The massive deployment of base stations is one of the key pillars of the fifth generation (5G) of mobile communications. However, this network densification entails high energy consumption that must be addressed to enhance the sustainability of this industry. This work faces this problem from a multi-objective optimization perspective, in which both energy efficiency and quality of service criteria are taken into account. To do so, several newly problem-specific operators have been designed so as to engineer hybrid multi-objective evolutionary metaheuristics (MOEAs) that bring expert knowledge of the domain to the search of the algorithms. These hybrid approaches have been able to improve upon canonical versions of the algorithms, clearly showing the contributions of our approach. Furthermore, this paper tests the hypothesis that the hybridization using several of those problem-specific operators simultaneously can enhance the search of MOEAs that are endowed only with a single one.