SOLVING VARIATIONAL PROBLEMS VIA EVOLUTIONARY ALGORITHM

V. Yu. Korda (), S. V. Berezovsky, A. S. Molev, V. F. Klepikov and L. P. Korda
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V. Yu. Korda: Institute of Electrophysics and Radiation Technologies, National Academy of Sciences of Ukraine, 28 Chernyshevsky St., P. O. Box 8812, Kharkov UA 61002, Ukraine
S. V. Berezovsky: Institute of Electrophysics and Radiation Technologies, National Academy of Sciences of Ukraine, 28 Chernyshevsky St., P. O. Box 8812, Kharkov UA 61002, Ukraine
A. S. Molev: Institute of Electrophysics and Radiation Technologies, National Academy of Sciences of Ukraine, 28 Chernyshevsky St., P. O. Box 8812, Kharkov UA 61002, Ukraine
V. F. Klepikov: Institute of Electrophysics and Radiation Technologies, National Academy of Sciences of Ukraine, 28 Chernyshevsky St., P. O. Box 8812, Kharkov UA 61002, Ukraine
L. P. Korda: Institute of Electrophysics and Radiation Technologies, National Academy of Sciences of Ukraine, 28 Chernyshevsky St., P. O. Box 8812, Kharkov UA 61002, Ukraine;

International Journal of Modern Physics C (IJMPC), 2013, vol. 24, issue 03, 1-13

Abstract: We present the evolutionary algorithm that evolves the population of numerical solutions of the variational problem. The evolved solutions are model-independent, smooth, can have a predefined shape (if needed), and satisfy boundary or any other additional conditions (if imposed). To exemplify the performance of the proposed algorithm, we show how to solve the variational problem of searching for the spatially modulated distribution of the field of order parameter that gives a minimum to the Landau-type thermodynamic potential in the theory of ferroelectrics with incommensurate phases.

Keywords: Variational problem; evolutionary computations; proper ferroelectrics; incommensurate phase; 77.80.B-; 61.44.Fw; 02.60.Pn; 64.70.Rh (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1142/S0129183113500095

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