摘要
The evaluation of the reliability of a multistate flow network (MFN) is primarily based on the <formula><tex>$d$</tex></formula> minimal path (MP), which is a special state vector formed by the addition of d MPs. The existing algorithm for searching <formula><tex>$d$</tex></formula>-MPs for all possible <formula><tex>$d$</tex></formula> is based on the addition of MPs and <formula><tex>$(d-1)$</tex></formula>-MPs to generate d-MP combinations. This algorithm always requires extra time for detecting and removing the <formula><tex>$d$</tex></formula>-MP combinations with infeasible states, redundant states, and&null 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&null faster than the existing algorithm. The time complexity and demonstration of the proposed algorithm are analyzed and provided using examples.