Clustering methods for the optimization of atomic cluster structure

In this work, we will present an approach to large scale global optimization based on some classical clustering methods. Algorithms based on clustering (e.g., Multi-level Single-Linkage) have been extremely successful at the beginning of global optimization, when the size of the problems to be solved was tiny. In recent years those techniques have been abandoned due to their inability to cope with large dimensional problems. We propose in this paper an approach which is based on the idea of clustering methods and which can be applied to specific classes of structured global optimization problems through the exploitation of small dimensional features. An example of this class of problems is that of energy minimization in atomic clusters, where despite the large dimension of the underlying problem, a limited number of significant geometric features can be identified as “signatures” of a solution. Based on these signatures, the decision whether to stop or continue a computational demanding optimization task can be done exploiting the similarity of different solutions in the feature space. Preliminary numerical results are provided which confirm the validity of the approach.