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Optimisation of algorithm control parameters in cultural differential evolution applied to molecular crystallography

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Abstract

Evolutionary search and optimisation algorithms have been used successfully in many areas of materials science and chemistry. In recent years, these techniques have been applied to, and revolutionised the study of crystal structures from powder diffraction data. In this paper we present the application of a hybrid global optimisation technique, cultural differential evolution (CDE), to crystal structure determination from powder diffraction data. The combination of the principles of social evolution and biological evolution, through the pruning of the parameter search space shows significant improvement in the efficiency of the calculations over traditional dictates of biological evolution alone. Results are presented in which a range of algorithm control parameters, i.e., population size, mutation and recombination rates, extent of culture-based pruning are used to assess the performance of this hybrid technique. The effects of these control parameters on the speed and efficiency of the optimisation calculations are discussed, and the potential advantages of the CDE approach demonstrated through an average 40% improvement in terms of speed of convergence of the calculations presented, and a maximum gain of 68% with larger population size.

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References

  1. Johnston R L, ed. Applications of Evolutionary Computation in Chemistry. In: Mingos D M P. Structure and Bonding. Berlin/Heidelberg: Springer, 2004, 110

  2. Harris K D M, Tremayne M, Kariuki B M. Contemporary advances in the use of powder X-ray diffraction for structure determination. Angewandte Chemie International Edition, 2001, 40: 1626–1651

    Article  Google Scholar 

  3. David W I F, Shankland K, McCusker L B, Baerlocher C, eds. Structure Determination from Powder Diffraction Data. Oxford: Oxford University Press, 2002

    Google Scholar 

  4. Reynolds R G. An introduction to cultural algorithms. In: Sebald A V, Fogel L J, eds. In: Proceedings of the Third Annual Conference on Evolutionary Programming. Singapore: World Scientific Press, 1994, 131–139

    Google Scholar 

  5. Reynolds R G. Cultural Algorithms: Theory and Applications. In: Corne D, Dorigo M, Glover F, eds. New Ideas in Optimisation. London: McGraw-Hill, 1999, 367–377

    Google Scholar 

  6. Engelbrecht A P. Computational Intelligence: An Introduction. Chichester: John Wiley & Sons, 2001, 171–175

    Google Scholar 

  7. Chong S Y, Tremayne M. Combined optimization using cultural and differential evolution: application to crystal structure solution from powder diffraction data. Chemical Communications, 2006, 4078–4080

  8. Storn R, Price K V. Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimisation, 1997, 11: 341–359

    Article  MATH  MathSciNet  Google Scholar 

  9. Chisholm K. Co-evolving draughts strategies with differential evolution. In: Corne D, Dorigo M, Glover F, eds. New Ideas in Optimisation. London: McGraw-Hill, 1999, 147–158

    Google Scholar 

  10. Feoktistov V. Differential Evolution: In Search of Solutions. New York: Springer, 2006

    MATH  Google Scholar 

  11. Wormington M, Panaccione C, Matney K M, Bowen D K. Characterisation of structures from X-ray scattering data using genetic algorithms. Philosophical Transactions of the Royal Society A, 1999, 357(1761): 2827–2848

    Article  Google Scholar 

  12. Bjorck M, Andersson G. GenX: an extensible X-ray reflectivity re-finement program utilizing differential evolution. Journal of Applied Crystallography, 2007, 40: 1174–1178

    Article  Google Scholar 

  13. Seaton C C, Blagden N. Designing molecular interfaces. American Crystallographic Association Transactions, 2004, 39: 90–102

    Google Scholar 

  14. Chakraborti N, Mishra P, Erkoc S. A study of the Cu clusters using Gray-coded genetic algorithms and differential evolution. Journal of Phase Equilibria and Diffusion, 2004, 25: 16–21

    Article  Google Scholar 

  15. McRee D E. Differential evolution for protein crystallographic optimizations. Acta Crystallographica, 2004, D60: 2276–2279

    Google Scholar 

  16. Thomsen R, Christensen M K. MolDock: A new technique for highaccuracy molecular docking. Journal of Medicinal Chemistry, 2006, 49: 3315–3321

    Article  Google Scholar 

  17. Oeckler O, Weber T, Kienle L, Mattausch H, Simon A. Cluster disorder and ordering principles in Al-stabilized “Lal”. Angewandte Chemie International Edition, 2005, 44: 3917–3921

