  Federated learning is a training paradigm according to which a server-based
model is cooperatively trained using local models running on edge devices and
ensuring data privacy. These devices exchange information that induces a
substantial communication load, which jeopardises the functioning efficiency.
The difficulty of reducing this overhead stands in achieving this without
decreasing the model's efficiency (contradictory relation). To do so, many
works investigated the compression of the pre/mid/post-trained models and the
communication rounds, separately, although they jointly contribute to the
communication overload. Our work aims at optimising communication overhead in
federated learning by (I) modelling it as a multi-objective problem and (II)
applying a multi-objective optimization algorithm (NSGA-II) to solve it. To the
best of the author's knowledge, this is the first work that \texttt{(I)}
explores the add-in that evolutionary computation could bring for solving such
a problem, and \texttt{(II)} considers both the neuron and devices features
together. We perform the experimentation by simulating a server/client
architecture with 4 slaves. We investigate both convolutional and
fully-connected neural networks with 12 and 3 layers, 887,530 and 33,400
weights, respectively. We conducted the validation on the \texttt{MNIST}
dataset containing 70,000 images. The experiments have shown that our proposal
could reduce communication by 99% and maintain an accuracy equal to the one
obtained by the FedAvg Algorithm that uses 100% of communications.
