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In this paper, we propose a method of getting near-optimal solutions not only satisfying the QoS requirements but also optimizing certain network resources such as bandwidth, end-to-end delay, in computationally feasible time, using the neural networks in our genetic algorithm to dynamically control the rate of mating and the mutation rate(GANN). The multicast routing are evaluated on three types of criteria: objective, fuzzy and subjective criteria.. The analysis of the algorithm presented, backed up by simulation results, confirms its superiority over the other algorithms. GANN scales very well to large networks and multicast groups. It produces low-cost trees at a significant higher speed. In summary, this algorithm is simple, efficient, and scalable to a large network size.