Extremal Energy Models and Global Optimization

The objective of global optimization (GO) is to find the absolutely best solution of nonlinear decision models that often have multiple—local and global—optima. Extremal energy point configuration models in computational chemistry and closely related areas provide a practically important, as well as numerically challenging area to test and apply GO strategies. First, we review several frequently used energy model forms. This is followed by a brief discussion related to one of these, the Lennard-Jones cluster (LJC) model posed as a GO problem. For illustration, LGO—an integrated model development and solver system for analyzing GO problems—is applied to solve small, yet non-trivial instances of the LJC model. We conclude by discussing the broad applicability of GO in this area, including possible energy model extensions.