Global Optimization for Molecular Clusters Using a New Smoothing Approach

Abstract

Strategies involving smoothing of the objective function have been used with some efficacy to help solve difficult global optimization problems arising in molecular chemistry. This paper proposes some new smoothing approaches and examines the utility of smoothing in global optimization. We first propose a new, simple algebraic way of smoothing the Lennard-Jones energy function, which is an important component of the energy in many molecular models. This simple smoothing technique is shown to have close similarities to previously-proposed, spatial averaging smoothing techniques. We then present some experimental studies of the behavior of local and global minimizers under smoothing of the potential energy in Lennard-Jones problems. An examination of minimizer trajectories from these smoothed problems shows significant limitations in the use of smoothing to directly solve global optimization methods. In light of these limitations, a new stochastic-perturbation method that combines smoothing and large-scale global optimization techniques is proposed. A set of experiments with the first phase of this algorithm on Lennard-Jones problems gives very promising results, and offers a clear indication that the use of smoothing in this context is helpful. These smoothing and global optimization techniques are designed to be applicable to a large class of empirical models for proteins.

Researc supported by AFOSR Grants No. AFOSR-90-0109 and F49620-94-1-0101,ARO Grants No. DAAL03-91-G-0151 and DAAH04-94-G-0228, and NSF Grant No. CCR-9101795.