Title: Direct search methods for optimization of Lennard-Jones clusters

The Lennard-Jones problem is defined as finding the coordinates of the system in the three-dimensional Euclidian space that represent a potential energy minimum. Lennard-Jones potential energy plays a key role in determining the stability of crowed and highly branched molecular such as protein. The main difficulty in solving this problem arises from the fact that the objective function is a non-convex and highly nonlinear function of many variables with a large number of local minima. Due to its importance, this problem has attracted many researchers from diverse fields. In this presentation, we present a deterministic global optimization approach, which is a combination of direct search methods with local heuristics, in the aim of finding the global optimum energy configuration of Lennard-Jones micro-clusters. With our method, global optima are located for micro-clusters of 2, 3, 4, 5, 8, 9, 11, 14, 15, 16, 17, 20, and 25. The results were compared to the ones based on LGO random sampling and branch and bound methods.