The evolution of mobile networks, from their inception to the latest 5G and envisioned 6G technologies, underscores a relentless pursuit of enhanced performance and connectivity. Amidst this technological advancement, the need for energy efficiency has become increasingly pronounced, given the environmental and operational costs associated with scaling the network infrastructure. Among these, the Cell Switch-Off (CSO) problem epitomizes the challenge of achieving energy efficiency by identifying which cells to deactivate to reduce power consumption without compromising network performance. This binary decision can be formulated as a multi-objective optimization problem that exhibits an inherent sparsity and that requires solutions that minimize resource utilization while maximizing outcomes. In this context, this study delves into the CSO problem within ultra-dense 5G networks, emphasizing the application of sparse multi-objective evolutionary algorithms (MOEAs). Recognizing the CSO problem’s sparse nature, this research compares the efficacy of specialized sparse MOEAs against traditional, non-specialized algorithms. Our comprehensive experimentation and analysis show that sparse MOEAs offer higher-quality solutions by effectively leveraging the sparsity characteristic. Despite the superior performance of sparse algorithms, our findings also acknowledge the potential utility of solutions generated by non-specialized algorithms to aid the decision-making processes of network operators.