A many-objective optimization algorithm for community detection in multi-layer networks is proposed. The method exploits the modularity concept as function to be simultaneously optimized on all the network layers to uncover multi-layer communities. In addition, three different strategies to choice the best solution from the set of solutions of the Pareto front are presented. Simulations on several synthetic networks reveal that our method is able to extract high quality communities. A comparison with state-of-the-art approaches shows that the method is competitive and, in many cases, it is also able to outperform existing community detection algorithms for multi-layer networks.