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Finding all multi-state minimal paths of a multi-state flow network via feasible circulations

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  • Niu, Yi-Feng
  • Wan, Xiao-Yu
  • Xu, Xiu-Zhen
  • Ding, Dong

Abstract

Multi-state minimal paths, called d-minimal paths (d-MPs), are a popular tool for computing the reliability of multi-state flow networks. Most of the existing algorithms seek for d-MPs by solving an NP-hard Diophantine system in terms of the implicit enumeration method that is simple yet inefficient. This paper focuses on the development of a novel method for finding all d-MPs. By exploring the relationship between d-MPs and feasible circulations that are a well-known network flow problem, this paper proposes a distinctive method integrating the traditional max-flow algorithm and a partition technique to find all d-MPs. The developed method seeks for d-MPs by solving feasible circulations, rather than by solving an NP-hard Diophantine system; additionally, it neither requires MPs nor generates duplicate d-MPs during the solution process. Both theoretical and experimental results demonstrate the advantage of the developed method, and a real delivery network example is presented to illustrate its application.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:reensy:v:204:y:2020:i:c:s095183202030689x
    DOI: 10.1016/j.ress.2020.107188
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    3. 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).
    4. Niu, Yi-Feng & Song, Yi-Fan & Xu, Xiu-Zhen & Zhao, Xia, 2022. "Efficient reliability computation of a multi-state flow network with cost constraint," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    5. Lin, Shuai & Jia, Limin & Zhang, Hengrun & Zhang, Pengzhu, 2022. "Reliability of high-speed electric multiple units in terms of the expanded multi-state flow network," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    6. 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).
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    9. 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.
    10. 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).
    11. Forghani-elahabad, Majid & Yeh, Wei-Chang, 2022. "An improved algorithm for reliability evaluation of flow networks," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    12. 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).
    13. 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).
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