Skip to main content
SpringerLink
Log in

Island models for cluster geometry optimization: how design options impact effectiveness and diversity

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

Designing island models is a challenging task for researchers. A number of decisions is required regarding the structure of the islands, how they are connected, how many individuals are migrated, which ones and how often. The impact of these choices is yet to be fully understood, specially since it may change between different problems and contexts. Cluster geometry optimization is a widely known and complex problem that provides a set of hard instances to assess and test optimization algorithms. The analysis presented in this paper reveals how design options for island models impact search effectiveness and population diversity, when seeking for the global optima of short-ranged Morse clusters. These outcomes support the definition of a robust and scalable island-based framework for cluster geometry optimization problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. http://physchem.ox.ac.uk/doye/jon/structures/Morse.html

  2. Alba, E., Tomassini, M.: Parallelism and evolutionary algorithms. Evol. Comput. IEEE Trans. 6(5), 443–462 (2002)

    Article  Google Scholar 

  3. Alba, E., Troya, J.: A survey of parallel distributed genetic algorithms. Complexity 4(4), 31–52 (1999)

    Article  MathSciNet  Google Scholar 

  4. Bethke, A.: Comparison of genetic algorithms and gradient-based optimizers on parallel processors: efficiency of use of processing capacity. Technical Report No. 197, University of Michigan, Logic of Computers Group, Ann Arbor (1976)

  5. Braun, H.: On solving travelling salesman problems by genetic algorithms. In: Schwefel, H.P., Männer, R. (eds.) Parallel Problem Solving From Nature, pp. 129–133. Springer, Berlin (1990)

    Google Scholar 

  6. Cantú-Paz, E.: A survey of parallel genetic algorithms. Calculateurs paralleles, reseaux et systems repartis 10(2), 141–171 (1998)

    Google Scholar 

  7. Cantú-Paz, E.: Migration policies, selection pressure, and parallel evolutionary algorithms. J. Heuristics 7, 311–334 (2001)

    Article  MATH  Google Scholar 

  8. Cantú-Paz, E., Goldberg, D.E.: Modeling idealized bounding cases of parallel genetic algorithms. In: Koza, J., Deb, K., Dorigo, M., Fogel, D., Garzon, M., Iba, H., Riolo, R. (eds.) Proceedings of the Second Annual Conference on Genetic Programming. Morgan Kaufmann, San Francisco (1997)

    Google Scholar 

  9. Cantú-Paz, E., Mejia-Olvera, M.: Experimental results in distributed genetic algorithms. In: International Symposium on Applied Corporate Computing, pp. 99–108 (1994)

  10. Cassioli, A., Locatelli, M., Schoen, F.: Global optimization of binary Lennard–Jones clusters. Optim. Methods Softw. 24, 819–835 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  11. Cassioli, A., Locatelli, M., Schoen, F.: Dissimilarity measures for population-based global optimization algorithms. Comput. Optim. Appl. 45, 257–281 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  12. Cheng, L.: A connectivity table for cluster similarity checking in the evolutionary optimization method. Chem. Phys. Lett. 389, 309–314 (2004)

    Article  Google Scholar 

  13. Cheng, L., Feng, Y., Yang, J., Yang, J.: Funnel hopping: searching the cluster potential energy surface over the funnels. J. Chem. Phys. 130(21), 214,112 (2009)

    Article  Google Scholar 

  14. Cheng, L., Yang, J.: Global minimum structures of morse clusters as a function of the range of the potential: \(81 \le \text{ n } \le 160\). J. Phys. Chem. A 111(24), 5287–5293 (2007)

    Article  Google Scholar 

  15. Cohoon, J., Hegde, S., Martin, W., Richards, D.: Punctuated equilibria: a parallel genetic algorithm. In: Proceedings of the Second International Conference on Genetic Algorithms and their applications, pp. 148–154. L. Erlbaum Associates Inc., Hillsdale (1987)

  16. Cohoon, J.P., Martin, W.N., Richards, D.S.: A multi-population genetic algorithm for solving the k-partition problem on hyper-cubes. In: Proceedings of the Fourth International Conference on Genetic Algorithms, vol. 91, pp. 244–248 (1991)

