Optimal Assignment of a Two Types of Components in a Multi-state Stochastic-flow Network

A real-life system is usually modeled to be a network with edges and nodes for the performance evaluation. This paper devotes to finding out the optimal two-type component assignment with maximal system reliability, in which the components are separated to be two sets: one assigned to edges and the other set assigned to nodes. Each component should be multistate due to complete failure, partial failure, maintenance, etc. Such a system according to a two-type component assignment is a stochastic-flow network. Furthermore, each component has a transmission cost in practice. Therefore, the system reliability is the probability that d units of demand are transmitted through the network successfully subject to a budget. A genetic algorithm based algorithm is developed to solve the proposed problem in which the system reliability according to a two-type component assignment is evaluated in terms of minimal paths and Recursive Sum of Disjoint Products. The experimental results show that the proposed algorithm can be executed in reasonable time.