A study on diversity for cluster geometry optimization

Diversity is a key issue to consider when designing evolutionary approaches for difficult optimization problems. In this paper, we address the development of an effective hybrid algorithm for cluster geometry optimization. The proposed approach combines a steady-state evolutionary algorithm and a straightforward local method that uses derivative information to guide search into the nearest local optimum. The optimization method incorporates a mechanism to ensure that the diversity of the population does not drop below a pre-specified threshold. Three alternative distance measures to estimate the dissimilarity between solutions are evaluated. Results show that diversity is crucial to increase the effectiveness of the hybrid evolutionary algorithm, as it enables it to discover all putative global optima for Morse clusters up to 80 atoms. A comprehensive analysis is presented to gain insight about the most important strengths and weaknesses of the proposed approach. The study shows why distance measures that consider structural information for estimating the dissimilarity between solutions are more suited to this problem than those that take into account fitness values. A detailed explanation for this differentiation is provided.

[1]  Natalio Krasnogor,et al.  Towards Robust Memetic Algorithms , 2005 .

[2]  Yong L. Xiao,et al.  Genetic algorithm: a new approach to the prediction of the structure of molecular clusters , 1993 .

[3]  L. Darrell Whitley,et al.  The GENITOR Algorithm and Selection Pressure: Why Rank-Based Allocation of Reproductive Trials is Best , 1989, ICGA.

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

[5]  Janez Demsar,et al.  Statistical Comparisons of Classifiers over Multiple Data Sets , 2006, J. Mach. Learn. Res..

[6]  Bernd Hartke,et al.  Global cluster geometry optimization by a phenotype algorithm with Niches: Location of elusive minima, and low-order scaling with cluster size , 1999, J. Comput. Chem..

[7]  Bernd Hartke.  Global geometry optimization of atomic and molecular clusters by genetic algorithms , 2001 .

[8]  William E. Hart,et al.  Recent Advances in Memetic Algorithms , 2008 .

[9]  J. Doye.  Physical Perspectives on the Global Optimization of Atomic Clusters , 2000, cond-mat/0007338.

[10]  Jim E. Smith,et al.  On Replacement Strategies in Steady State Evolutionary Algorithms , 2007, Evolutionary Computation.

[11]  Jorge M. C. Marques,et al.  Analysis of Locality in Hybrid Evolutionary Cluster Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

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

[13]  Fabio Schoen,et al.  Global Optimization of Morse Clusters by Potential Energy Transformations , 2004, INFORMS J. Comput..

[14]  Kalyanmoy Deb,et al.  A Comparative Analysis of Selection Schemes Used in Genetic Algorithms , 1990, FOGA.

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

[16]  Dario Floreano,et al.  Measures of Diversity for Populations and Distances Between Individuals with Highly Reorganizable Genomes , 2004, Evolutionary Computation.

[17]  Denitsa Alamanova,et al.  Structure and energetics of nickel, copper, and gold clusters , 2005 .

[18]  Zeiri.  Prediction of the lowest energy structure of clusters using a genetic algorithm. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  B. Hartke.  Global geometry optimization of clusters using genetic algorithms , 1993 .

[20]  Fabio Schoen,et al.  Fast Global Optimization of Difficult Lennard-Jones Clusters , 2002, Comput. Optim. Appl..

[21]  Fabio Schoen,et al.  Global optimization of binary Lennard–Jones clusters , 2009, Optim. Methods Softw..

[22]  R. Johnston,et al.  A genetic algorithm for the structural optimization of Morse clusters , 2000 .

[23]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[24]  Bernd Hartke,et al.  Application of Evolutionary Algorithms to Global Cluster Geometry Optimization , 2004 .

[25]  Edmund K. Burke,et al.  Multimeme Algorithms for Protein Structure Prediction , 2002, PPSN.

[26]  Zbigniew Michalewicz,et al.  Advances in Metaheuristics for Hard Optimization , 2008, Advances in Metaheuristics for Hard Optimization.

[27]  Andrea Grosso,et al.  A Population-based Approach for Hard Global Optimization Problems based on Dissimilarity Measures , 2007, Math. Program..

[28]  William M. Spears,et al.  Adapting Crossover in Evolutionary Algorithms , 1995, Evolutionary Programming.

[29]  F. Stillinger.  Exponential multiplicity of inherent structures , 1999 .

[30]  Graham Kendall,et al.  Advanced Population Diversity Measures in Genetic Programming , 2002, PPSN.

[31]  S. Ronald,et al.  More distance functions for order-based encodings , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[32]  Éric D. Taillard,et al.  Few statistical tests for proportions comparison , 2008, Eur. J. Oper. Res..

[33]  Fabio Schoen,et al.  Dissimilarity measures for population-based global optimization algorithms , 2010, Comput. Optim. Appl..

[34]  Wayne J. Pullan,et al.  An unbiased population‐based search for the geometry optimization of Lennard–Jones clusters: 2 ≤ N ≤ 372 , 2005, J. Comput. Chem..

[35]  Roy L. Johnston,et al.  Applications of Evolutionary Computation in Chemistry , 2004 .

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

[37]  Jinlong Yang,et al.  Global minimum structures of morse clusters as a function of the range of the potential: 81, 2007, The journal of physical chemistry. A.

[38]  Wensheng Cai,et al.  A connectivity table for cluster similarity checking in the evolutionary optimization method , 2004 .

[39]  Julian Lee,et al.  Unbiased global optimization of Lennard-Jones clusters for N < or =201 using the conformational space annealing method. , 2003, Physical review letters.

[40]  G. Aromí,et al.  Synthesis of 3d metallic single-molecule magnets , 2006 .

[41]  Natalio Krasnogor,et al.  Multimeme Algorithms Using Fuzzy Logic Based Memes For Protein Structure Prediction , 2005 .

[42]  Francisco Herrera,et al.  Real-Coded Memetic Algorithms with Crossover Hill-Climbing , 2004, Evolutionary Computation.

[43]  José Rogan,et al.  Diversity driven unbiased search of minimum energy cluster configurations , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[44]  D. Wales,et al.  How the range of pair interactions governs features of multidimensional potentials , 1990 .

[45]  Jorge M. C. Marques,et al.  A Self-Adaptive Evolutionary Algorithm for Cluster Geometry Optimization , 2008, 2008 Eighth International Conference on Hybrid Intelligent Systems.

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

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

[48]  Kenneth A. De Jong,et al.  Generation Gaps Revisited , 1992, FOGA.

[49]  Fabio Schoen,et al.  Efficient Algorithms for Large Scale Global Optimization: Lennard-Jones Clusters , 2003, Comput. Optim. Appl..

[50]  C. J. Tsai,et al.  Use of the histogram and jump‐walking methods for overcoming slow barrier crossing behavior in Monte Carlo simulations: Applications to the phase transitions in the (Ar)13 and (H2O)8 clusters , 1993 .

[51]  Jorge M. C. Marques,et al.  Designing Efficient Evolutionary Algorithms for Cluster Optimization: A Study on Locality , 2008, Advances in Metaheuristics for Hard Optimization.

[52]  Mark Wineberg,et al.  Distance between Populations , 2003, GECCO.

[53]  R. S. Berry,et al.  Structures of large Morse clusters , 1999 .