Abstract
A node-based sequential implicit enumeration method is provided, including: setting a multistate flow network, building an integer programming model of the multistate flow network, and finding a solution set of level number 1 and a number of elements in the solution set from the integer programming model according to the flow conservation law, then using one of the elements to sequentially find a solution set of a next level number and a number of elements in the solution set until the level number being N−1 to complete a new complete solution set, afterward, sequentially returning to the preceding level numbers to determine whether there are other elements in the solution set, and if so, repeating above steps to produce another new complete solution set until the solution sets of all level numbers have been checked, and determining the final complete solution set as a set of the minimal path satisfying the required flow, so as to find all d-MP in the integer programming model of the multistate flow network efficiently.