Advertisement

Designing Efficient Evolutionary Algorithms for Cluster Optimization: A Study on Locality

  • Francisco B. Pereira
  • JorgeM.C. Marques
  • Tiago Leitão
  • Jorge Tavares
Part of the Natural Computing Series book series (NCS)

Abstract

Cluster geometry optimization is an important problem from the Chemistry area. Hybrid approaches combining evolutionary algorithms and gradient-driven local search methods are one of the most efficient techniques to perform a meaningful exploration of the solution space to ensure the discovery of low energy geometries. Here we performa comprehensive study on the locality properties of this approach to gain insight to the algorithm’s strengths andweaknesses.Theanalysis is accomplished through the application of several static measures to randomly generated solutions in order to establish the main properties of an extended set of mutation and crossover operators. Locality analysis is complemented with additional results obtained from optimization runs. The combination of the outcomes allows us to propose a robust hybrid algorithm that is able to quickly discover the arrangement of the cluster’s particles that correspond to optimal or near-optimal solutions.

Keywords

Mutation Rate Locality Analysis Crossover Operator Genetic Operator Atom Cluster 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. E. Jones. On the Determination of Molecular Fields. II. From the Equation of State of a Gas. Proc. Roy. Soc. A, 106, 463–477, 1924Google Scholar
  2. 2.
    J. E. Lennard-Jones. Cohesion. Proc. Phys. Soc., 43, 461–482, 1931Google Scholar
  3. 3.
    P. Morse. Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels. Phys. Rev., 34, 57–64, 1929Google Scholar
  4. 4.
    J. P. K. Doye, R. Leary, M. Locatelli and F. Schoen. Global Optimization of Morse Clusters by Potential Energy Transformations, Informs Journal on Computing, 16, 371–379, 2004CrossRefGoogle Scholar
  5. 5.
    R. L. Johnston. Evolving Better Nanoparticles: Genetic Algorithms for Optimising Cluster Geometries, Dalton Transactions, 22, 4193–4207, 2003Google Scholar
  6. 6.
    D. M. Deaven and K. Ho. Molecular Geometry Optimization with a Genetic Algorithm, Phys. Rev. Lett. 75, 288–291, 1995Google Scholar
  7. 7.
    B. Hartke. Global Geometry Optimization of Atomic and molecular Clusters by Genetic Algorithms, In L. Spector et al. (Eds.), Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), 1284–1291Google Scholar
  8. 8.
    B. Hartke. Application of Evolutionary Algorithms to Global Cluster Geometry Optimization, In R. L. Johnston (Ed.), Applications of Evolutionary Computation in Chemistry, Structure and Bonding, 110, 33–53, 2004Google Scholar
  9. 9.
    F. Manby, R. L. Johnston and C. Roberts. Predatory Genetic Algorithms. Commun. Math. Comput. Chem. 38, 111–122, 1998Google Scholar
  10. 10.
    W. Pullan. An Unbiased Population-Based Search for the Geometry Optimization of Lennard-Jones Clusters: 2≤N≤372. Journal of Computational Chemistry, 6(9), 899–906, 2005CrossRefGoogle Scholar
  11. 11.
    C. Roberts, R. L. Johnston and N. Wilson (2000). A Genetic Algorithm for the Structural Optimization of Morse Clusters. Theor. Chem. Acc., 104, 123–130, 2000Google Scholar
  12. 12.
    Y. Zeiri. Prediction of the Lowest Energy Structure of Clusters Using a Genetic Algorithm, Phys. Rev., 51, 2769–2772, 1995Google Scholar
  13. 13.
    J. Gottlieb and C. Eckert. A Comparison of Two Representations for the Fixed Charge Transportation Problem, In M. Schoenauer et al. (Eds.), Parallel Problem Solving from Nature (PPSN VI), 345–354, Spinger-Verlag LNCS, 2000Google Scholar
  14. 14.
