An Efficient Method to Find All d-MPs in Multistate Two-Terminal Networks

Many systems in the real-world are multi-state systems composed of multi-state components (nodes and arcs) in which the reliability of the system can be calculated in terms of the lower bound points of level d, called d-Minimal Paths (d-MPs). Such systems (oil/gas production, power transmission and distribution networks, etc.) may be considered as network flows whose arcs have independent and discrete random capacities. In this paper, we present a new algorithm to generate all d-MPs candidates for all d levels. Our algorithm is based on the incremental enumeration of the different d-MPs. In the beginning, we determine the list of all minimal paths (also called 1-MPs). The latter will then be used to generate the 2-MPs. Then from 1-MPS and 2-MPs we generate 3-MPs...and so on. The greatest contribution of our method is the use of a technique which makes it possible to know, at each level i, which minimal paths can lead to valid (i+1)-MPs without resorting to an additional validation process. This has reduced the execution time compared to the existing algorithms to find all d-MPs for all possible d values.