A new hybrid inequality BAT for comprehensive all-level d-MP identification using minimal paths in Multistate Flow Network reliability analysis

Abstract

In various network applications like wireless sensors, utilities, IoT, and transport systems, multistate flow networks (MFNs) serve as valuable models. A d-level minimal path (d-MP) is a unique type of MFN characterized by having a maximum flow of d without any redundant arcs. Assessing MFN reliability is critical and often relies on the d-MP algorithm, a foundational method for calculating reliability. Existing d-MP algorithms, however, lack the capability to concurrently identify all-level d-MPs. We propose a novel algorithm, the Hybrid Inequality Binary-Addition-Tree (IBAT), which overcomes existing limitations by concurrently discovering all-level d-MPs (decision-making points), thus enabling more informed decision-making. This hybrid IBAT combines the IBAT with several key techniques: the path-based layered-search algorithm (PLSA), sequential verification, the MP-to-arc state transformation, the cycle test, and the logarithmic prime pairwise comparison method (LPM). In contrast to existing methods, our BAT-based approach consistently showcases superior performance in the parallelized retrieval of all-level d-MPs, as substantiated through experiments conducted on 12 benchmark MFNs. Compared to existing methods, our BAT-based approach demonstrates superior performance in parallelized retrieval of all-level d-MPs in the execution times in discovering d-MPs across all levels, as validated by experiments on 12 benchmark MFNs.