Critical applications which need to deliver multimedia through the Internet, may achieve the required quality of service thanks to the Content-Aware Networks (CAN). The key element of CAN is an efficient decision algorithm responsible for the selection of the best content source and routing paths for content delivery. This paper proposes a two-phase decision algorithm, exploiting the Evolutionary Multiobjective Optimization (EMO) approach. It allows to consider valid information in different time scales, adapting decision-maker to the evolving network and server conditions as well as to get the optimal solution in different shapes of Pareto front. The simulation experiments performed in a large-scale network model, confirm the effectiveness of the proposed two-phase EMO algorithm, comparing to other multi-criteria decision algorithms used in CAN.