  We discuss a novel genetic algorithm that can be used to find global minima
on the potential energy surface of disordered ceramics and alloys using a
real-space symmetry adapted crossover. Due to a high number of symmetrically
equivalent solutions of many alloys a conventional genetic algorithms using
reasonable population sizes are unable to locate the global minima for even the
smallest systems. We demonstrate the superior performance of the use of
symmetry adapted crossover by the comparison of that of a conventional GA for
finding global minima of two binary Ising-type alloys that either order or
phase separate at low temperature. Comparison of different representations and
crossover operations show that the use of real-space crossover outperforms
crossover operators working on binary representations by several orders of
magnitude.