  17. Darby, S., Mortimer-Jones, T.V., Johnston, R.L., Roberts, C.: Theoretical study of Cu–Au nanoalloy clusters using a genetic algorithm. J. Chem. Phys. 116, 1536–1550 (2002)

    Article  Google Scholar 

  18. De Jong, K.: An analysis of the behavior of a class of genetic adaptive systems. Ph.D. thesis (1975)

  19. De Jong, K.A., Sarma, J.: Generation gaps revisited. In: Foundations of Genetic Algorihtms 2, pp. 19–28 (1992)

  20. Deaven, D.M., Ho, K.M.: Molecular geometry optimization with a genetic algorithm. Phys. Rev. Lett. 75, 288–291 (1995)

    Article  Google Scholar 

  21. Doye, J.P., Wales, D.J.: Structural consequences of the range of the interatomic potential a menagerie of clusters. J. Chem. Soc. Faraday Trans. 93(24), 4233–4243 (1997)

    Article  Google Scholar 

  22. Doye, J.P.K., Leary, R.H., Locatelli, M., Schoen, F.: Global optimization of Morse clusters by potential energy transformations. INFORMS J. Comput. 16, 371–379 (2004)

    Article  MATH  Google Scholar 

  23. Dugan, N., Erkoc, S.: Genetic algorithm—Monte Carlo hybrid geometry optimization method for atomic clusters. Comput. Mater. Sci. 45(1), 127–132 (2009)

    Article  Google Scholar 

  24. Eldredge, N., Gould, S.J.: Punctuated equilibria: an alternative to phyletic gradualism. In: Schopf, T.J.M. (ed.) Models in Paleobiology, pp. 82–115. Freeman Cooper, San Francisco (1972)

    Google Scholar 

  25. Feng, Y., Cheng, L., Liu, H.: Putative global minimum structures of morse clusters as a function of the range of the potential: \(161 \le \text{ n } \le 240\). J. Phys. Chem. A 113(49), 13651–13655 (2009)

    Article  Google Scholar 

  26. Fernández, F., Tomassini, M., Punch, W., Sánchez, J.: Experimental study of multipopulation parallel genetic programming. In: Poli, R., Banzhaf, W., Langdon, W.B., Miller, J.F., Nordin, P., Fogarty, T.C. (eds.) Genetic Programming, vol. 1802, pp. 283–293. Springer, Berlin (2000)

    Chapter  Google Scholar 

  27. Fernández, F., Tomassini, M., Vanneschi, L.: An empirical study of multipopulation genetic programming. Genet. Program. Evol. Mach. 4, 21–51 (2003)

    Article  MATH  Google Scholar 

  28. Goldberg, D.E., Deb, K.: A comparative analysis of selection schemes used in genetic algorithms. In: Rawlins, G. (ed.) Foundations of Genetic Algorithms, pp. 69–93. Morgan Kaufmann, San Mateo (1991)

    Google Scholar 

  29. Grefenstette, J.J.: Parallel Adaptive Algorithms for Function Optimization: (preliminary Report). Vanderbilt University, Computer Science Department (1981)

  30. Gregurick, S.K., Alexander, M.H., Hartke, B.: Global geometry optimization of \(\text{(Ar) }_{n}\) and \(\text{ B(Ar) }_{n}\) clusters using a modified genetic algorithm. J. Chem. Phys. 104, 2684–2691 (1996)

    Article  Google Scholar 

  31. Grosso, A., Locatelli, M., Schoen, F.: A population-based approach for hard global optimization problems based on dissimilarity measures. Math. Program. 110, 373–404 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  32. Grosso, P.B.: Computer simulations of genetic adaptation: parallel subcomponent interaction in a multilocus model. Ph.D. thesis (1985)

  33. Guimarães, F.F., Belchior, J.C., Johnston, R.L., Roberts, C.: Global optimization analysis of water clusters \((\text{ h }_{2}\text{ o })_{n}\) \((11\le \text{ n }\le 13)\) through a genetic evolutionary approach. J. Chem. Phys. 116, 8327–8333 (2002)

