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In this paper, we present an algorithm based on the GRASP meta-heuristic for solving a dynamic assignment problem in a P2P network designed for sending real-time video over the Internet. In a highly dynamic P2P topology, the frequent connections and disconnections of nodes are the main obstacle we face when trying to offer a high quality-of-experience (QoE) to clients. We first introduce the P2P network architecture where this node dynamics occurs. This architecture employs a multi-source streaming approach where the stream is decomposed into several flows sent by different peers to each client, including some level of redundancy, in order to cope with the fluctuations in network connectivity. Then, we present the GRASP-based algorithm developed in order to tackle the problem of maintaining connectivity in presence of node dynamics by periodically reassigning network connections; these assignments are performed so as to maximize the global expected QoE, calculated using the recently proposed PSQA methodology. Additionally, we provide a variation of the GRASP-based algorithm, based on the Random Neural Network model. Finally, we show the results obtained when these algorithms are applied to a case study based on real life data.