A maximal flow method to search for d-MPs in stochastic-flow networks

Lin, Yi‐Kuei; Chen, Shin Guang

doi:10.1016/j.jocs.2017.09.009

Cited by 21 publications

(24 citation statements)

References 19 publications

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“…Equation ( 6) pinpoints the relationship between the current state of e i and the flow through e i ( 1 ≤ i ≤ m). Generally, the algorithms [22,[26][27][28][29][30] grounded on Lemma 1 consist of three steps:…”

Section: E Fundamental Results For Solving D-mps a State Vector X Is A D-mp If And Only If (1) M(x) � D And (2) M(x −mentioning

confidence: 99%

“…Step [30], the comparison method [22,26,28], and the cycle-checking method [27]. e direct verification method is mainly based on the definition of d-MPs, that is, every d-MP candidate x derived from Lemma 1 is verified to determine whether it satisfies M(x − 0(e i )) < d for each x i > 0.…”

Section: E Fundamental Results For Solving D-mps a State Vector X Is A D-mp If And Only If (1) M(x) � D And (2) M(x −mentioning

confidence: 99%

“…e multistate network discussed herein satisfies the following assumptions [28,30]. ( [14], the Sum of Disjoint Products method [18][19][20], or the State Space Decomposition method [21] are available to calculate R d .…”

Section: Preliminariesmentioning

confidence: 99%

“…e model by Lin et al [22] applicable to both directed networks and undirected networks has been widely used by most of the existing algorithms [26][27][28][29][30]. For example, Lin [26] proposed a simple method to solve d-MPs of a network with unreliable nodes; Yeh [27] proposed a cycle-checking method to verify whether a feasible solution to the model is a d-MP; Chen and Lin [28] suggested the fast enumeration method to solve all of the feasible solutions to the model; Forghani-Elahabad and Bonani [29] proposed an improved enumeration method to search for d-MPs.…”

Section: Introductionmentioning

confidence: 99%

“…For example, Lin [26] proposed a simple method to solve d-MPs of a network with unreliable nodes; Yeh [27] proposed a cycle-checking method to verify whether a feasible solution to the model is a d-MP; Chen and Lin [28] suggested the fast enumeration method to solve all of the feasible solutions to the model; Forghani-Elahabad and Bonani [29] proposed an improved enumeration method to search for d-MPs. Lin and Chen [30] recently proposed a new max-flow evaluation method to find d-MPs.…”

Section: Introductionmentioning

confidence: 99%

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A Minimal Path-Based Method for Computing Multistate Network Reliability

Niu

2020

Complexity

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Most of modern technological networks that can perform their tasks with various distinctive levels of efficiency are multistate networks, and reliability is a fundamental attribute for their safe operation and optimal improvement. For a multistate network, the two-terminal reliability at demand level d, defined as the probability that the network capacity is greater than or equal to a demand of d units, can be calculated in terms of multistate minimal paths, called d-minimal paths (d-MPs) for short. This paper presents an efficient algorithm to find all d-MPs for the multistate two-terminal reliability problem. To advance the solution efficiency of d-MPs, an improved model is developed by redefining capacity constraints of network components and minimal paths (MPs). Furthermore, an effective technique is proposed to remove duplicate d-MPs that are generated multiple times during solution. A simple example is provided to demonstrate the proposed algorithm step by step. In addition, through computational experiments conducted on benchmark networks, it is found that the proposed algorithm is more efficient.

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