Route discovery in infrastructure based network is an important problem. Normally, route selection or route discovery is done based on the shortest path principle. In infrastructure based networks، a number of issues for route discovery need to be addressed as the packet flow are prone to errors making the routing operation failure. Reliability, for example، is an important issue for route discovery. Ensuring Quality of Service (QoS) is important and is to be taken care while forwarding a packet flow. In this paper، a model for route discovery in infrastructure based networks using GA is being proposed. Out of many paths available from the gateway of the network to the final destination, the one is selected which satisfies the desired QoS. Two important QoS parameters، path loss and processing time at the router (Base Station), have been considered. The experimental results for both the QoS parameters reveal the efficacy of the model.