Finding all the Lower Boundary Points in a Multistate Two-Terminal Network

Forghani-elahabad, Majid; Bonani, Luiz Henrique

doi:10.1109/tr.2017.2712661

Cited by 44 publications

(18 citation statements)

References 38 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%

“…In this section, we investigate the efficiency of the proposed algorithm. As mentioned in Section 2.2, Lemma 1 proposed by Lin et al [22] is one of the most important models with respect to d-MPs, and is also the foundation of most of the existing methods [26][27][28][29][30]. As an improvement to Lemma 1, eorem 2 is the foundation of the proposed algorithm.…”

Section: Efficiency Investigation By Numerical Examplesmentioning

confidence: 95%

“…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. 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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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%

Section: Efficiency Investigation By Numerical Examplesmentioning

confidence: 95%

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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“…Provided that all d-minimal paths are known, R d equals the union probability of these d-minimal paths, which can be achieved by the sum of disjoint products technique [14][15][16]. Thus, efficient search of d-minimal paths is the primary goal to all of the d-minimal path methods [2,[17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Capacity Reliability Calculation and Sensitivity Analysis for a Stochastic Transport Network

Niu

et al. 2020

IEEE Access

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A major performance index for analyzing a stochastic transport network is the two-terminal capacity reliability R d , defined as the probability that d units of goods can be successfully transported via stochastic arc capacities from the source to the destination. This paper presents an efficient d-minimal path method to calculate R d based on some newly obtained results. The proposed method uses a simple method to check d-minimal path candidates and a more efficient approach to remove duplicate d-minimal paths that are the biggest obstacle in solving d-minimal paths, along with an indication of the advantage over the existing methods. Besides, sensitivity analysis is adopted to explore the most important arc whose reliability change affects the network reliability most significantly, which helps supervisor identify and enhance the critical arcs for improving the network reliability more effectively. Computational and application examples demonstrate the efficiency and utility of the method, respectively.

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“…A lot of algorithms are available in literature including approximation algorithm [10] and exact evaluation algorithms [11,12] to provide the solution for stochastic network reliability problems. Most of the approaches are based on d-minimal path sets [11], [13][14][15] and d-minimal cut sets [16][17][18]. Then finally these generated d-minimal path sets (cutsets) are used to evaluate exact reliability of a network using any of the method such as Inclusion-Exclusion, Sum of Disjoint Product (SDP) etc.…”

Section: Introductionmentioning

confidence: 99%