Scaling behavior of genetic algorithms applied to surface structural determination by LEED

Surface structural determination by low energy electron diffraction (LEED) requires a fitting procedure between the theoretical and experimental I(V) curves. This fitting procedure is quantified through an R-factor methodology. However, the R-factor space topology presents a large number of local minima. Thus, the task of identifying the global minimum, i.e. the task of finding the correct surface structure, requires a global optimization method that is able to determine the surface structure of complex systems. In this work we present the results of the application of genetic algorithms to three different systems, including performance tests and a comparison with another optimization method previously applied to the LEED problem, simulated annealing. We also present a scaling relationship of the computational effort versus the number of parameters to be fitted for the genetic algorithm method.