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Solving Variational Problems Via Evolutionary Algorithm

Author

Listed:
  • 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;
    NSC Kharkov Institute of Physics and Technology, National Academy of Sciences of Ukraine, 1 Akademicheskaya St., Kharkov UA 61108, Ukraine)

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.

Suggested Citation

  • V. Yu. Korda & S. V. Berezovsky & A. S. Molev & V. F. Klepikov & L. P. Korda, 2013. "Solving Variational Problems Via Evolutionary Algorithm," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(03), pages 1-13.
    • Handle: RePEc:wsi:ijmpcx:v:24:y:2013:i:03:n:s0129183113500095
    DOI: 10.1142/S0129183113500095
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