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This paper introduces the idea of using Genetic Algorithms as an optimization technique to select the appropriate traffic of a computer network with fixed topology. The ultimate goal in computer network design is to have a high utilization of the network resources such that low level of congestion, high throughput and minimum delay over the channels are achieved. This is why we need to minimizing the delay over the network such that the constraints on the total capacity and traffic are satisfied. On doing this, we developed a set of experiment to test the performance of GAs. We also compared our results with [1] for the ATM network. Experimental results show that our setup experiments for GAs can provide good results in solving such a problem.