A simple vectorization algorithm to address the d-MP problem without generating duplicate candidates

Majid Forghani-elahabad, Emílio Francesquini, Wei-Chang Yeh


The reliability of a multistate flow network (MFN) can be evaluated indirectly based  on d-minimal paths (d-MPs). In fact, with all the d-MPs at hand, an MFN’s reliability can be  computed by calculating a union probability. Hence the determination of all d-MPs in an MFN  has been a very attractive problem in the last decades. As a result, many algorithms have been  proposed to solve the d-MP problem. However, as the number of d-MPs grows exponentially with  the size of the network, the available algorithms in the literature are not so practical. Here, we  propose a vectorization algorithm to address the problem and show its practical efficiency using  three benchmarks. The numerical results show that the vectorization algorithm solves the problem  more than three times faster than the non-vectorization one in some cases.  


System reliability; Vectorization algorithm; d-MP problem; Multistate flow network

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DOI: https://doi.org/10.5540/03.2021.008.01.0346


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