Genetic algorithms (GA) are efficient global optimization techniques in which the fittest individuals of a population survive and spawn next improved generations. They give the opportunity to find some rough crystal structure models of powders. In order to refine the structural model it is essential to use a full-profile fitting of powder patterns by Rietveld method. That fitting is based on non-linear least-square method (NLSM) requiring good initial approximations of refined parameters. Thereby its convergence for solutions found by conventional GA is unlikely in cases of complicated multi-phases samples. This work is dedicated to GA spread-out to Rietveld method including full-profile fitting and refinement of crystal structure models. A two-level hybrid genetic algorithm has been developed for this purpose. The hybrid algorithm is based on composition of the dual GA with the NLSM designed as follows. First-level GA chromosomes comprise values of profile and structure parameters used in the Rietveld method. Second-level GA chromosome is a bit string containing one bit per each parameter, where bit values define parameters to be refined with the NLSM on a current iteration. GA fitness function is based on the usual weighted profile R-factor (Rwp). The first-level GA is helpful in searching initial parameter values of acceptable Rwp and overcoming local minima. The second-level GA manages NLSM full-profile fitting with found initial parameter values. It also gives the opportunity to reduce dimensionality of the problem by using number of the user-defined parametric masks that correspond to empiric refinement techniques. The algorithm was implemented as a shell over the full-profile analysis program DDM [1] and was tested on some powder patterns of single and multi-phases samples with known stable crystal structures. 1. Solovyov L. A. // J. Appl. Cryst. 2004. 37. 743-749.

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1. RETRIEVE for XRD phase and structure analysis of powder patterns