Global Optimization of Tersoff Clusters Using Differential Evolution with Inexact Line Search

Abstract

Differential Evolution with Inexact Line Search (DEILS) is proposed to determination of the ground-state geometry of atom clusters. DEILS algorithm adopts probabilistic inexact line search method in acceptance rule of differential evolution to accelerate the convergence as the region of global minimum is approached. More realistic many-body potential energy functions, namely the Tersoff and Tersoff-like semi-empirical potentials for silicon, are considered. Numerical studies indicate that the new algorithm is considerably faster and more reliable than original differential evolution algorithm, especially for large-scale global optimization problem of MBP6/Si(C). Moreover, some ground-state solutions, which are superior to the known best solution given in literature, are reported.