Comparison of Taboo Search Methods for Atomic Cluster Global Optimization with a Basin-Hopping Algorithm

The basin-hopping algorithm (BHA) allows for the efficient exploration of atomic cluster potential energy surfaces by random perturbations in configuration space, followed by energy minimizations. Here, the taboo search method is incorporated to prevent the search from revisiting recently visited regions of the search space. Two taboo search modes are implemented, one mode resets the search to random coordinates upon encountering the taboo region, while the other simply rejects any proposed move into the taboo region. These two modes are tested and compared on a variety of potential energy surfaces─several clusters where atomic interactions are described by the Lennard-Jones potential, and Au₅₅ where a semi-empirical tight binding potential is used to describe atomic interactions. Some differences in performance between the two taboo search modes were noted for LJ₃₈ and Au₅₅, with the mode that rejects all hops into the taboo region performing better, offering a means to improve the efficiency of the BHA for multifunnel systems. However, both taboo search modes failed to significantly improve performance on multifunnel systems where more than two funnels were present in the system.