Searching for d-MPs for All Level d in Multistate Two-Terminal Networks Without Duplicates

The reliability evaluation of multistate networks is primarily using minimal path (cut) vectors, namely <italic>d</italic>-MPs (<italic>d</italic>-MCs), which are the lower (upper) boundary vectors that satisfy the system demand <italic>d</italic>. The generation of all <italic>d-</italic>MPs (<italic>d-</italic>MCs) is an NP-hard problem. Thus, it is important to develop an efficient algorithm to search for <italic>d-</italic>MPs (<italic>d-</italic>MCs). Existing algorithms searching for <italic>d-</italic>MPs based on MPs all generate duplicate <italic>d-</italic>MP candidates, and extra steps are required to detect and remove those duplicates. In this article, we propose an improved algorithm to search for <italic>d-</italic>MPs for all <italic>d</italic> levels without generating duplicate <italic>d-</italic>MP candidates for two-terminal multistate networks. First, we discover and prove the mechanism of generating duplicate <italic>d-</italic>MP candidates based on MPs. Second, a novel method is proposed to prevent generating duplicate <italic>d-</italic>MP candidates. Third, an improved algorithm is developed by combining the proposed method to search for <italic>d-</italic>MPs without generating duplicate <italic>d-</italic>MP candidates for all <italic>d</italic> levels. Through computational experiments, it is found that the proposed algorithm is more efficient than existing algorithms for finding all <italic>d-</italic>MPs for all possible <italic>d</italic> values.