COMPARISON STUDY OF PIVOT METHODS FOR GLOBAL OPTIMIZATION

We compare two implementations of a new algorithm called the pivot met hod for the location of the global minimum of a multiple minima proble m. The pivot method uses a series of randomly placed probes in phase s pace, moving the worst probes to be near better probes iteratively unt il the system converges. The original implementation, called the ''low est energy pivot method,'' chooses the pivot probes with a probability based on the energy of the probe. The second approach, called the ''n earest neighbor pivot method,'' chooses the pivot probes to be the nea rest neighbor points in the phase space. We examine the choice of dist ribution by comparing the efficiency of the methods for Gaussian versu s generalized q-distribution, based on the Tsallis entropy in the relo cation of the probes. The two implementations of the method are tested with a series of test functions and with several Lennard-Jones cluste rs of various sizes. It appears that the nearest neighbor pivot method using the generalized q-distribution is superior to previous methods. (C) 1997 American Institute of Physics.