Journal of Global Optimization

, Volume 63, Issue 4, pp 677–707 | Cite as

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

  • António LeitãoEmail author
  • Francisco Baptista Pereira
  • Penousal Machado


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.


Cluster geometry optimization Island models Diversity 


  1. 1.
  2. 2.
    Alba, E., Tomassini, M.: Parallelism and evolutionary algorithms. Evol. Comput. IEEE Trans. 6(5), 443–462 (2002)CrossRefGoogle Scholar
  3. 3.
    Alba, E., Troya, J.: A survey of parallel distributed genetic algorithms. Complexity 4(4), 31–52 (1999)MathSciNetCrossRefGoogle Scholar
  4. 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)Google Scholar
  5. 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. 6.
    Cantú-Paz, E.: A survey of parallel genetic algorithms. Calculateurs paralleles, reseaux et systems repartis 10(2), 141–171 (1998)Google Scholar
  7. 7.
    Cantú-Paz, E.: Migration policies, selection pressure, and parallel evolutionary algorithms. J. Heuristics 7, 311–334 (2001)zbMATHCrossRefGoogle Scholar
  8. 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. 9.
    Cantú-Paz, E., Mejia-Olvera, M.: Experimental results in distributed genetic algorithms. In: International Symposium on Applied Corporate Computing, pp. 99–108 (1994)Google Scholar
  10. 10.
    Cassioli, A., Locatelli, M., Schoen, F.: Global optimization of binary Lennard–Jones clusters. Optim. Methods Softw. 24, 819–835 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Cassioli, A., Locatelli, M., Schoen, F.: Dissimilarity measures for population-based global optimization algorithms. Comput. Optim. Appl. 45, 257–281 (2010)zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Cheng, L.: A connectivity table for cluster similarity checking in the evolutionary optimization method. Chem. Phys. Lett. 389, 309–314 (2004)CrossRefGoogle Scholar
  13. 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)CrossRefGoogle Scholar
  14. 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)CrossRefGoogle Scholar
  15. 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)Google Scholar
  16. 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)Google Scholar
  17. 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)CrossRefGoogle Scholar
  18. 18.
    De Jong, K.: An analysis of the behavior of a class of genetic adaptive systems. Ph.D. thesis (1975)Google Scholar
  19. 19.
    De Jong, K.A., Sarma, J.: Generation gaps revisited. In: Foundations of Genetic Algorihtms 2, pp. 19–28 (1992)Google Scholar
  20. 20.
    Deaven, D.M., Ho, K.M.: Molecular geometry optimization with a genetic algorithm. Phys. Rev. Lett. 75, 288–291 (1995)CrossRefGoogle Scholar
  21. 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)CrossRefGoogle Scholar
  22. 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)zbMATHCrossRefGoogle Scholar
  23. 23.
    Dugan, N., Erkoc, S.: Genetic algorithm—Monte Carlo hybrid geometry optimization method for atomic clusters. Comput. Mater. Sci. 45(1), 127–132 (2009)CrossRefGoogle Scholar
  24. 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. 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)CrossRefGoogle Scholar
  26. 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)CrossRefGoogle Scholar
  27. 27.
    Fernández, F., Tomassini, M., Vanneschi, L.: An empirical study of multipopulation genetic programming. Genet. Program. Evol. Mach. 4, 21–51 (2003)zbMATHCrossRefGoogle Scholar
  28. 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. 29.
    Grefenstette, J.J.: Parallel Adaptive Algorithms for Function Optimization: (preliminary Report). Vanderbilt University, Computer Science Department (1981)Google Scholar
  30. 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)CrossRefGoogle Scholar
  31. 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)zbMATHMathSciNetCrossRefGoogle Scholar
  32. 32.
    Grosso, P.B.: Computer simulations of genetic adaptation: parallel subcomponent interaction in a multilocus model. Ph.D. thesis (1985)Google Scholar
  33. 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)CrossRefGoogle Scholar
  34. 34.
    Hartke, B.: Global geometry optimization of clusters using genetic algorithms. J. Phys. Chem. 97(39), 9973–9976 (1993)CrossRefGoogle Scholar
  35. 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)CrossRefGoogle Scholar
  36. 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)CrossRefGoogle Scholar
  37. 37.
    Hobday, S., Smith, R.: Optimisation of carbon cluster geometry using a genetic algorithm. J. Chem. Soc. Faraday Trans. 93(22), 3919–3926 (1997)CrossRefGoogle Scholar
  38. 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)Google Scholar
  39. 39.
    Holland, J.: Iterative circuit computers. In: Western Joint IRE-AIEE-ACM Computer Conference, pp. 259–265. ACM (1960)Google Scholar
  40. 40.
    Iwamatsu, M.: Global geometry optimization of silicon clusters using the space-fixed genetic algorithm. J. Chem. Phys. 112, 10976–10983 (2000)CrossRefGoogle Scholar
  41. 41.
