Many real-world networks such as freight, power and long distance transportation networks are represented as multi-source multi-sink stochastic flow network. The objective is to transmit flow successfully between the source and the sink nodes. The reliability of the capacity vector of the assigned components is used an indicator to find the best flow strategy on the network. The Components Assignment Problem (CAP) deals with searching the optimal components to a given network subject to one or more constraints. The CAP in multi-source multi-sink stochastic flow networks with multiple commodities has not yet been discussed, so our paper investigates this scenario to maximize the reliability of the capacity vector subject to an assignment budget. The mathematical formulation of the problem is defined, and a proposed solution based on genetic algorithms is developed consisting of two steps. The first searches the set of components with the minimum cost and the second searches the flow vector of this set of components with maximum reliability. We apply the solution approach to three commonly used examples from the literature with two sets of available components to demonstrate its strong performance.
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