Reliability evaluation in terms of flow data mining for multistate networks
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Reliability evaluation in terms of flow data mining for multistate networks Yi-Kuei Lin1,2,3 · Shin-Guang Chen4,5 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Network reliability is famous for its problem solving ability in several real-life applications. However, due to its NP-hard nature (Ball in IEEE Trans Reliab 35(3):230–238, 1986), researchers are devoted to the improvement of computational efficiency in various approaches. Although flow in networks depicts its combination properties, only few of them are useful in the calculation of network reliability. In some point of views, we call it mining in flow data. This paper presents techniques of how to efficiently do the flow data mining tasks. A skill based on backtrack and maximal flow is illustrated with examples and benchmarks. The results show that the proposed approach is valuable in the calculation of network reliability. Keywords Flow data mining · Minimum path · Lower boundary vectors · Exact enumeration · Maximum flow
1 Introduction Network reliability is famous for its problem solving ability in several real-life applications. However, due to its NP-hard nature (Ball 1986), researchers are devoted to the improvement of its computational efficiency by various approaches. For example, Lin (2001) firstly simplified the three-stage-method (TSM) (Lin et al. 1995) for easy computation. Chen and Lin (2012)
B
Shin-Guang Chen [email protected] Yi-Kuei Lin [email protected]
1
Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu 300, Taiwan
2
Department of Business Administration, Asia University, Taichung, Taiwan
3
College of Mechanical and Electrical Engineering, Wenzhou University, Zhejiang, China
4
Institute of Industrial Management, Tungnan University, New Taipei City 222, Taiwan
5
Department of Sports Medicine, Kaohsiung Medical University, Kaohsiung 807, Taiwan
123
Annals of Operations Research
improved greatly the minimal path sets searching efficiency. Lin and Chen (2017a, 2019) began to improve the searching efficiency of minimal path vectors, etc. More recently related researches are the works of Xu et al. (2019) for search minimal paths, the works of Forghanielahabad and Kagan (2019) for considering budget constraint, and the works of Yeh and Zuo (2019) for all d problem. In big data point of views, the flow combination is also a kind of big data. For example, a simple (12, 17) (nodes, edges) grid network would have 38 minimal paths. This results in a flow combination in O(d 38 ). However, only few of them are useful in reliability calculation. When we deeply mine the flow data as well as the system state vectors, the calculation of network reliability may get a new direction of improvement in efficiency. To our knowledge, a close related flow data mining is very limited in the literature. This article proposes a new searching direction based on flow data mining and system vector mining, and results in a more efficient algorithm for reliability evaluation
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