All d-MPs for All d Level Searching Method for Multistate Network in Resilience Process

The all-level
d
minimal path vectors (
d-
MPs) are an important input for obtaining the performance metric of multistate networks, which is the basis of resilience evaluation and analysis. During the resilience process, network configurations may change, leading to changes in the
d
-MPs. However, when the network configurations are changed, the repeated searching of
d-
MPs is time consuming because it is an NP-hard problem. Thus, a framework is proposed to obtain the
d-
MPs in different situations during the resilience process. First, two
d-
MP updating algorithms are used instead of repeated searching of the
d-
MPs when the maximum states of the components are changed. Taking the original
d-
MPs as the input, the proposed method updates the
d-
MPs by deleting the unqualified
d-
MPs or adding the qualified
d-
MPs during the resilience process. Second, a
d-
MP searching algorithm is employed to search the new
d-
MPs derived from the new components that are brought in during the recovery phase. Computational experiments show that the proposed updating methods are more efficient than the existing
d-
MP searching algorithm. Furthermore, the proposed new
d-
MP searching algorithm outperforms the repeated searching of
d-
MPs. In addition, the proposed method can be applied to network design and optimal phase settings, where multiple attempts at network configuration adjustments may be necessary.