Fast Algorithm for Searching $d$ -MPs for all Possible $d$

The evaluation of the reliability of a multistate flow network (MFN) is primarily based on the d minimal path (MP), which is a special state vector formed by the addition of d MPs. The existing algorithm for searching d-MPs for all possible d is based on the addition of MPs and (d - 1)-MPs to generate d-MP combinations. This algorithm always requires extra time for detecting and removing the d-MP combinations with infeasible states, redundant states, and/or duplicates. A more efficient addition-based algorithm is proposed to overcome the obstacles of the existing algorithm. Experiment shows that the proposed new algorithm is up to 14 000 faster than the existing algorithm. The time complexity and demonstration of the proposed algorithm are analyzed and provided using examples.