  We consider heterogeneous wireless networks in the physical interference
model and introduce a new formulation of the optimization problem underlying
their management. This formulation targets the minimization of power
consumption by integrating base-station activation and many-to-many
associations into the same mixed-integer nonlinear programming (MINLP) problem.
We also introduce HetNetGA, a genetic algorithm tailored to solving the MINLP
problem without further smoothing or approximation. We give computational
results in scenarios involving both macrocells and picocells. Some results
align well with what is expected, but others are unexpected, pointing
essentially to the need to better understand the role of macrocells in such
networks.
