  We consider heterogeneous wireless networks in the physical interference
model and introduce a new formulation of the mixed-integer nonlinear
programming problem that addresses base-station activation and many-to-many
associations while minimizing power consumption. We also introduce HetNetGA, a
genetic algorithm that can tackle the problem without any approximations.
Though unsuitable for practical deployment, HetNetGA enables the investigation
of such networks' true possibilities. Results for scenarios involving both
macrocells and picocells often align with what is expected, but sometimes are
unexpected and essentially point to the need to better understand the role of
macrocells in helping provide capacity while remaining energetically
advantageous.
