Pivot method for global optimization

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Abstract
A pivot algorithm for the location of a global minimum of a multiple-minimum problem is presented. The pivot method uses a series of randomly placed probes in phase space, moving the worst probes to be near better probes iteratively until the system converges. The approach chooses nearest-neighbor pivot probes to search the entire phase space by using a nonlocal distribution for the placement of the relocated probes. To test the algorithm, a standard suite of functions is given, as well as the energies and geometric structures of Lennard-Jones clusters, demonstrating the extreme efficiency of the method. Significant improvement over previous methods for high-dimensional systems is shown.