An improved bounding algorithm for approximating multistate network reliability based on state-space decomposition method

Abstract

The evaluation of two-terminal multistate network reliability precisely is a NP-hard problem. Approximating the reliability bounds with state space decomposition is an effective method to tradeoff the computational effort and the acceptable reliability approximate value when the scale of the network is relatively large. This decomposition process cannot avoid the shortage of a large amount of computational effort consumed by sets of unspecified states with little contributions to reliability bounds. Thus, preset critical values are used to filter out sets of unspecified states with less probability. However, managers cannot predict the preset critical value that satisfies their demand. Therefore, we first proposed a serial bounding algorithm based on the breadth-first mechanism, wherein sets of unspecified states on the same generation are all decomposed before moving to the next generation. The mechanism of combining serial computing with parallel computing is further developed to fully utilize computer capability. In addition, the preset critical values are not required before running the algorithm. The results of efficiency comparison demonstrate that the proposed algorithm can significantly improve the efficiency for approximating multistate network reliability. Stability investigations show that the computational efficiency of the proposed algorithm is more stable and effective under various component state distributions.