Ordering Heuristics for Reliability Evaluation of Multistate Networks

Abstract

This paper develops ordering heuristics to improve the efficiency of reliability evaluation for multistate two-terminal networks given all minimal path vectors ( $ d $ -MPs for short). In the existing methods, all $d$ -MPs are treated equally. However, we find that the importance of each $d$ -MP is different, and different orderings affect the efficiency of reliability evaluation. Based on the above observations, we introduce the length definitions for $d$ -MPs in a multistate two-terminal network, and develop four ordering heuristics, called O1, O2, O3, and O4, to improve the efficiency of the Recursive Sum of Disjoint Products (RSDP) method for evaluating network reliability. The results show that the proposed ordering heuristics can significantly improve the reliability evaluation efficiency, and O1 performs the best among the four methods. In addition, an ordering heuristic is developed for the reliability evaluation of multistate two-terminal networks given all minimal cut vectors ( $d$ -MCs).