Abstract— We consider the problem of minimizing the resources used for network coding while achieving the desired throughput in a multicast scenario. Since this problem is NPhard, we seek a method for quickly finding sufficiently good solutions. To this end, we take evolutionary approaches based on a Genetic Algorithm. In this paper, we extend the evolutionary algorithm that we previously proposed in three perspectives. First, whereas the previous algorithm can be applied to only acyclic networks, we devise a modified evaluation method that works also with networks with cycles. Second, we introduce a new set of GA components that in our experiments outperforms the one used in the previous algorithm. Third, we present a new framework of the evolutionary approach, where fitness evaluation and population management are done in a decentralized manner with a limited amount of coordination. The new framework enables a network coding protocol where the resources used for coding are opti...