IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v282y2020i3p1107-1114.html
   My bibliography  Save this article

A novel minimal cut-based algorithm to find all minimal capacity vectors for multi-state flow networks

Author

Listed:
  • Huang, Ding-Hsiang
  • Huang, Cheng-Fu
  • Lin, Yi-Kuei

Abstract

Real systems, such as computer systems, can be modeled as network topologies with vertices and edges. Owing to equipment failures and maintenance requirements, the capacities of edges have several states. Such systems are regarded as multi-state flow networks (MSFN). System reliability of an MSFN is the probability that the required flow (i.e., demand) can successfully be sent from the source to the sink. By adopting a minimal path (MP) approach, system reliability can be computed in terms of all minimal capacity vectors meeting the demand d. A minimal capacity vector is called a d-MP. Although several algorithms have been presented in the literature for finding all d-MP, improving efficiency in the search for all d-MP is always a challenge. A group approach with both the concepts of minimal cut and MP is developed in this study, narrowing the search range of feasible flow vectors. An algorithm based on the group approach is then proposed to improve the efficiency of the d-MP search. According to the structure of the proposed algorithm, parallel computing can be implemented with significant improvement in the efficiency of the d-MP generation, where the proposed algorithm is compared with previous ones based on three benchmarks, in terms of CPU time.

