  The organization of fog devices into fog colonies has reduced the complexity
management of fog domains. One of the main influencing factors on this
complexity is the large number of devices, i.e. the high scale level of the
infrastructure. Fog colonies are subsets of fog devices that are managed
independently from the other colonies. Thus, the number of devices involved in
the management of a colony is much smaller. Previous studies have evaluated the
influence of the fog colony layout on system performance metrics. We propose to
use a hierarchical clustering as the base definition of the fog colony layout
of the fog infrastructure. The dendrogram obtained from this hierarchical
clustering includes all the colony candidates. A genetic algorithm is in charge
of selecting the subset of colony candidates that optimizes the two performance
metrics under study: the network communication time between users and
applications, and the execution time of the algorithms that manage internally
the placement of the applications in each colony. We implemented the NSGA-II, a
common multi-objective approach for GAs, to evaluate our proposal. The results
show that a meta-heuristic such as a GA improves the performance metrics by
defining the fog colony layout through the use of the dendrogram. Nine
different experiment scenarios, varying the number of applications and fog
devices, were studied. In the worst of the cases, 137 generations were enough
to the results of the GA dominated the solutions obtained with two control
algorithms. The number of genetic solutions and their homogeneous distribution
in the Pareto front were also satisfactory.
