A method introduced by Stillinger for finding global minima of potential surfaces and for achieving the optimization objectives of simulated annealing is shown to require caution in some of its applications. In particular, a range parameter is varied to eliminate secondary minima on the potential surface or hypersurface of the objective function of interest. We show that in some cases, using minimizations on the simplified surface to reveal minima on the more complex surface require scrutiny of

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... the sequences of low-energy minima, as functions of the range parameter whose variation controls the complexity of the surface.