ABCluster: the artificial bee colony algorithm for cluster global optimization.

Global optimization of cluster geometries is of fundamental importance in chemistry and an interesting problem in applied mathematics. In this work, we introduce a relatively new swarm intelligence algorithm, i.e. the artificial bee colony (ABC) algorithm proposed in 2005, to this field. It is inspired by the foraging behavior of a bee colony, and only three parameters are needed to control it. We applied it to several potential functions of quite different nature, i.e., the Coulomb-Born-Mayer, Lennard-Jones, Morse, Z and Gupta potentials. The benchmarks reveal that for long-ranged potentials the ABC algorithm is very efficient in locating the global minimum, while for short-ranged ones it is sometimes trapped into a local minimum funnel on a potential energy surface of large clusters. We have released an efficient, user-friendly, and free program "ABCluster" to realize the ABC algorithm. It is a black-box program for non-experts as well as experts and might become a useful tool for chemists to study clusters.

[1]  Dervis Karaboga,et al.  A comprehensive survey: artificial bee colony (ABC) algorithm and applications , 2012, Artificial Intelligence Review.

[2]  J. Doye,et al.  Structural consequences of the range of the interatomic potential A menagerie of clusters , 1997, cond-mat/9709201.

[3]  Dervis Karaboga,et al.  A comparative study of Artificial Bee Colony algorithm , 2009, Appl. Math. Comput..

[4]  Haiyan Jiang,et al.  An Efficient Method Based on Lattice Construction and the Genetic Algorithm for Optimization of Large Lennard-Jones Clusters. , 2004, The journal of physical chemistry. A.

[5]  Ho,et al.  Molecular geometry optimization with a genetic algorithm. , 1995, Physical review letters.

[6]  Roy L. Johnston,et al.  A mixed structural motif in 34-Atom Pd-Pt clusters , 2007 .

[7]  F. Calvo,et al.  Accurate melting temperatures for neon and argon from ab initio Monte Carlo simulations. , 2008, Angewandte Chemie.

[8]  Jonathan Doye,et al.  Thermodynamics of Global Optimization , 1998 .

[9]  L. Wille.  Minimum-energy configurations of atomic clusters: new results obtained by simulated annealing , 1987 .

[10]  Harold A. Scheraga,et al.  Structure and free energy of complex thermodynamic systems , 1988 .

[11]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[12]  David N. Freeman.  Access time , 2003 .

[13]  Mauricio Terrones,et al.  Curved nanostructured materials , 2003 .

[14]  Lead clusters: different potentials, different structures , 2004, cond-mat/0405234.

[15]  Rosato,et al.  Tight-binding potentials for transition metals and alloys. , 1993, Physical review. B, Condensed matter.

[16]  Jun Zhang,et al.  Third-Order Incremental Dual-Basis Set Zero-Buffer Approach: An Accurate and Efficient Way To Obtain CCSD and CCSD(T) Energies. , 2013, Journal of chemical theory and computation.

[17]  Jouni Lampinen,et al.  A Trigonometric Mutation Operation to Differential Evolution , 2003, J. Glob. Optim..

[18]  Xueguang Shao,et al.  Structural Distribution of Lennard-Jones Clusters Containing 562 to 1000 Atoms. , 2004, The journal of physical chemistry. A.

[19]  Max Born,et al.  Zur Gittertheorie der Ionenkristalle , 1932 .

[20]  Erber,et al.  Comment on "Method of constrained global optimization" , 1995, Physical review letters.

[21]  David J. Wales,et al.  Surveying a complex potential energy landscape: Overcoming broken ergodicity using basin-sampling , 2013 .

[22]  Roy L. Johnston,et al.  Investigation of the structures of MgO clusters using a genetic algorithm , 2001 .

[23]  Jonathan P. K. Doye,et al.  On potential energy surfaces and relaxation to the global minimum , 1996 .

[24]  Dharmender Kumar,et al.  A review on Artificial Bee Colony algorithm , 2013 .

[25]  David Romero,et al.  The optimal geometry of Lennard-Jones clusters: 148-309 , 1999 .

[26]  J. Doye,et al.  Evolution of the Potential Energy Surface with Size for Lennard-Jones Clusters , 1999, cond-mat/9903305.

[27]  M J Elrod,et al.  Many-body effects in intermolecular forces. , 1994, Chemical reviews.

