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In Multi-agent systems, the study of language and communication is an active field of research In this paper we present the application of evolutionary strategies to the self-emergence of a common lexicon in a population of agents By modeling the vocabulary or lexicon of each agent as an association matrix or look-up table that maps the meanings (i.e the objects encountered by the agents or the states of the environment itself) into symbols or signals we check whether it is possible for the population to converge in an autonomous, decentralized way to a common lexicon, so that the communication efficiency of the entire population is optimal We have conducted several experiments, from the simplest case of a 2×2 association matrix (i.e two meanings and two symbols) to a 3×3 lexicon case and in both cases we have attained convergence to the optimal communication system by means of evolutionary strategies To analyze the convergence of the population of agents we have defined the population's consensus when all the agents (i.e the 100% of the population) share the same association matrix or lexicon As a general conclusion we have shown that evolutionary strategies are powerful enough optimizers to guarantee the convergence to lexicon consensus in a population of autonomous agents.