Using evolutionary algorithm for generation of dense families of circulant networks

In this paper we consider the combinatorial optimization problem of the search for dense families of circulant networks with a good ratio between the order and diameter for a given degree. In particular, we distinguish the optimal families having the minimum possible diameter for a given degree and order of a graph. This work describes a new way of generation of analytical parametric descriptions of dense families of circulant networks using evolutionary algorithms. We present the families of circulants of degree 4 and 6 obtained by means of evolutionary algorithms. Some of these families of degree 6 improve previously known results