Network densification with deployments of many small base stations (SBSs) is a key enabler technology for the fifth generation (5G) cellular networks, and it is also clearly in conflict with one of the target design requirements of 5G systems: a 90% reduction of the power con- sumption. In order to address this issue, switching off a number of SBSs in periods of low traffic demand has been standardized as an recognized strategy to save energy. But this poses a challenging NP-complete opti- mization problem to the system designers, which do also have to provide the users with maxima capacity. This is a multi-objective optimization problem that has been tackled with multi-objective evolutionary algo- rithms (MOEAs). In particular, a problem-specific search operator with problem-domain information has been devised so as to engineer hybrid MOEAs. It is based on promoting solutions that activate SBSs which may serve users with higher data rates, while also deactivating those not serving any user at all. That is, it tries to improve the two problem objectives simultaneously. The resulting hybrid algorithms have shown to reach better approximations to the Pareto fronts than the canonical algorithms over a set of nine scenarios with increasing diversity in SBSs and users.