[28]  J. Doye,et al.  Structural transitions and global minima of sodium chloride clusters , 1998, cond-mat/9801152.

[29]  Jun Zhang,et al.  Understanding lanthanoid(III) hydration structure and kinetics by insights from energies and wave functions. , 2014, Inorganic chemistry.

[30]  J. Doye,et al.  Structural relaxation in atomic clusters: master equation dynamics. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[31]  C. Levinthal.  Are there pathways for protein folding , 1968 .

[32]  Zhanghui Chen,et al.  PDECO: Parallel differential evolution for clusters optimization , 2013, J. Comput. Chem..

[33]  R. Johnston.  Evolving better nanoparticles: Genetic algorithms for optimising cluster geometries , 2003 .

[34]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

[35]  N. Watari,et al.  Electronic structure of H adsorbed on Pt13 clusters , 1997 .

[36]  David J Wales,et al.  Symmetrisation schemes for global optimisation of atomic clusters. , 2013, Physical chemistry chemical physics : PCCP.

[37]  Jonathan P. K. Doye,et al.  The favored cluster structures of model glass formers , 2003 .

[38]  Jonathan P. K. Doye.  Identifying structural patterns in disordered metal clusters , 2003 .

[39]  R. Johnston,et al.  Global optimization of clusters using electronic structure methods , 2013 .

[40]  Janet E. Jones.  On the determination of molecular fields. —II. From the equation of state of a gas , 1924 .

[41]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[42]  Jorge Nocedal,et al.  On the limited memory BFGS method for large scale optimization , 1989, Math. Program..

[43]  Ya Li,et al.  Protein secondary structure optimization using an improved artificial bee colony algorithm based on AB off-lattice model , 2014, Eng. Appl. Artif. Intell..

[44]  David S. Goodsell,et al.  Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function , 1998 .

[45]  Raju P. Gupta.  Lattice relaxation at a metal surface , 1981 .

[46]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[47]  Marco Dorigo,et al.  Swarm intelligence: from natural to artificial systems , 1999 .

[48]  P. Morse.  Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels , 1929 .

[49]  J. Doye,et al.  Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms , 1997, cond-mat/9803344.

[50]  R. Zwanzig,et al.  Levinthal's paradox. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[51]  Dzugutov.  Glass formation in a simple monatomic liquid with icosahedral inherent local order. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[52]  M. Hunger,et al.  Anomalous diamagnetic susceptibility in 13-atom platinum nanocluster superatoms. , 2014, Angewandte Chemie.

[53]  T. Kühne,et al.  Foraging on the potential energy surface: a swarm intelligence-based optimizer for molecular geometry. , 2012, The Journal of chemical physics.

[54]  Yanchao Wang,et al.  Crystal structure prediction via particle-swarm optimization , 2010 .

[55]  Daniel Sebastiani,et al.  Efficient implementation and application of the artificial bee colony algorithm to low-dimensional optimization problems , 2014, Comput. Phys. Commun..

[56]  D. Wales,et al.  Quasi-combinatorial energy landscapes for nanoalloy structure optimisation. , 2015, Physical chemistry chemical physics : PCCP.

[57]  Sanyang Liu,et al.  Improved artificial bee colony algorithm for global optimization , 2011 .

[58]  H. Häkkinen,et al.  The gold-sulfur interface at the nanoscale. , 2012, Nature chemistry.

[59]  Monatomic model of icosahedrally ordered metallic glass formers , 1993 .

[60]  Jonathan P. K. Doye,et al.  TOPICAL REVIEW: The effect of the range of the potential on the structure and stability of simple liquids: from clusters to bulk, from sodium to ? , 1996 .

[61]  H. Scheraga,et al.  Global optimization of clusters, crystals, and biomolecules. , 1999, Science.

[62]  Dervis Karaboga,et al.  AN IDEA BASED ON HONEY BEE SWARM FOR NUMERICAL OPTIMIZATION , 2005 .

[63]  D. Wales,et al.  Communication: a new paradigm for structure prediction in multicomponent systems. , 2013, The Journal of chemical physics.

[64]  Daniel Sebastiani,et al.  Artificial Bee Colony Optimization of Capping Potentials for Hybrid Quantum Mechanical/Molecular Mechanical Calculations. , 2011, Journal of chemical theory and computation.