Optimisation of algorithm control parameters in cultural differential evolution applied to molecular crystallography

Evolutionary search and optimisation algorithms have been used successfully in many areas of materials science and chemistry. In recent years, these techniques have been applied to, and revolutionised the study of crystal structures from powder diffraction data. In this paper we present the application of a hybrid global optimisation technique, cultural differential evolution (CDE), to crystal structure determination from powder diffraction data. The combination of the principles of social evolution and biological evolution, through the pruning of the parameter search space shows significant improvement in the efficiency of the calculations over traditional dictates of biological evolution alone. Results are presented in which a range of algorithm control parameters, i.e., population size, mutation and recombination rates, extent of culture-based pruning are used to assess the performance of this hybrid technique. The effects of these control parameters on the speed and efficiency of the optimisation calculations are discussed, and the potential advantages of the CDE approach demonstrated through an average 40% improvement in terms of speed of convergence of the calculations presented, and a maximum gain of 68% with larger population size.