    Article  Google Scholar 

  34. Hartke, B.: Global geometry optimization of clusters using genetic algorithms. J. Phys. Chem. 97(39), 9973–9976 (1993)

    Article  Google Scholar 

  35. Hartke, B.: Global cluster geometry optimization by a phenotype algorithm with niches: location of elusive minima, and low-order scaling with cluster size. J. Comput. Chem. 20(16), 1752–1759 (1999)

    Article  Google Scholar 

  36. Hartke, B.: Application of evolutionary algorithms to global cluster geometry optimization. In: Johnston, R.L. (ed.) Applications of Evolutionary Computation in Chemistry, vol. 110, pp. 33–53. Springer, Berlin (2004)

    Chapter  Google Scholar 

  37. Hobday, S., Smith, R.: Optimisation of carbon cluster geometry using a genetic algorithm. J. Chem. Soc. Faraday Trans. 93(22), 3919–3926 (1997)

    Article  Google Scholar 

  38. Holland, J.: A universal computer capable of executing an arbitrary number of sub-programs simultaneously. In: Eastern Joint IRE-AIEE-ACM Computer Conference, pp. 108–113. ACM (1959)

  39. Holland, J.: Iterative circuit computers. In: Western Joint IRE-AIEE-ACM Computer Conference, pp. 259–265. ACM (1960)

  40. Iwamatsu, M.: Global geometry optimization of silicon clusters using the space-fixed genetic algorithm. J. Chem. Phys. 112, 10976–10983 (2000)

    Article  Google Scholar 

  41. Johnston, R.L.: Evolving better nanoparticles: genetic algorithms for optimising cluster geometries. Dalton Trans. 22, 4193–4207 (2003)

    Article  Google Scholar 

  42. Jones, J.E.: On the determination of molecular fields. II. From the equation of state of a gas. R. Soc. Lond. Proc. Ser. A 106, 463–477 (1924)

    Article  Google Scholar 

  43. Krasnogor, N.: Towards robust memetic algorithms. In: Hart, W.E., Krasnogor, N., Smith, J.E. (eds.) Recent Advances in Memetic Algorithms, pp. 185–207. Springer, Berlin (2004)

    Google Scholar 

  44. Krasnogor, N., Blackburne, B., Burke, E.K., Hirst, J.D.: Multimeme algorithms for protein structure prediction. In: Merelo, J.J., Adamidis, P., Beyer, H.G. (eds.) Parallel Problem Solving from Nature–PPSN VII, pp. 769–778. Springer, Berlin (2002)

    Chapter  Google Scholar 

  45. Lee, J., Lee, I.H., Lee, J.: Unbiased global optimization of Lennard-Jones clusters for \(n\le 201\) using the conformational space annealing method. Phys. Rev. Lett. 91(8), 080,201 (2003)

    Article  Google Scholar 

  46. Leitão, A., Pereira, F.B., Machado, P.: Enhancing cluster geometry optimization with island models. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC 2012, Brisbane, Australia, June 10–15, 2012, pp. 1–8. IEEE (2012)

  47. Lennard-Jones, J.E.: Cohesion. Proc. Phys. Soc. 43, 461–482 (1931)

    Article  Google Scholar 

  48. Lin, S., Punch III, W., Goodman, E.: Coarse-grain parallel genetic algorithms: categorization and new approach. In: Proceedings of the 6th IEEE Symposium on Parallel and Distributed Processing, pp. 28–37 (1994)

  49. Liu, D.C., Nocedal, J.: On the limited memory bfgs method for large scale optimization. Math. Program. 45, 503–528 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  50. Locatelli, M., Schoen, F.: Fast global optimization of difficult Lennard-Jones clusters. Comput. Optim. Appl. 21, 55–70 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  51. Locatelli, M., Schoen, F.: Efficient algorithms for large scale global optimization: Lennard-Jones clusters. Comput. Optim. Appl. 26, 173–190 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  52. Lozano, M., Herrera, F., Krasnogor, N., Molina, D.: Real-coded memetic algorithms with crossover hill-climbing. Evol. Comput. 12(3), 273–302 (2004)

