  We present an evolutionary construction technique of formation energy convex
hull to search for thermodynamically stable compounds. In this technique,
candidates with a wide variety of chemical compositions and crystal structures
are created by systematically applying evolutionary operators, "mating",
"mutation", and "adaptive mutation", to two target compounds, and the convex
hull is directly updated through the evolution. We applied the technique to
carbon-hydrogen binary system at 10 GPa and obtained 15 hydrocarbons within the
convex hull distance less than 0.5 mRy/atom: graphane, polybutadiene,
polyethylene, butane, ethane, methane, three molecular compounds of ethane and
methane, and six molecular compounds of methane and hydrogen. These results
suggest that our evolutionary construction technique is useful for the
exploration of stable phases under extreme conditions and the synthesis of new
compounds.
