  Graph vertex coloring with a given number of colors is a well-known and
much-studied NP-complete problem.The most effective methods to solve this
problem are proved to be hybrid algorithms such as memetic algorithms or
quantum annealing. Those hybrid algorithms use a powerful local search inside a
population-based algorithm.This paper presents a new memetic algorithm based on
one of the most effective algorithms: the Hybrid Evolutionary Algorithm HEA
from Galinier and Hao (1999).The proposed algorithm, denoted HEAD - for HEA in
Duet - works with a population of only two individuals.Moreover, a new way of
managing diversity is brought by HEAD.These two main differences greatly
improve the results, both in terms of solution quality and computational
time.HEAD has produced several good results for the popular DIMACS benchmark
graphs, such as 222-colorings for \textless{}dsjc1000.9\textgreater{},
81-colorings for \textless{}flat1000\_76\_0\textgreater{} and even 47-colorings
for \textless{}dsjc500.5\textgreater{} and 82-colorings for
\textless{}dsjc1000.5\textgreater{}.
