  In 2020 Bang-Jensen et. al. generalized the Haj\'os join of two graphs to the
class of digraphs and generalized several results for vertex colorings in
digraphs. Although, as a consequence of these results, a digraph can be
obtained by Haj\'os constructions (directed Haj\'os join and identifying
non-adjacent vertices), determining the Haj\'os constructions to obtain the
digraph is a complex problem. In particular, Bang-Jensen et al. posed the
problem of determining the Haj\'os operations to construct the symmetric
5-cycle from the complete symmetric digraph of order 3 using only Haj\'os
constructions. We successfully adapted a rank-based genetic algorithm to solve
this problem by the introduction of innovative recombination and mutation
operators from graph theory. The Haj\'os Join became the recombination operator
and the identification of independent vertices became the mutation operator. In
this way, we were able to obtain a sequence of only 16 Haj\'os operations to
construct the symmetric cycle of order 5.
