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

Capacity Reliability Calculation and Sensitivity Analysis for a Stochastic Transport Network

“…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].…”

“…A path is a set of arcs that connect the source node to the destination node, and a minimal path is such a path that deletion of any arc will disconnect the source node to the destination node [26]. The model of Lin et al [17] is applicable to both directed networks and undirected networks, so it is widely used by many algorithms [2,18,19,21,23,24] to search for d-minimal paths. For example, Lin [18] proposed a method to solve dminimal paths of a network with unreliable nodes; Yeh [19] presented a technique called cycle-checking method to verify whether d-minimal path candidates are d-minimal paths; Chen and Lin [21] utilized the fast enumeration method to solve d-minimal path candidates.…”

“…For example, Lin [18] proposed a method to solve dminimal paths of a network with unreliable nodes; Yeh [19] presented a technique called cycle-checking method to verify whether d-minimal path candidates are d-minimal paths; Chen and Lin [21] utilized the fast enumeration method to solve d-minimal path candidates. Forghani-elahabad et al [23,24] put forward an improved method to search for dminimal path candidates. Xu et al [2] made some necessary improvements to the model of Lin et al [17], and presented an improved method.…”

“…It is noted that verifying d-minimal paths and removing duplicate d-minimal paths are two important steps of most of the existing algorithms [2,[17][18][19]21,23,24]. While the cyclechecking method is efficient in verifying d-minimal path candidates, it is not applicable to undirected networks.…”

Reliability Evaluation of High Speed Train Bogie System Based on Stochastic Network Flow Model

“…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.…”