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P2P-based optimization has recently gained interest among distributed function optimization scientists. Several well-known optimization heuristics have been recently re-designed to exploit the peculiarity of such a distributed environment. The final goal is to perform high quality function optimization by means of inexpensive, fully decentralized machines, which may either be purposely organized in a P2P network, or voluntarily join a running P2P optimization task. In this paper we present the GoDE algorithm (Gossip-based Differential Evolution), which obtains remarkable results on several test functions. We describe in detail the algorithm design and the epidemic mechanism that greatly improves the performance. Experimental results in a simulated environment show how GoDE adapts to network scale and how the epidemic communication protocol can make the algorithm achieve good results even in presence of a high churn rate.