Suggested Citation

  • Huang, Ding-Hsiang & Huang, Cheng-Fu & Lin, Yi-Kuei, 2020. "A novel minimal cut-based algorithm to find all minimal capacity vectors for multi-state flow networks," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1107-1114.
    • Handle: RePEc:eee:ejores:v:282:y:2020:i:3:p:1107-1114
    DOI: 10.1016/j.ejor.2019.10.030
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221719308653
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2019.10.030?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. Sebastio, Stefano & Trivedi, Kishor S. & Wang, Dazhi & Yin, Xiaoyan, 2014. "Fast computation of bounds for two-terminal network reliability," European Journal of Operational Research, Elsevier, vol. 238(3), pages 810-823.
    2. Liu, Yu & Chen, Yiming & Jiang, Tao, 2018. "On sequence planning for selective maintenance of multi-state systems under stochastic maintenance durations," European Journal of Operational Research, Elsevier, vol. 268(1), pages 113-127.
    3. Cheng-Fu Huang, 2019. "Evaluation of system reliability for a stochastic delivery-flow distribution network with inventory," Annals of Operations Research, Springer, vol. 277(1), pages 33-45, June.
    4. Yeh, Wei-Chang & Chu, Ta-Chung, 2018. "A novel multi-distribution multi-state flow network and its reliability optimization problem," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 209-217.
    5. Yeh, Cheng-Ta & Fiondella, Lance, 2017. "Optimal redundancy allocation to maximize multi-state computer network reliability subject to correlated failures," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 138-150.
    6. Majid Forghani-elahabad & Nelson Kagan, 2019. "Reliability evaluation of a stochastic-flow network in terms of minimal paths with budget constraint," IISE Transactions, Taylor & Francis Journals, vol. 51(5), pages 547-558, May.
    7. Yan, Zhou & Qian, Meng, 2007. "Improving efficiency of solving d-MC problem in stochastic-flow network," Reliability Engineering and System Safety, Elsevier, vol. 92(1), pages 30-39.
    8. Jane, Chin-Chia & Laih, Yih-Wenn, 2017. "Distribution and reliability evaluation of max-flow in dynamic multi-state flow networks," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1045-1053.
    9. Yeh, Cheng-Ta, 2019. "An improved NSGA2 to solve a bi-objective optimization problem of multi-state electronic transaction network," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    10. Bai, Guanghan & Zuo, Ming J. & Tian, Zhigang, 2015. "Search for all d-MPs for all d levels in multistate two-terminal networks," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 300-309.
    11. Jane, Chin-Chia & Laih, Yih-Wenn, 2010. "A dynamic bounding algorithm for approximating multi-state two-terminal reliability," European Journal of Operational Research, Elsevier, vol. 205(3), pages 625-637, September.
    12. Niu, Yi-Feng & Gao, Zi-You & Lam, William H.K., 2017. "A new efficient algorithm for finding all d-minimal cuts in multi-state networks," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 151-163.
    13. Xiu-Zhen Xu & Yi-Feng Niu & Qing Li, 2018. "Performance Assessment of a Freight Network with Stochastic Capacities," Complexity, Hindawi, vol. 2018, pages 1-9, September.
    14. Tian, Zhigang & Levitin, Gregory & Zuo, Ming J., 2009. "A joint reliability–redundancy optimization approach for multi-state series–parallel systems," Reliability Engineering and System Safety, Elsevier, vol. 94(10), pages 1568-1576.
    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. Xu, Xiu-Zhen & Zhou, Run-Hui & Wu, Guo-Lin & Niu, Yi-Feng, 2024. "Evaluating the transmission distance-constrained reliability for a multi-state flow network," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    2. Zhang, Hanxiao & Sun, Muxia & Li, Yan-Fu, 2022. "Reliability–redundancy allocation problem in multi-state flow network: Minimal cut-based approximation scheme," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    3. Alkaff, Abdullah, 2021. "Discrete time dynamic reliability modeling for systems with multistate components," Reliability Engineering and System Safety, Elsevier, vol. 209(C).
    4. Xu, Xiu-Zhen & Niu, Yi-Feng & Song, Yi-Fan, 2021. "Computing the reliability of a stochastic distribution network subject to budget constraint," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    5. Yeh, Cheng-Ta & Lin, Yi-Kuei & Yeng, Louis Cheng-Lu & Huang, Pei-Tzu, 2021. "Reliability evaluation of a multistate railway transportation network from the perspective of a travel agent," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    6. Esha Datta & Neeraj Goyal, 2023. "An efficient sum of disjoint product method for reliability evaluation of stochastic flow networks using d-MPs," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(4), pages 1228-1246, 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. Cheng-Fu Huang & Ding-Hsiang Huang & Yi-Kuei Lin, 2022. "System reliability analysis for a cloud-based network under edge server capacity and budget constraints," Annals of Operations Research, Springer, vol. 312(1), pages 217-234, May.
    2. Zhang, Hanxiao & Sun, Muxia & Li, Yan-Fu, 2022. "Reliability–redundancy allocation problem in multi-state flow network: Minimal cut-based approximation scheme," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    3. Huang, Cheng-Hao & Huang, Ding-Hsiang & Lin, Yi-Kuei, 2023. "Network reliability prediction for random capacitated-flow networks via an artificial neural network," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    4. Forghani-elahabad, Majid & Kagan, Nelson & Mahdavi-Amiri, Nezam, 2019. "An MP-based approximation algorithm on reliability evaluation of multistate flow networks," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    5. Zhou, Yifan & Liu, Libo & Li, Hao, 2022. "Reliability estimation and optimisation of multistate flow networks using a conditional Monte Carlo method," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    6. Yeh, Wei-Chang, 2020. "A new method for verifying d-MC candidates," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    7. Ding-Hsiang Huang & Cheng-Fu Huang & Yi-Kuei Lin, 2019. "Reliability Evaluation for a Stochastic Flow Network Based on Upper and Lower Boundary Vectors," Mathematics, MDPI, vol. 7(11), pages 1-12, November.
    8. Yi-Feng Niu & Can He & De-Qiang Fu, 2022. "Reliability assessment of a multi-state distribution network under cost and spoilage considerations," Annals of Operations Research, Springer, vol. 309(1), pages 189-208, February.
    9. Huang, Ding-Hsiang & Huang, Cheng-Fu & Lin, Yi-Kuei, 2020. "Exact project reliability for a multi-state project network subject to time and budget constraints," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    10. Niu, Yi-Feng, 2021. "Performance measure of a multi-state flow network under reliability and maintenance cost considerations," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    11. Huang, Cheng-Fu & Huang, Ding-Hsiang & Lin, Yi-Kuei, 2022. "Network reliability evaluation for multi-state computing networks considering demand as the non-integer type," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    12. Kozyra, Paweł Marcin, 2023. "The usefulness of (d,b)-MCs and (d,b)-MPs in network reliability evaluation under delivery or maintenance cost constraints," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    13. Yeh, Cheng-Ta & Lin, Yi-Kuei & Yeng, Louis Cheng-Lu & Huang, Pei-Tzu, 2021. "Reliability evaluation of a multistate railway transportation network from the perspective of a travel agent," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    14. Chang, Ping-Chen & Huang, Ding-Hsiang & Lin, Yi-Kuei & Nguyen, Thi-Phuong, 2021. "Reliability and maintenance models for a time-related multi-state flow network via d-MC approach," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    15. Niu, Yi-Feng & Wan, Xiao-Yu & Xu, Xiu-Zhen & Ding, Dong, 2020. "Finding all multi-state minimal paths of a multi-state flow network via feasible circulations," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    16. Zaretalab, Arash & Sharifi, Mani & Guilani, Pedram Pourkarim & Taghipour, Sharareh & Niaki, Seyed Taghi Akhavan, 2022. "A multi-objective model for optimizing the redundancy allocation, component supplier selection, and reliable activities for multi-state systems," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    17. Monfared, M.A.S. & Rezazadeh, Masoumeh & Alipour, Zohreh, 2022. "Road networks reliability estimations and optimizations: A Bi-directional bottom-up, top-down approach," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    18. Yeh, Wei-Chang & Tan, Shi-Yi & Zhu, Wenbo & Huang, Chia-Ling & Yang, Guang-yi, 2022. "Novel binary addition tree algorithm (BAT) for calculating the direct lower-bound of the highly reliable binary-state network reliability," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    19. Yi-Kuei Lin & Lance Fiondella & Ping-Chen Chang, 2022. "Reliability of time-constrained multi-state network susceptible to correlated component faults," Annals of Operations Research, Springer, vol. 311(1), pages 239-254, April.
    20. Ouyang, Zhiyuan & Liu, Yu & Ruan, Sheng-Jia & Jiang, Tao, 2019. "An improved particle swarm optimization algorithm for reliability-redundancy allocation problem with mixed redundancy strategy and heterogeneous components," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 62-74.

    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:ejores:v:282:y:2020:i:3:p:1107-1114. 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/locate/eor .

    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.