    Johnston, R.L.: Evolving better nanoparticles: genetic algorithms for optimising cluster geometries. Dalton Trans. 22, 4193–4207 (2003)CrossRefGoogle Scholar
  42. 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)CrossRefGoogle Scholar
  43. 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. 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)CrossRefGoogle Scholar
  45. 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)CrossRefGoogle Scholar
  46. 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)Google Scholar
  47. 47.
    Lennard-Jones, J.E.: Cohesion. Proc. Phys. Soc. 43, 461–482 (1931)CrossRefGoogle Scholar
  48. 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)Google Scholar
  49. 49.
    Liu, D.C., Nocedal, J.: On the limited memory bfgs method for large scale optimization. Math. Program. 45, 503–528 (1989)zbMATHMathSciNetCrossRefGoogle Scholar
  50. 50.
    Locatelli, M., Schoen, F.: Fast global optimization of difficult Lennard-Jones clusters. Comput. Optim. Appl. 21, 55–70 (2002)zbMATHMathSciNetCrossRefGoogle Scholar
  51. 51.
    Locatelli, M., Schoen, F.: Efficient algorithms for large scale global optimization: Lennard-Jones clusters. Comput. Optim. Appl. 26, 173–190 (2003)zbMATHMathSciNetCrossRefGoogle Scholar
  52. 52.
    Lozano, M., Herrera, F., Krasnogor, N., Molina, D.: Real-coded memetic algorithms with crossover hill-climbing. Evol. Comput. 12(3), 273–302 (2004)CrossRefGoogle Scholar
  53. 53.
    Mahfoud, S.W.: Niching methods for genetic algorithms. Ph.D. thesis (1995)Google Scholar
  54. 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)CrossRefGoogle Scholar
  55. 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. 56.
    Morse, P.M.: Diatomic molecules according to the wave mechanics. ii. vibrational levels. Phys. Rev. 34(1), 57–64 (1929)zbMATHCrossRefGoogle Scholar
  57. 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)Google Scholar
  58. 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)CrossRefGoogle Scholar
  59. 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)Google Scholar
  60. 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)Google Scholar
  61. 61.
    Pereira, F., Marques, J.: A study on diversity for cluster geometry optimization. Evol. Intell. 2, 121–140 (2009)CrossRefGoogle Scholar
  62. 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)Google Scholar
  63. 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)Google Scholar
  64. 64.
    Pullan, W.: Genetic operators for the atomic cluster problem. Comput. Phys. Commun. 107(1–3), 137–148 (1997)zbMATHCrossRefGoogle Scholar
  65. 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)CrossRefGoogle Scholar
  66. 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)CrossRefGoogle Scholar
  67. 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)CrossRefGoogle Scholar
  68. 68.
    Sastry, K., Xiao, G.: Cluster optimization using extended compact genetic algorithm. Urbana 51, 61,801 (1989)Google Scholar
  69. 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)Google Scholar
  70. 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)CrossRefGoogle Scholar
  71. 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)Google Scholar
  72. 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)Google Scholar
  73. 73.
    Smirnov, B.M., Strizhev, A.Y., Berry, R.S.: Structures of large Morse clusters. J. Chem. Phys. 110, 7412–7420 (1999)CrossRefGoogle Scholar
  74. 74.
    Smith, J.: On replacement strategies in steady state evolutionary algorithms. Evol. Comput. 15, 29–59 (2007)CrossRefGoogle Scholar
  75. 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. 76.
    Taillard, É.D., Waelti, P., Zuber, J.: Few statistical tests for proportions comparison. Eur. J. Oper. Res. 185(3), 1336–1350 (2008)zbMATHCrossRefGoogle Scholar
  77. 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)Google Scholar
  78. 78.
    Tanese, R.: Distributed genetic algorithm. In: Proceedings of the Third International Conference on Genetic Algorithms, pp. 434–439 (1989)Google Scholar
  79. 79.
    Tanese, R.: Distributed genetic algorithms for function optimization. Tech. rep. (1989)Google Scholar
  80. 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)CrossRefGoogle Scholar
  81. 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. 82.
    Whitley, D., Starkweather, T.: Genitor II: a distributed genetic algorithm. J. Exp. Theor. Artif. Intell. 2(3), 189–214 (1990)CrossRefGoogle Scholar
  83. 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)Google Scholar
  84. 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)CrossRefGoogle Scholar
  85. 85.
    Zeiri, Y.: Prediction of the lowest energy structure of clusters using a genetic algorithm. Phys. Rev. E 51(4), R2769 (1995)CrossRefGoogle Scholar
  86. 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)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • António Leitão
    • 1
    Email author
  • Francisco Baptista Pereira
    • 1
    • 2
  • Penousal Machado
    • 1
  1. 1.Department of Informatics Engineering, CISUCUniversity of CoimbraCoimbraPortugal
  2. 2.Instituto Politécnico de Coimbra, ISECCoimbraPortugal

Personalised recommendations