We apply a recently introduced method for global optimization to determine the ground state energy and configuration for model metallic clusters. The global minimum for a given N-atom cluster is found by following the damped dynamics of the N particle system on an evolving potential energy surface. In this application, the time dependent interatomic potential interpolates adiabatically between the Lennard-Jones (LJ) and the Sutton-Chen (SC) forms. Starting with an ensemble of initial conditions corresponding to the ground state configuration of the Lennard-Jones cluster, the system asymptotically reaches the ground state of the Sutton-Chen cluster. We describe the method and present results for specific cluster size N = 15, when the ground state symmetry of LJ(N) and SCN differ.