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From its advent, Genetic Algorithm (GA) is used for finding an optimal (or near optimal) solution for a complex optimization problem whose solution can not be found easily by the conventional analytic methods. Fair rate allocation strategies which are developed by many researchers are based on solving a form of constrained optimization problem. However, they do not necessarily lead to high-speed and scalable solutions. There are plenty of high-speed fair rate allocation methods in the literature, some of them are based on fuzzy controllers for improving the convergence speed, but are not necessarily optimal. Hence, in the current research, the GAs have been used for finding the optimum membership functions which must be used in the fuzzy controller. The simulation results show that using the mixed fuzzy-genetic approach improves the conventional methods in convergence speed and results in fewer oscillations.