  Locating the global minimum of a complex potential energy surface is
facilitated by considering a homotopy, namely a family of surfaces that
interpolate continuously from an arbitrary initial potential to the system
under consideration. Different strategies can be used to follow the evolving
minima. It is possible to enhance the probability of locating the global
minimum through a heuristic choice of interpolation schemes and parameters, and
the continuously evolving potential landscape reduces the probability of
trapping in local minima. In application to a model problem, finding the
ground--state configuration and energy of rare--gas (Lennard--Jones) atomic
clusters, we demonstrate the utility and efficacy of this method.
