIM Report Series Research in Management ERS-2003-092-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.
    8. Lawrence V. Snyder & Mark S. Daskin, 2005. "Reliability Models for Facility Location: The Expected Failure Cost Case," Transportation Science, INFORMS, vol. 39(3), pages 400-416, August.
    9. X-Y Li & Y P Aneja & F Baki, 2010. "An ant colony optimization metaheuristic for single-path multicommodity network flow problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(9), pages 1340-1355, September.
    10. Ahmadi, Reza H. & Kouvelis, Panagiotis, 1999. "Design of electronic assembly lines: An analytical framework and its application," European Journal of Operational Research, Elsevier, vol. 115(1), pages 113-137, May.
    11. Ojeong Kwon & Donghan Kang & Kyungsik Lee & Sungsoo Park, 1999. "Lagrangian relaxation approach to the targeting problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 640-653, September.
    12. Ali Diabat & Jean-Philippe Richard & Craig Codrington, 2013. "A Lagrangian relaxation approach to simultaneous strategic and tactical planning in supply chain design," Annals of Operations Research, Springer, vol. 203(1), pages 55-80, March.
    13. Foad Iravani & Sriram Dasu & Reza Ahmadi, 2012. "A Hierarchical Framework for Organizing a Software Development Process," Operations Research, INFORMS, vol. 60(6), pages 1310-1322, December.
    14. Leyla Ozsen & Mark S. Daskin & Collette R. Coullard, 2009. "Facility Location Modeling and Inventory Management with Multisourcing," Transportation Science, INFORMS, vol. 43(4), pages 455-472, November.
    15. Marshall L. Fisher, 2004. "Comments on ÜThe Lagrangian Relaxation Method for Solving Integer Programming ProblemsÝ," Management Science, INFORMS, vol. 50(12_supple), pages 1872-1874, December.
    16. Mark S. Daskin, 2008. "What you should know about location modeling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 283-294, June.
    17. Kaiyue Zheng & Laura A. Albert, 2019. "Interdiction models for delaying adversarial attacks against critical information technology infrastructure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(5), pages 411-429, August.
    18. Snyder, Lawrence V. & Daskin, Mark S. & Teo, Chung-Piaw, 2007. "The stochastic location model with risk pooling," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1221-1238, June.
    19. Cattrysse, D. G. & van Wassenhove, L. N., 1990. "A Survey Of Algorithms For The Generalized Assignment Problem," Econometric Institute Archives 272389, Erasmus University Rotterdam.
    20. Xinyu Wu & Ruixiang Cheng & Chuntian Cheng, 2022. "A Simplified Solution Method for End-of-Term Storage Energy Maximization Model of Cascaded Reservoirs," Energies, MDPI, vol. 15(12), pages 1-18, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:navres:v:37:y:1990:i:1:p:151-164. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.