An Improved Merge Search Approach to Evaluate Reliability in Multistate Network Systems

Many real-world problems, such as power line transmission planning, computer network management, water pipe planning, and traffic flow planning, can be modeled using multistate network systems. One of the most interesting aspects of these problems is that one typically wishes to know the reliability of such a plan, namely the network reliability. To evaluate the reliability of a specific network system, the three-stage method (TSM) is typically applied. TSM consists of 1) finding all minimal paths, 2) finding all <formula><tex>$d$</tex></formula>-system vectors, and 3) calculating the union probability for reliability, where 1) is one of the most challenging problems discussed in the literature. This article proposes an improved merge search method that combines the advantages of both enumeration and searching technologies. A step-by-step exploration of the proposed method is presented and several benchmark comparisons are performed using well-known algorithms to demonstrate the efficiency of the proposed method. The results show that the computation time of the proposed algorithm can save as much as 10 times against the well-known methods in the literature.