IDEAS home Printed from https://ideas.repec.org/a/spr/aqjoor/v22y2024i4d10.1007_s10288-023-00555-3.html
   My bibliography  Save this article

An optimal algorithm for variable knockout problems

Author

Listed:
  • J. E. Beasley

    (Brunel University)

Abstract

We consider a class of problems related to variable knockout, where knockout means set a variable to zero. Given an optimisation problem formulated as a zero–one integer program the question we consider in this paper is what might be an appropriate set of variables to knockout of the problem, in order that the optimal solution to the problem that remains after variable knockout has a desired property. This property might be related to the optimal solution value after knockout, or require the problem after knockout to be infeasible. We present an algorithm for the optimal solution of this knockout problem. Computational results are given for an illustrative example based upon shortest path interdiction using publicly available shortest path test problems.

Suggested Citation

  • J. E. Beasley, 2024. "An optimal algorithm for variable knockout problems," 4OR, Springer, vol. 22(4), pages 419-433, December.
    • Handle: RePEc:spr:aqjoor:v:22:y:2024:i:4:d:10.1007_s10288-023-00555-3
    DOI: 10.1007/s10288-023-00555-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10288-023-00555-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10288-023-00555-3?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Smith, J. Cole & Song, Yongjia, 2020. "A survey of network interdiction models and algorithms," European Journal of Operational Research, Elsevier, vol. 283(3), pages 797-811.
    2. Wei, Ningji & Walteros, Jose L., 2022. "Integer programming methods for solving binary interdiction games," European Journal of Operational Research, Elsevier, vol. 302(2), pages 456-469.
    3. Leitner, Markus & Ljubić, Ivana & Monaci, Michele & Sinnl, Markus & Tanınmış, Kübra, 2023. "An exact method for binary fortification games," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1026-1039.
    4. Lan, Guanghui & DePuy, Gail W. & Whitehouse, Gary E., 2007. "An effective and simple heuristic for the set covering problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1387-1403, February.
    5. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    6. Leonardo Lozano & J. Cole Smith, 2017. "A Backward Sampling Framework for Interdiction Problems with Fortification," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 123-139, February.
    7. Beasley, J. E., 1987. "An algorithm for set covering problem," European Journal of Operational Research, Elsevier, vol. 31(1), pages 85-93, July.
    8. Naji-Azimi, Zahra & Toth, Paolo & Galli, Laura, 2010. "An electromagnetism metaheuristic for the unicost set covering problem," European Journal of Operational Research, Elsevier, vol. 205(2), pages 290-300, September.
    9. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    10. 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.
    11. Beasley, J. E. & Chu, P. C., 1996. "A genetic algorithm for the set covering problem," European Journal of Operational Research, Elsevier, vol. 94(2), pages 392-404, October.
    12. Alberto Caprara & Paolo Toth & Matteo Fischetti, 2000. "Algorithms for the Set Covering Problem," Annals of Operations Research, Springer, vol. 98(1), pages 353-371, December.
    13. Beasley, J. E. & Jornsten, K., 1992. "Enhancing an algorithm for set covering problems," European Journal of Operational Research, Elsevier, vol. 58(2), pages 293-300, April.
    14. Victor Reyes & Ignacio Araya, 2021. "A GRASP-based scheme for the set covering problem," Operational Research, Springer, vol. 21(4), pages 2391-2408, December.
    Full references (including those not matched with items on IDEAS)

    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. Gao, Chao & Yao, Xin & Weise, Thomas & Li, Jinlong, 2015. "An efficient local search heuristic with row weighting for the unicost set covering problem," European Journal of Operational Research, Elsevier, vol. 246(3), pages 750-761.
    2. Patrizia Beraldi & Andrzej Ruszczyński, 2002. "The Probabilistic Set-Covering Problem," Operations Research, INFORMS, vol. 50(6), pages 956-967, December.
    3. 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.
    4. Naji-Azimi, Zahra & Toth, Paolo & Galli, Laura, 2010. "An electromagnetism metaheuristic for the unicost set covering problem," European Journal of Operational Research, Elsevier, vol. 205(2), pages 290-300, September.
    5. Lan, Guanghui & DePuy, Gail W. & Whitehouse, Gary E., 2007. "An effective and simple heuristic for the set covering problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1387-1403, February.
    6. Masoud Yaghini & Mohammad Karimi & Mohadeseh Rahbar, 2015. "A set covering approach for multi-depot train driver scheduling," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 636-654, April.
    7. Nguyen, Tri-Dung, 2014. "A fast approximation algorithm for solving the complete set packing problem," European Journal of Operational Research, Elsevier, vol. 237(1), pages 62-70.
    8. Helena R. Lourenço & José P. Paixão & Rita Portugal, 2001. "Multiobjective Metaheuristics for the Bus Driver Scheduling Problem," Transportation Science, INFORMS, vol. 35(3), pages 331-343, August.
    9. Victor Reyes & Ignacio Araya, 2021. "A GRASP-based scheme for the set covering problem," Operational Research, Springer, vol. 21(4), pages 2391-2408, December.
    10. Owais, Mahmoud & Moussa, Ghada S. & Hussain, Khaled F., 2019. "Sensor location model for O/D estimation: Multi-criteria meta-heuristics approach," Operations Research Perspectives, Elsevier, vol. 6(C).
    11. Helena Ramalhinho-Lourenço, 2001. "The crew-scheduling module in the GIST system," Economics Working Papers 547, Department of Economics and Business, Universitat Pompeu Fabra.
    12. Bautista, Joaquín & Pereira, Jordi, 2006. "Modeling the problem of locating collection areas for urban waste management. An application to the metropolitan area of Barcelona," Omega, Elsevier, vol. 34(6), pages 617-629, December.
    13. Leitner, Markus & Ljubić, Ivana & Monaci, Michele & Sinnl, Markus & Tanınmış, Kübra, 2023. "An exact method for binary fortification games," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1026-1039.
    14. Dimitris Bertsimas & Dan A. Iancu & Dmitriy Katz, 2013. "A New Local Search Algorithm for Binary Optimization," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 208-221, May.
    15. Yagiura, Mutsunori & Kishida, Masahiro & Ibaraki, Toshihide, 2006. "A 3-flip neighborhood local search for the set covering problem," European Journal of Operational Research, Elsevier, vol. 172(2), pages 472-499, July.
    16. Jordi Pereira & Igor Averbakh, 2013. "The Robust Set Covering Problem with interval data," Annals of Operations Research, Springer, vol. 207(1), pages 217-235, August.
    17. Jans, Raf & Degraeve, Zeger, 2008. "A note on a symmetrical set covering problem: The lottery problem," European Journal of Operational Research, Elsevier, vol. 186(1), pages 104-110, April.
    18. 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.
    19. Li, Shengyin & Huang, Yongxi, 2014. "Heuristic approaches for the flow-based set covering problem with deviation paths," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 72(C), pages 144-158.
    20. Youngho Lee & Hanif D. Sherali & Ikhyun Kwon & Seongin Kim, 2006. "A new reformulation approach for the generalized partial covering problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(2), pages 170-179, March.

    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:spr:aqjoor:v:22:y:2024:i:4:d:10.1007_s10288-023-00555-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.