Global optimization on an evolving energy landscape

Abstract

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 (LennardJones) atomic clusters, we demonstrate the utility and efficacy of this method.

Global Optimization by Adiabatic Switching

“…As we have emphasized elsewhere [16], the present method is heuristic, and thus some exploration of different switching functions, variation in the adiabaticity and damping parameters, and indeed the choice of initial potential, V 0 ( r) is necessary.…”

“…The simplest procedure is to introduce damping into the equations of motion and allow the system to evolve to a position of rest in a potential minimum; by starting with an ensemble of initial configurations and varying the available parameters, a number of minima can be located, and the putative global minimum can be recognized. Elsewhere [16] we have suggested the conjugate gradient [22] or simulated annealing (SA) [23] as other possible methods for locating the minima. It is likely that of these, the conjugate gradient technique will be more efficient as compared to SA though some SA variants [24] may also provide a suitable method for following the evolving minima.…”

“…The adiabatic optimization method [16], is a heuristic technique for locating minima. The essential idea is as follows.…”

“…A number of other techniques can be used to follow the evolving minima. Applications have been made to determining the ground state configurations of simple cluster systems [16].…”

“…We have recently proposed a new method of global optimization wherein time-dependence is introduced in the potential energy landscape [16]. The evolving landscape is designed in a manner such that asymptotically, the potential energy surface develops into the surface of interest.…”