Solving Flow Allocation Problems and Optimizing System Reliability of Multisource Multisink Stochastic Flow Network
Moatamad Hassan
Department of Mathematics, Aswan University, Egypt
Abstract: Flow allocation problem is one of the important steps in reliability evaluation or optimization of a stochastic flow network. In a single source single sink networks it is easy to determine the flow on each path by using one of best known methods. While, in the case of multisource multisink flow network the flow allocation problem becomes more complicated and few studies have dealt with it. This paper investigates the flow allocation problem of multisource multisink stochastic-flow network with assuming that there are several sorts of resource flows transmitting through that network with unreliable nodes. The mathematical formulation of the problem is modified to increase the efficiency of obtaining optimal solutions that satisfy all constraints. A Genetic Algorithm (GA) is proposed to solve the flow allocation problem in existing multisource multisink networks such that the reliability of the system capacity vector is maximized. The results obtained for test cases are compared with other proposed methods to show that the proposed algorithm is efficient in obtaining optimal solutions that satisfy all constraints, and it achieves a maximum value of reliability of the system capacity vector. Finally, the proposed GA has employed to optimize the system reliability of multisource multisink stochastic flow networks.
Keywords: Flow allocation problem, stochastic-flow network, GA.
Received August 26, 2013; accepted February 4, 2015