    Article  Google Scholar 

  53. Mahfoud, S.W.: Niching methods for genetic algorithms. Ph.D. thesis (1995)

  54. Marques, J.M.C., Llanio-Trujillo, J.L., Abreu, P.E., Pereira, F.B.: How different are two chemical structures? J. Chem. Inf. Model. 50(12), 2129–2140 (2010)

    Article  Google Scholar 

  55. Martin, W.N., Lienig, J., Cohoon, J.P.: Island (migration) Models: Evolutionary Algorithms Based on Punctuated Equilibria. Oxford University Press Inc, New York (1997)

    Google Scholar 

  56. Morse, P.M.: Diatomic molecules according to the wave mechanics. ii. vibrational levels. Phys. Rev. 34(1), 57–64 (1929)

    Article  MATH  Google Scholar 

  57. Munetomo, M., Takai, Y., Sato, Y.: An efficient migration scheme for subpopulation-based asynchronously parallel genetic algorithms. In: Proceedings of the 5th International Conference on Genetic Algorithms, p. 649. Morgan Kaufmann Publishers Inc. (1993)

  58. Niesse, J.A., Mayne, H.R.: Global geometry optimization of atomic clusters using a modified genetic algorithm in space-fixed coordinates. J. Chem. Phys. 105, 4700–4706 (1996)

    Article  Google Scholar 

  59. Pelta, D.A., Krasnogor, N.: Multimeme algorithms using fuzzy logic based memes for protein structure prediction. In: Recent Advances in Memetic Algorithms, pp. 49–64. Springer, Berlin (2005)

  60. Pereira, F., Marques, J.: A self-adaptive evolutionary algorithm for cluster geometry optimization. In: Proceedings of the 8th International Conference on Hybrid Intelligent Systems, pp. 678–683 (2008)

  61. Pereira, F., Marques, J.: A study on diversity for cluster geometry optimization. Evol. Intell. 2, 121–140 (2009)

    Article  Google Scholar 

  62. Pereira, F., Marques, J., Leitao, T., Tavares, J.: Analysis of locality in hybrid evolutionary cluster optimization. In: Evolutionary Computation, 2006. CEC 2006. IEEE Congress on, pp. 2285–2292 (2006)

  63. Pereira, F.B., Marques, J., Leitao, T., Tavares, J.: Designing efficient evolutionary algorithms for cluster optimization: a study on locality. In: Advances in Metaheuristics for Hard Optimization. Natural Computing Series, pp. 223–250. Springer, Berlin (2008)

  64. Pullan, W.: Genetic operators for the atomic cluster problem. Comput. Phys. Commun. 107(1–3), 137–148 (1997)

    Article  MATH  Google Scholar 

  65. Pullan, W.: An unbiased population-based search for the geometry optimization of Lennard-Jones clusters: \(2 \le \text{ n } \le 372\). J. Comput. Chem. 26(9), 899–906 (2005)

    Article  Google Scholar 

  66. Rata, I., Shvartsburg, A.A., Horoi, M., Frauenheim, T., Siu, K.W.M., Jackson, K.A.: Single-parent evolution algorithm and the optimization of Si clusters. Phys. Rev. Lett. 85, 546–549 (2000)

    Article  Google Scholar 

  67. Roberts, C., Johnston, R.L., Wilson, N.T.: A genetic algorithm for the structural optimization of morse clusters. Theor. Chem. Acc. Theory Comput. Model. 104, 123–130 (2000)

    Article  Google Scholar 

  68. Sastry, K., Xiao, G.: Cluster optimization using extended compact genetic algorithm. Urbana 51, 61,801 (1989)

    Google Scholar 

  69. Sekaj, I.: Robust parallel genetic algorithms with re-initialisation. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Guervós, J.J.M., Bullinaria, J.A., Rowe, J.E., Tiño, P., Kabán, A., Schwefel, H.P. (eds.) Parallel Problem Solving from Nature—PPSN VIII, vol. 3242, pp. 411–419. Springer, Berlin (2004)

