Low Energy Electron Diffraction (LEED) has been used extensively in the study of surface structures. Structures are typically determined in a trial and error process whereby theoretical calculations for an initially proposed structure are refined until a good fit to experimentally measured data is found. In this thesis LEED has been used to study the structure of the clean Ni(llO) and N i(lll) surfaces. For the clean Ni(llO) surface a 7% relaxation in the outermost Ni layer spacing is found compared to 0% for the N i(lll) surface. The variation in surface relaxation is explained in terms of the reduccd valence electron density and atomic packing density at the surface. The trial and error approach to determining structures is not only time consuming but can also be highly inaccurate. An automated approach to structure determination using an Evolutionary Strategy called Differential Evolution is developed in this work. The algorithm is found to be extremely fast and reliable and provides a 25-37% increase in speed compared to the best competing method.