Abstract
In this paper, we consider the problem of the study of polycrystalline substances: restoration of a substance atomic structure by full-profile analysis of powder diffraction data. This task is specific since it is not necessary to find very good solutions on average, but it is necessary to find the best one at least sometimes. To solve this problem, it is proposed to use an evolutionary algorithm based on the cooperative island model. The article describes the main stages and features of the algorithm and notes the qualitative advantages of this model in comparison with other methods (including evolutionary). The description of innovations proposed and the results of computational experiments are given. Conclusions from the experimental results are given, and further prospects for improving the efficiency of this method were noted.
Highlights
To develop materials with specified properties, we need to have fundamental knowledge that determines the structure and properties of matter at the atomic level
Direct space methods began their development with the advent of high-speed computers in the 1990s, including the Monte-Carlo method [1, 2], genetic algorithms [3, 4], and simulated annealing [5, 6]
This paper suggests ways to improve the genetic algorithm itself, which can make it less dependent on non-optimal settings
Summary
To develop materials with specified properties, we need to have fundamental knowledge that determines the structure and properties of matter at the atomic level. A common problem with these methods is the deterioration of convergence with increasing complexity of the structures being solved, which is associated with a nonlinear increase in the probability of stagnation in the numerous local minima of the hypersurface of the the objective function In practice, their application is limited by the number of degrees of freedom of the determined atomic coordinates. To search for the coordinates of atoms of a substance, it is proposed to use an evolutionary algorithm with an island model of cooperation of parallel operating evolutionary processes with the exchange of part of the solutions among the islands This approach leads to a quantitative improvement in the efficiency of the algorithm due to the wide coverage of the search space in populations on different islands and to the ability to find solutions to such complex structures that could not be solved using evolutionary processes without the exchange. The article is structured as follows: Chapter 2 discusses the specifics of the problem and the proposed approach to its solution; Chapter 3 describes the essence of the proposed cooperative exchange among evolutionary processes; Chapter 4 describes the new local search operator used to optimize the crystal structure; Chapter 5 presents the results of the experiments performed; and there are conclusions, acknowledgment, and references
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