An important factor in the increasing number of crystal structures determined by PXRD is the development of direct space structure solution techniques [1], in which a range of predicted structural models are compared with the experimental powder data using a global optimisation technique to locate the best crystal structure solution.  A number of optimisation algorithms have been applied to this problem, but our work has focussed recently on the development of the Cultural Differential Evolution (CDE) technique [2,3].  This approach combines the traditional biological dictates of mating, mutation and natural selection in the Differential Evolution method (DE) [4,5], a relatively new algorithm that follows similar principles to conventional genetic algorithms, with an approach that models human social behaviour or cultural selection. 

We will present the progress that we have made in the development of the CDE algorithm in which ‘cultural’ behaviour or ‘peer pressure’ – in this case, the distribution in values of structural parameters in each generation – is used to guide and enhance the DE process.  This approach uses social factors to guide and speed-up evolution but natural biological selection to drive the optimisation process.  By optimisation of search control parameters such as population size, mutation rate and the degree of cultural pruning, we will demonstrate significant improvement in efficiency of our structure solution calculation in all test cases, over the DE method alone.  The advantages of cultural pruning when using relatively large population sizes with relatively high population diversity will also be presented.

Although the main focus of this presentation will be on the development and the improvements in efficiency of the CDE approach, potential pitfalls in the direct space structure solution process using any form of optimisation technique, will also be discussed.  Examples will include the effects of preferred orientation on the location of the global structure solution and refinement minima [6], and limitations that should be considered when defining structural models for use in direct-space structure solution approaches.

[1]  M. Tremayne (2004), M., Phil. Trans. R. Soc. Lond. A, 362, 2691.
[2]  S.Y. Chong, M. Tremayne (2006), Chem. Comm., 4078.
[3]  A. P. Engelbrecht (2002), in Computational Intelligence: An Introduction, John Wiley & Sons, Chichester, p171.
[4]  K.V. Price (1999), in New Ideas in Optimization (ed: Corne, D.; Dorigo, M.; Glover, F.), McGraw-Hill, London.
[5]  M. Tremayne, C.C. Seaton, C. Glidewell (2002), Acta. Cryst., B58, 823.
[6]  S.Y. Chong, C.C. Seaton, B.M. Kariuki, M. Tremayne (2006), Acta Cryst., B62, 862.

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1. Cultural Differential Evolution: combined optimisation applied to structure solution from powder diffraction data