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Network reliability evaluation for flow networks is an important issue in quality management. Many real-life systems can be modeled as stochastic-flow networks, in which each branch is multistate due to complete failure, partial failure, maintenance, etc. That is, each branch has several capacities with a probability distribution, and may fail. Hence, network reliability is the probability that a specified flow can be transmitted through the network successfully. Although there are many researches related to the evaluation of network reliability for a stochastic-flow network, how to assign a set of multistate components to the network so that the network reliability is maximal is never discussed. Therefore, this paper devotes to evaluating the optimal network reliability under components-assignments subject to a transmission budget, in which the transmission cost depends on each component's capacity. The network reliability under a components-assignment can be computed in terms of minimal paths, and state-space decomposition. Subsequently, we propose an optimization method based on a genetic algorithm. The experimental results show that the proposed method can be executed efficiently in a reasonable time.