A hybrid LBFGS-DE algorithm for global optimization of the Lennard-Jones cluster problem

Abstract

A limited memory BFGS (L-BFGS) algorithm is combined with a population based modified differential evolution (DE) algorithm for determining global minimum potential energy configurations of atom clusters using the unbiased potential Lennard-Jones function. Computational results for a C coded implementation are presented for clusters containing from 2 to 50 atoms. The hybrid algorithm is found to be a more reliable algorithm than a randomized L-BFGS algorithm alone in determining minimum energy clusters.