In this paper a cluster head election problem is studied for a cooperative wireless network. The nodes in the cluster use random linear network coding to enhance the throughput performance in spreading the data for a file download service. Some of the nodes in the cluster will access through their cellular link parts of a file to be exchanged among all the cooperative nodes. In such a wireless environment, network coding enhances significantly the throughput performance. A good choice of the nodes acting as information sources for the cluster depends on their position and cellular link throughput and turns to be of utmost importance for the achievement of high performance levels. Therefore, a cluster head election algorithm is needed, which shall be fast in converging to either the optimal or, alternatively, a satisfactory sub-optimal solution. We propose to use the evolutionary theory. Results of our investigations are introduced with reference to a high performing implementation of a genetic algorithm under different network conditions both in static and in mobile environments.