IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v93y2020ics0305048318307205.html
   My bibliography  Save this article

Efficient Benders decomposition for distance-based critical node detection problem

Author

Listed:
  • Hooshmand, F.
  • Mirarabrazi, F.
  • MirHassani, S.A.

Abstract

This paper addresses the critical node detection problem which seeks a subset of nodes for removal in order to maximize the disconnectivity of the residual graph with respect to a specific distance-based measure, namely the Wiener index. Such a measure is defined based on the all-pair shortest path distances in the residual graph so that the longer the total length of shortest paths, the greater the value of the disconnectivity measure. In the literature, a mixed integer linear programming model and an exact iterative-based method have been presented for this problem; however, both approaches become very time-consuming on graphs having large diameter and non-unit edge lengths. To overcome this shortcoming, in this paper, we present a new formulation for the problem and solve it by Benders decomposition algorithm. We improve the performance of Benders algorithm by several techniques (including analytical calculation of dual variables, generation of good-quality initial optimality cuts, considering master's optimality cuts as lazy constraints, etc.) to reduce the total running time. The extensive computational experiments on instances, taken from the literature or generated randomly, confirm the effectiveness of the new approaches.

Suggested Citation

  • Hooshmand, F. & Mirarabrazi, F. & MirHassani, S.A., 2020. "Efficient Benders decomposition for distance-based critical node detection problem," Omega, Elsevier, vol. 93(C).
  • Handle: RePEc:eee:jomega:v:93:y:2020:i:c:s0305048318307205
    DOI: 10.1016/j.omega.2019.02.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048318307205
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.omega.2019.02.006?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. Joe Naoum-Sawaya & Christoph Buchheim, 2016. "Robust Critical Node Selection by Benders Decomposition," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 162-174, February.
    2. Mariel, Katharina & Minner, Stefan, 2017. "Benders decomposition for a strategic network design problem under NAFTA local content requirements," Omega, Elsevier, vol. 68(C), pages 62-75.
    3. Georgios Saharidis & Marianthi Ierapetritou, 2013. "Speed-up Benders decomposition using maximum density cut (MDC) generation," Annals of Operations Research, Springer, vol. 210(1), pages 101-123, November.
    4. Marco Di Summa & Andrea Grosso & Marco Locatelli, 2012. "Branch and cut algorithms for detecting critical nodes in undirected graphs," Computational Optimization and Applications, Springer, vol. 53(3), pages 649-680, December.
    5. Wheatley, David & Gzara, Fatma & Jewkes, Elizabeth, 2015. "Logic-based Benders decomposition for an inventory-location problem with service constraints," Omega, Elsevier, vol. 55(C), pages 10-23.
    6. Jélvez, Enrique & Morales, Nelson & Nancel-Penard, Pierre & Peypouquet, Juan & Reyes, Patricio, 2016. "Aggregation heuristic for the open-pit block scheduling problem," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1169-1177.
    7. Mehdi Hemmati & J. Cole Smith & My Thai, 2014. "A cutting-plane algorithm for solving a weighted influence interdiction problem," Computational Optimization and Applications, Springer, vol. 57(1), pages 71-104, January.
    8. Gerald Brown & Matthew Carlyle & Javier Salmerón & Kevin Wood, 2006. "Defending Critical Infrastructure," Interfaces, INFORMS, vol. 36(6), pages 530-544, December.
    9. Alexander Veremyev & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2014. "An integer programming framework for critical elements detection in graphs," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 233-273, July.
    10. F. Hooshmand & S. A. MirHassani, 2018. "An Effective Bilevel Programming Approach for the Evasive Flow Capturing Location Problem," Networks and Spatial Economics, Springer, vol. 18(4), pages 909-935, December.
    11. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    12. Stephen P. Borgatti, 2006. "Identifying sets of key players in a social network," Computational and Mathematical Organization Theory, Springer, vol. 12(1), pages 21-34, April.
    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. Afkham, Maryam & Ramezanian, Reza & Shahparvari, Shahrooz, 2022. "Balancing traffic flow in the congested mass self-evacuation dynamic network under tight preparation budget: An Australian bushfire practice," Omega, Elsevier, vol. 111(C).
    2. Zhu, Xuedong & Son, Junbo & Zhang, Xi & Wu, Jianguo, 2023. "Constraint programming and logic-based Benders decomposition for the integrated process planning and scheduling problem," Omega, Elsevier, vol. 117(C).
    3. Zhou, Yangming & Wang, Gezi & Hao, Jin-Kao & Geng, Na & Jiang, Zhibin, 2023. "A fast tri-individual memetic search approach for the distance-based critical node problem," European Journal of Operational Research, Elsevier, vol. 308(2), pages 540-554.
    4. Hosseinali Salemi & Austin Buchanan, 2022. "Solving the Distance-Based Critical Node Problem," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1309-1326, May.
    5. Wen, Tao & Chen, Yu-wang & Syed, Tahir abbas & Wu, Ting, 2024. "ERIUE: Evidential reasoning-based influential users evaluation in social networks," Omega, Elsevier, vol. 122(C).
    6. Li Zeng & Changjun Fan & Chao Chen, 2023. "Leveraging Minimum Nodes for Optimum Key Player Identification in Complex Networks: A Deep Reinforcement Learning Strategy with Structured Reward Shaping," Mathematics, MDPI, vol. 11(17), pages 1-13, August.

