Search for d-MPs without duplications in multistate two-terminal networks

A general method for the reliability evaluation of multistate networks is using minimal path vectors (d-MPs for short). Most reported works on generating d-MPs are based on minimal paths (MPs for short). Currently, all reported MP-based algorithms generate duplicated d-MPs during the search process and additional recursive comparison is required to remove those duplications. However, the number of duplications increases substantially with the size of network. Thus, a more efficient algorithm is needed to search for all d-MPs without duplications. In this study, we proposed an improved algorithm based on the breadth-first search to search for d-MPs without duplications. The mechanism on generating duplicated d-MPs is investigated. A novel approach is incorporated into the existing algorithm to generate the d-MPs without duplications. Through computational experiments, it is found that the proposed algorithm is more efficient than existing algorithms for finding all d-MPs.