  70. Shao, X., Cheng, L., Cai, W.: A dynamic lattice searching method for fast optimization of Lennard-Jones clusters. J. Comput. Chem. 25(14), 1693–1698 (2004)

    Article  Google Scholar 

  71. Skolicki, Z.: An analysis of island models in evolutionary computation. In: Proceedings of the 2005 Workshops on Genetic and Evolutionary Computation, GECCO ’05, pp. 386–389. ACM (2005)

  72. Skolicki, Z., De Jong, K.: The influence of migration sizes and intervals on island models. In: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, GECCO ’05, pp. 1295–1302. ACM (2005)

  73. Smirnov, B.M., Strizhev, A.Y., Berry, R.S.: Structures of large Morse clusters. J. Chem. Phys. 110, 7412–7420 (1999)

    Article  Google Scholar 

  74. Smith, J.: On replacement strategies in steady state evolutionary algorithms. Evol. Comput. 15, 29–59 (2007)

    Article  Google Scholar 

  75. Stillinger, F.H.: Exponential multiplicity of inherent structures. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 59, 48–51 (1999)

    Google Scholar 

  76. Taillard, É.D., Waelti, P., Zuber, J.: Few statistical tests for proportions comparison. Eur. J. Oper. Res. 185(3), 1336–1350 (2008)

    Article  MATH  Google Scholar 

  77. Tanese, R.: Parallel genetic algorithms for a hypercube. In: Proceedings of the Second International Conference on Genetic Algorithms and Their Application, pp. 177–183. L. Erlbaum Associates Inc. (1987)

  78. Tanese, R.: Distributed genetic algorithm. In: Proceedings of the Third International Conference on Genetic Algorithms, pp. 434–439 (1989)

  79. Tanese, R.: Distributed genetic algorithms for function optimization. Tech. rep. (1989)

  80. Tsai, C.J., Jordan, K.D.: 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 \(\text{(Ar) }_{13}\) and \((\text{ H }_{2}\text{ O })_{8}\) clusters. J. Chem. Phys. 99, 6957–6970 (1993)

    Article  Google Scholar 

  81. Whitley, D., Rana, S., Heckendorn, R.: The island model genetic algorithm: on separability, population size and convergence. J. Comput. Inf. Technol. 7, 33–48 (1999)

    Google Scholar 

  82. Whitley, D., Starkweather, T.: Genitor II: a distributed genetic algorithm. J. Exp. Theor. Artif. Intell. 2(3), 189–214 (1990)

    Article  Google Scholar 

  83. Whitley, L.D.: The genitor algorithm and selection pressure: why rank-based allocation of reproductive trials is best. In: Proceedings of the 3rd International Conference on Genetic Algorithms, pp. 116–123 (1989)

  84. Xiao, Y., Williams, D.E.: Genetic algorithm: a new approach to the prediction of the structure of molecular clusters. Chem. Phys. Lett. 215, 17–24 (1993)

    Article  Google Scholar 

  85. Zeiri, Y.: Prediction of the lowest energy structure of clusters using a genetic algorithm. Phys. Rev. E 51(4), R2769 (1995)

    Article  Google Scholar 

  86. Zhao, J., Xie, R.H.: Genetic algorithms for the geometry optimization of atomic and molecular clusters. J. Comput. Theor. Nanosci. 1(2), 117–131 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Informatics Engineering, CISUC, University of Coimbra, 3030-290, Coimbra, Portugal

    António Leitão, Francisco Baptista Pereira & Penousal Machado

  2. Instituto Politécnico de Coimbra, ISEC, Rua Pedro Nunes, 3030-199, Coimbra, Portugal

    Francisco Baptista Pereira

Authors
  1. António Leitão
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francisco Baptista Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Penousal Machado
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to António Leitão.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Leitão, A., Pereira, F.B. & Machado, P. Island models for cluster geometry optimization: how design options impact effectiveness and diversity. J Glob Optim 63, 677–707 (2015). https://doi.org/10.1007/s10898-015-0302-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-015-0302-7

Keywords

Search

Navigation