Irredundant Subset Cut Enumeration for Reliability Evaluation of Flow Networks

Abstract

Capacity Related Reliability (CRR) is an important performance index for flow networks. Most of the CRR evaluation techniques proposed in literature, which deal with subset cut enumeration from minimal cut sets, generate a large number of redundant subsets. The efforts in validating these subsets as cuts and then removing the redundant subset cuts makes these approaches computationally inefficient. To solve this problem, this paper proposes a new subset cut enumeration technique using a proposed decomposition method to avoid generating higher order redundant subset cuts of the network, where order refers to the number of links present in the cut. The proposed decomposition method decomposes a cut into new cuts if the cut has a subset in already enumerated valid subset cuts. Such newly generated cuts do not have any subset which is equal to or a superset of already enumerated valid subset cuts. Therefore, if the subsets of these newly generated cuts qualify as valid subset cuts, then none of them are equal to or a superset of any earlier valid subset cuts. The subset cut enumeration technique, along with the decomposition method, completely eliminates the chances of generating higher order redundant subset cuts. However, it leaves a small chance of generating redundant subset cuts as sometimes an already enumerated valid subset cut may become a superset of a valid subset cut, enumerated from a minimal cut treated later, making previously enumerated valid subset cut(s) redundant.