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An MP-based approximation algorithm on reliability evaluation of multistate flow networks

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  • Forghani-elahabad, Majid
  • Kagan, Nelson
  • Mahdavi-Amiri, Nezam

Abstract

In recent decades, multistate two-terminal reliability problem has attracted several researchers, and accordingly many exact and approximation approaches have been proposed in the literature in terms of minimal cuts (MCs) or minimal paths (MPs) to address this problem. Here, an MP-based approximation approach is developed based on exact algorithms. With all the MPs at hand, the approach rearranges the MPs ascendingly with respect to their lengths and then sets the flow on some MPs to be zero which turns to reduce the computing cost in solving the problem. We provide the complexity results, and by employing some benchmarks and one thousand randomly generated networks illustrate that not only in many cases the proposed approach determines very good approximate solutions much faster than the exact algorithms, but also in many other cases it even determines exact solutions significantly faster than the available exact algorithms in the literature. Moreover, the Dolan-Moré performance profile affirms the efficiency of our proposed algorithm. Finally, we state how to compute the system reliability by using the d-MPs, and show that from a very good approximation set of d-MPs, the system reliability is approximated with a very good accuracy.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:reensy:v:191:y:2019:i:c:s0951832018314911
    DOI: 10.1016/j.ress.2019.106566
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    References listed on IDEAS

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    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.
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    4. 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.
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    7. 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.
    8. Schneider, Kellie & Rainwater, Chase & Pohl, Ed & Hernandez, Ivan & Ramirez-Marquez, Jose Emmanuel, 2013. "Social network analysis via multi-state reliability and conditional influence models," Reliability Engineering and System Safety, Elsevier, vol. 109(C), pages 99-109.
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    Cited by:

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    4. 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).
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    7. 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).
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    10. 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).
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    13. Yeh, Wei-Chang, 2024. "A new hybrid inequality BAT for comprehensive all-level d-MP identification using minimal paths in Multistate Flow Network reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    14. 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).
    15. Yeh, Wei-Chang, 2022. "Novel self-adaptive Monte Carlo simulation based on binary-addition-tree algorithm for binary-state network reliability approximation," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    16. Hao, Zhifeng & Yeh, Wei-Chang & Liu, Zhenyao & Forghani-elahabad, Majid, 2020. "General multi-state rework network and reliability algorithm," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    17. 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).
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