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Search for all d-MPs for all d levels in multistate two-terminal networks

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  • Bai, Guanghan
  • Zuo, Ming J.
  • Tian, Zhigang

Abstract

A general method for reliability evaluation of multistate network is using minimal path vectors. A minimal path (MP) vector to system state d is called a d-MP. Most reported works on generating d-MPs are for a particular d value. However, if all d-MPs for all possible integer d values are required, we need to call such methods multiple times with respect to all d values. A more efficient method is desirable to generate all d-MPs. In this paper, we develop a recursive algorithm based on breadth-first search to search for all the d-MPs for all possible d values. The relationships among d-MPs for different d levels are revealed. Each d-MP candidate can be generated by a combination of one (d-1)-MP and the vector form of one binary minimal path. Thus, we can use binary MPs as building blocks to generate 2-MP candidates, and use 2-MPs and binary MPs as building blocks to generate 3-MP candidates … and so forth. When the d-MPs with respect to the maximum d value have been found, all the d-MPs for all possible d values are obtained. A heuristic for pre-processing the MPs is proposed to improve the efficiency of the algorithm. Through computational experiments, it is found that the proposed algorithm is more efficient than existing algorithms for finding all d-MPs for all possible d values. In addition, we show that the proposed algorithm can also be used to generate a subset of d-MPs for all or some d values given a subset of MPs. The generated subset of d-MPs can be used for lower reliability bound evaluation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:142:y:2015:i:c:p:300-309
    DOI: 10.1016/j.ress.2015.04.013
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    References listed on IDEAS

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    Cited by:

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    5. 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).
    6. 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.
    7. 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.
    8. 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.
    9. Wang, Shuang & Jia, Haiying & Lu, Jing & Yang, Dong, 2023. "Crude oil transportation route choices: A connectivity reliability-based approach," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    10. 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).
    11. Yeh, Wei-Chang, 2021. "Novel binary-addition tree algorithm (BAT) for binary-state network reliability problem," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    12. Yeh, Wei-Chang, 2023. "QB-II for evaluating the reliability of binary-state networks," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    13. Yeh, Wei-Chang & Tan, Shi-Yi & Forghani-elahabad, Majid & Khadiri, Mohamed El & Jiang, Yunzhi & Lin, Chen-Shiun, 2022. "New binary-addition tree algorithm for the all-multiterminal binary-state network reliability problem," Reliability Engineering and System Safety, Elsevier, vol. 224(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. Yeh, Wei-Chang, 2022. "Novel direct algorithm for computing simultaneous all-level reliability of multistate flow networks," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    16. Hao, Zhifeng & Yeh, Wei-Chang & Zuo, Ming & Wang, Jing, 2020. "Multi-distribution multi-commodity multistate flow network model and its reliability evaluation algorithm," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    17. 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).
    18. Bai, Guanghan & Tian, Zhigang & Zuo, Ming J., 2016. "An improved algorithm for finding all minimal paths in a network," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 1-10.
    19. 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).
    20. 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).
    21. 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).
    22. 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).
    23. 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).
    24. Yeh, Wei-Chang, 2021. "Novel Algorithm for Computing All-Pairs Homogeneity-Arc Binary-State Undirected Network Reliability," Reliability Engineering and System Safety, Elsevier, vol. 216(C).

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