Comparing efficiencies of genetic and minima hopping algorithms for crystal structure prediction

Abstract

In this work several crystal structure prediction problems which have been studied by first-principles evolutionary algorithms recently are revisited. We increased the system size to see how the search efficiency changes with respect to problem size. We find that the relative performance and underlying mechanism of genetic algorithms in crystal structure searches for Al(x)Sc(1-x) strongly depend on the system composition as well as the size of the problem. Because of this strong dependence, caution should be taken in generalizing performance comparison from one problem to another even though they may appear to be similar. We also investigate the performance of the search algorithm for crystal structure prediction of boron with and without a priori knowledge of the lattice vectors. The results show that the degree of difficulty increases dramatically if the lattice vectors of the crystal are allowed to vary during the search. Comparison of the minima hopping algorithm with the genetic algorithm at small (<10 atoms) to larger problem sizes is also carried out. At the small sizes we have tested, both methods show comparable efficiency. But at large sizes the genetic algorithm becomes advantageous over minima hopping.