An algorithm to search for multi-state minimal cuts in multi-state flow networks containing state heterogeneous components

The reliability and resilience of multi-state flow networks (MFNs) are crucial for the safe operation of complex network systems, with the multi-state minimal cut (d-MC) method being fundamental for evaluating these metrics. Existing research mainly focuses on d-MC in MFNs with state weakly homogeneous components (SWHCs), where the state space consists of continuously increasing integers. However, real-world MFNs often include state heterogeneous components (SHCs). This study presents an algorithm to search for all multi-state minimal cuts (d-MC*) in MFNs with SHCs. The algorithm first defines d-MC* and its generation model, along with two methods to reduce candidates. A definition-based verification method for d-MC* candidates is also proposed. Then, a comprehensive comparison is conducted with existing approaches through both theoretical analysis and numerical experiments, illustrating the significant advantages of the new algorithm in terms of accuracy and efficiency for processing MFNs containing SHCs. Additionally, the selection of the optimal max-flow algorithm among three popular choices is analyzed. Finally, the practicality of the proposed d-MC* algorithm is demonstrated on a real-world network. This study fills the gap in existing research on MFNs containing SHCs and provides important theoretical support and guidance for the design, operation, and maintenance of network systems.