This article presents an approach applying a multiobjective evolutionary approach for the problem of designing Content Distribution Networks in the context of smart cities. The problem at had is NP-hard problem, thus efficient alternatives to exact methods are needed to solve the problem in reasonable execution times. A specific multiobjective evolutionary algorithm is proposed to solve the problem, using ad-hoc solutions representations and operators to optimize system- and user-related metrics. The main results over real problem instances show that the solutions computed the proposed multiobjective evolutionary algorithm are highly competitive in both cost and quality of service when compared with solutions found using an exact method. The computed solutions demanded significantly less time to be found and provide high diversity, accounting for different trade-offs between the problem objectives.