POTENTIAL TRANSFORMATION-METHODS FOR LARGE-SCALE GLOBAL OPTIMIZATION

Several techniques for global optimization treat the objective functio n f as a force field potential. In the simplest case, trajectories of the differential equation mx = -del f sample regions of low potential while retaining the energy to surmount passes that might block the way to regions of even lower local minima. A potential transformation is an increasing function V:R --> R. It determines a new potential g = V( f) with the same minimizers as f, and new trajectories satisfying mx = -del g = -df/dV del f. We discuss a class of potential transformation s that greatly increase the df attractiveness of low local minima and that provide, as a special case, a new approach to an equation propose d by Griewank for global optimization. Practical methods for implement ing these ideas are discussed.