Improved algorithm for d-minimal cuts in reliability evaluation of multi-state flow networks

Multi-state flow networks (MFNs) play an important role in modelling several real-world systems with multiple working states corresponding to specific probability distributions. Reliability is an important index for the design and maintenance of MFNs, which is often obtained using d-minimal cuts (d-MCs). However, finding all d-MCs is an NP-hard problem. Traditional algorithms tend to generate undesired d-MC candidates, such as non-real or duplicate d-MCs, which require time-consuming post-processing, significantly impacting algorithmic efficiency. This study investigates the mechanism behind the generation of such undesired candidates and presents new theoretical findings to identify them. Existing algorithms are refined by eliminating redundant steps to verify real d-MCs. For duplicate d-MCs, a prevention mechanism is introduced by limiting the maximum states of specific components. Based on these, an improved algorithm is proposed to verify real d-MCs and prevent the generation of duplicate d-MCs. Both time complexity analysis and computational experiments demonstrate the superior efficiency of the proposed algorithm compared with existing methods.