    J. Gottlieb and G. Raidl. Characterizing Locality in Decoder-Based EAs for the Multidimensional Knapsack Problem, In C. Fonlupt et al. (Eds.), Artificial Evolution: Fourth European Conference, 38–52, Springer-Verlag LNCS, 1999Google Scholar
  15. 15.
    G. Raidl and J. Gottlieb. Empirical Analysis of Locality, Heritability and Heuristic Bias in Evolutionary Algorithms: A Case Study for the Multidimensional Knapsack Problem. Evolutionary Computation, 13(4), 441–475, 2005Google Scholar
  16. 16.
    F. Rothlauf and D. Goldberg, Prüfernumbers and Genetic Algorithms: A Lesson on Hoe the Low Locality on an Encoding Can Harm the Performance of Gas, In M. Schoeneauer et al. (Eds.), Parallel Problem Solving from Nature PPSN VI, 395–404, 2000Google Scholar
  17. 17.
    F. Rothlauf. On the Locality of Representations, In E. Cantú-Paz et al. (Eds.), Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2003), Part II, 1608–1609, 2003Google Scholar
  18. 18.
    B. Sendhoff, M. Kreutz and W. Seelen. A Condition for the Genotype-Phenotype Mapping: Causality. In T. Bäck (Ed.), Proceedings of the 7th International Conference on Genetic Algorithms (ICGA-97), 73–80, 1997Google Scholar
  19. 19.
    F. B. Pereira, J. M. C. Marques, T. Leitão, J. Tavares. Analysis of Locality in Hybrid Evolutionary Cluster Optimization. In G. Yen et al. (Eds.), Proceedings of the IEEE Congress on Evolutionary Computation (CEC-2006), pp. 8049–8056, 2006Google Scholar
  20. 20.
    J. P. K. Doye and D. J. Wales. Structural Consequences of the Range of the Interatomic Potential. A Menagerie of Clusters. J. Chem. Soc. Faraday Trans. 93, 4233–4243, 1997Google Scholar
  21. 21.
    D. J. Wales et al. The Cambridge Cluster Database, URL: http://www-wales.ch.cam.ac.uk/CCD.html, accessed on January 2007Google Scholar
  22. 22.
    D. C. Liu and J. Nocedal. On the Limited Memory Method for Large Scale Optimization, Mathematical Programming B, 45, 503–528, 1989Google Scholar
  23. 23.
    J. Nocedal. Large Scale Unconstrained Optimization, In A. Watson and I. Duff (Eds.), The State of the Art in Numerical Analysis, 311–338, 1997Google Scholar
  24. 24.
    S. Wright. The Roles of Mutation, Inbreeding, Crossbreeding and Selection in Evolution. In Proceedings of the 6th International Conference on Genetics, Vol. 1, 356–366, 1932Google Scholar
  25. 25.
    T. Jones and S. Forrest. Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms. In L. Eshelman (Ed.), Proceedings of the 6th International Conference on Genetic Algorithms (ICGA-95), 184–192, 1995Google Scholar
  26. 26.
    P. Merz. Memetic Algorithms for Combinatorial Optimization Problems: Fitness Landscapes and Effective Search Strategies. Ph.D. Thesis, Department of Electrical Engineering and Computer Science, University of Siegen, Germany, 2000Google Scholar
  27. 27.
    E. D. Weinberger. Correlated and Uncorrelated Fitness Landscapes and How to Tell the Difference, Biological Cybernetics, 63, 325–336, 1990zbMATHCrossRefGoogle Scholar
  28. 28.
    W. Hart, T. Kammeyer, R. Belew. The Role of Development in Genetic Algorithms. In D. Whitley and M. Vose, (Eds.), Foundations of Genetic Algorithms 3, Morgan Kaufmann, pp. 315–332, 1995Google Scholar
  29. 29.
    D. Thierens, D. Goldberg. Mixing in Genetic Algorithms. In S. Forrest (Ed.), Proceedings of the Fifth International Conference on Genetic Algorithms (ICGA-93), Morgan Kaufmann, pp. 38–45, 1993Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Francisco B. Pereira
    • 1
  • JorgeM.C. Marques
    • 2
  • Tiago Leitão
    • 3
  • Jorge Tavares
    • 3
  1. 1.Instituto Superior de Engenharia de CoimbraCoimbraPortugal
  2. 2.Departamento de QuimicaUniversidade de CoimbraCoimbraPortugal
  3. 3.Centro de Informatica e SistemasUniversidade de CoimbraCoimbraPortugal

Personalised recommendations