    Article  Google Scholar 

  18. Burgi H B, Hauser J, Weber T, Neder R B. Supramolecular architecture in a disordered perhydrotriphenylene inclusion compound from diffuse X-ray diffraction data. Crystal Growth and Design, 2005, 5: 2073–2083

    Article  Google Scholar 

  19. Tremayne M, Seaton C C, Glidewell C. Structures of three substituted arenesulfonamides from X-ray powder diffraction data using the differential evolution technique. Acta Crystallographica, 2002, B58: 823–834

    Google Scholar 

  20. Seaton C C, Tremayne M. Differential evolution: crystal structure determination of a triclinic polymorph of adipamide from powder diffraction data. Chemical Communications, 2002, 880–881

  21. Chong S Y, Seaton C C, Kariuki B M, Tremayne M. Molecular versus crystal symmetry in tri-substituted triazine, benzene and isocyanurate derivatives. Acta Crystallographica, 2006, B62: 864–874

    Google Scholar 

  22. Price K V. An introduction to differential evolution. In: Corne D, Dorigo M, Glover F, eds. New Ideas in Optimisation. London: McGraw-Hill, 1999, 77–108

    Google Scholar 

  23. Harris K D M, Johnston R L, Kariuki B M. The genetic algorithm: Foundations and applications in structure solution from powder diffraction data. Acta Crystallographica, 1998, A54: 632–645

    Google Scholar 

  24. Cheung E Y, McCabe E E, Harris K D M, Johnston R L, Raja K M P, Balaram P. C-H… O hydrogen bond mediated chain reversal in a peptide containing a γ-amino acid residue, determined directly from powder X-ray diffraction data. Angewandte Chemie International Edition, 2002, 41: 494–496

    Article  Google Scholar 

  25. Gao F, Liu H, Zhao Q, Cui G. Hybrid model of genetic algorithm and cultural algorithms for optimisation problem. In: Proceedings of Simulated Evolution and Learning, LNCS, 2006, 4247: 441–448

    Article  Google Scholar 

  26. Xue Z G, Guo Y N. Improved cultural algorithm based on genetic algorithm. In: Proceedings of IEEE International Conference on Integration Technology, 2007, 117–122

  27. Gao F, Zhao Q, Liu H W, Cui G. Cultural genetic algorithm for constrained optimisation problem. Dynamics of Continuous Discrete and Impulsive Systems-Series B-Applications and Algorithms, 2007, 1: 85–90

    Google Scholar 

  28. Nguyen T T, Yao X. An experimental study of hybridizing cultural algorithms and local search. International Journal of Neural Systems, 2008, 18: 1–17

    Article  Google Scholar 

  29. Becerra R L, Coello Coello A C. Cultured differential evolution for constrained optimisation. Computer Methods in Applied Mechanical Engineering, 2006, 195: 4303–4322

    Article  MATH  Google Scholar 

  30. Becerra R L, Coello Coello A C. Optimisation with constraints using a cultured differential evolution approach. In: Proceedings of GECCO2005: Genetic and Evolutionary Computation Conference, 2005, 1–2: 27–34

    Article  Google Scholar 

  31. Chong S Y. Development of novel evolutionary algorithms for crystal structure determination from powder diffraction data. PhD Thesis. Birmingham: University of Birmingham, 2006

    Google Scholar 

  32. Rossi M, Meyer R, Constantinou P, Caruso F, Castelbuono D, O’Brien M, Narasimhan V. Molecular structure and activity toward DNA of baicalein, a flavone constituent of the asian herbal medicine “Shosaiko-to”. Journal of Natural Products, 2001, 64: 26–31

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Chemistry, University of Birmingham, Birmingham, B15 2TT, UK

    Maryjane Tremayne, Samantha Y. Chong & Duncan Bell

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  1. Maryjane Tremayne
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  2. Samantha Y. Chong
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  3. Duncan Bell
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Correspondence to Maryjane Tremayne.

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Tremayne, M., Chong, S.Y. & Bell, D. Optimisation of algorithm control parameters in cultural differential evolution applied to molecular crystallography. Front. Comput. Sci. China 3, 101–108 (2009). https://doi.org/10.1007/s11704-009-0009-3

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  • DOI: https://doi.org/10.1007/s11704-009-0009-3

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