Predicting the Structure of Alloys Using Genetic Algorithms

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, 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.