An MP-based approximation algorithm on reliability evaluation of multistate flow networks

Abstract

In recent decades, multistate two-terminal reliability problem has attracted several researchers, and accordingly many exact and approximation approaches have been proposed in the literature in terms of minimal cuts (MCs) or minimal paths (MPs) to address this problem. Here, an MP-based approximation approach is developed based on exact algorithms. With all the MPs at hand, the approach rearranges the MPs ascendingly with respect to their lengths and then sets the flow on some MPs to be zero which turns to reduce the computing cost in solving the problem. We provide the complexity results, and by employing some benchmarks and one thousand randomly generated networks illustrate that not only in many cases the proposed approach determines very good approximate solutions much faster than the exact algorithms, but also in many other cases it even determines exact solutions significantly faster than the available exact algorithms in the literature. Moreover, the Dolan-Moré performance profile affirms the efficiency of our proposed algorithm. Finally, we state how to compute the system reliability by using the d-MPs, and show that from a very good approximation set of d-MPs, the system reliability is approximated with a very good accuracy.