An Infeasible Point Method for Minimizing the Lennard-JonesPotential
Computational Optimization and Applications
Computational Optimization and Applications
Global Optima of Lennard-Jones Clusters
Journal of Global Optimization
Minimum Inter-Particle Distance at Global Minimizers of Lennard-Jones Clusters
Journal of Global Optimization
Minimal interatomic distance in Morse clusters
Journal of Global Optimization
Efficient Algorithms for Large Scale Global Optimization: Lennard-Jones Clusters
Computational Optimization and Applications
Docking of Atomic Clusters Through Nonlinear Optimization
Journal of Global Optimization
An Iterative Global Optimization Algorithm for Potential Energy Minimization
Computational Optimization and Applications
Minimal inter-particle distance in atom clusters
Acta Cybernetica
A Combined Global & Local Search (CGLS) Approach to Global Optimization
Journal of Global Optimization
Global Optimization of Morse Clusters by Potential Energy Transformations
INFORMS Journal on Computing
A particle swarm pattern search method for bound constrained global optimization
Journal of Global Optimization
Global Search Method for Parallel Machine Scheduling
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Clustering high dimensional data: A graph-based relaxed optimization approach
Information Sciences: an International Journal
Parallelization of the discrete gradient method of non-smooth optimization and its applications
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartIII
Self-adaptive mate choice for cluster geometry optimization
Proceedings of the 15th annual conference on Genetic and evolutionary computation
A nested heuristic for parameter tuning in Support Vector Machines
Computers and Operations Research
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The minimization of the potential energy function of Lennard-Jones atomic clusters has attracted much theoretical as well as computational research in recent years. One reason for this is the practical importance of discovering low energy configurations of clusters of atoms, in view of applications and extensions to molecular conformation research; another reason of the success of Lennard Jones minimization in the global optimization literature is the fact that this is an extremely easy-to-state problem, yet it poses enormous difficulties for any unbiased global optimization algorithm.In this paper we propose a computational strategy which allowed us to rediscover most putative global optima known in the literature for clusters of up to 80 atoms and for other larger clusters, including the most difficult cluster conformations. The main feature of the proposed approach is the definition of a special purpose local optimization procedure aimed at enlarging the region of attraction of the best atomic configurations. This effect is attained by performing first an optimization of a modified potential function and using the resulting local optimum as a starting point for local optimization of the Lennard Jones potential.Extensive numerical experimentation is presented and discussed, from which it can be immediately inferred that the approach presented in this paper is extremely efficient when applied to the most challenging cluster conformations. Some attempts have also been carried out on larger clusters, which resulted in the discovery of the difficult optimum for the 102 atom cluster and for the very recently discovered new putative optimum for the 98 atom cluster.