    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. Marco Di Summa & Syed Md Omar Faruk, 2023. "Critical node/edge detection problems on trees," 4OR, Springer, vol. 21(3), pages 439-455, September.
    2. Hassan Zohali & Bahman Naderi & Vahid Roshanaei, 2022. "Solving the Type-2 Assembly Line Balancing with Setups Using Logic-Based Benders Decomposition," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 315-332, January.
    3. 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.
    4. Chen, Wei & Jiang, Manrui & Jiang, Cheng & Zhang, Jun, 2020. "Critical node detection problem for complex network in undirected weighted networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    5. Zhang, Jian & Nault, Barrie R. & Dimitrakopoulos, Roussos G., 2019. "Optimizing a mineral value chain with market uncertainty using benders decomposition," European Journal of Operational Research, Elsevier, vol. 274(1), pages 227-239.
    6. Hosseinali Salemi & Austin Buchanan, 2022. "Solving the Distance-Based Critical Node Problem," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1309-1326, May.
    7. Foad Mahdavi Pajouh, 2020. "Minimum cost edge blocker clique problem," Annals of Operations Research, Springer, vol. 294(1), pages 345-376, November.
    8. Alexander Veremyev & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2014. "An integer programming framework for critical elements detection in graphs," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 233-273, July.
    9. Zhu, Xuedong & Son, Junbo & Zhang, Xi & Wu, Jianguo, 2023. "Constraint programming and logic-based Benders decomposition for the integrated process planning and scheduling problem," Omega, Elsevier, vol. 117(C).
    10. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    11. Zhong, Haonan & Mahdavi Pajouh, Foad & A. Prokopyev, Oleg, 2023. "On designing networks resilient to clique blockers," European Journal of Operational Research, Elsevier, vol. 307(1), pages 20-32.
    12. Guo, Penghui & Zhu, Jianjun, 2023. "Capacity reservation for humanitarian relief: A logic-based Benders decomposition method with subgradient cut," European Journal of Operational Research, Elsevier, vol. 311(3), pages 942-970.
    13. Hammad, Ahmed W A & Akbarnezhad, Ali & Rey, David, 2017. "Sustainable urban facility location: Minimising noise pollution and network congestion," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 107(C), pages 38-59.
    14. N. Beheshti Asl & S. A. MirHassani, 2019. "Accelerating benders decomposition: multiple cuts via multiple solutions," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 806-826, April.
    15. T. N. Dinh & M. T. Thai & H. T. Nguyen, 2014. "Bound and exact methods for assessing link vulnerability in complex networks," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 3-24, July.
    16. Bernardetta Addis & Roberto Aringhieri & Andrea Grosso & Pierre Hosteins, 2016. "Hybrid constructive heuristics for the critical node problem," Annals of Operations Research, Springer, vol. 238(1), pages 637-649, March.
    17. Ningji Wei & Jose L. Walteros & Foad Mahdavi Pajouh, 2021. "Integer Programming Formulations for Minimum Spanning Tree Interdiction," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1461-1480, October.
    18. Simon Emde & Shohre Zehtabian & Yann Disser, 2023. "Point-to-point and milk run delivery scheduling: models, complexity results, and algorithms based on Benders decomposition," Annals of Operations Research, Springer, vol. 322(1), pages 467-496, March.
    19. Ventresca, Mario & Harrison, Kyle Robert & Ombuki-Berman, Beatrice M., 2018. "The bi-objective critical node detection problem," European Journal of Operational Research, Elsevier, vol. 265(3), pages 895-908.
    20. Bernardetta Addis & Roberto Aringhieri & Andrea Grosso & Pierre Hosteins, 2016. "Hybrid constructive heuristics for the critical node problem," Annals of Operations Research, Springer, vol. 238(1), pages 637-649, 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:eee:jomega:v:93:y:2020:i:c:s0305048318307205. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/375/description#description .

    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.