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Kramers problem in evolutionary strategies.

J Dunkel1, W Ebeling, L Schimansky-Geier

  • 1Institut für Physik, Humboldt-Universität zu Berlin, Germany. dunkel@physik.hu-berlin.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
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This study compares escape rates of Smoluchowski and Fisher-Eigen processes in double-well potentials. A combined Fisher-Eigen and Smoluchowski strategy proves most effective for barrier surmounting.

Area of Science:

  • Physics
  • Computational Biology
  • Biophysics

Background:

  • Metastable systems exhibit complex dynamics.
  • Understanding escape rates is crucial for modeling barrier crossing phenomena.
  • Brownian motion and evolutionary strategies offer frameworks for studying these dynamics.

Purpose of the Study:

  • To compare the escape rates of the Smoluchowski process and the Fisher-Eigen process.
  • To evaluate the efficiency of physically and biologically inspired evolutionary strategies for barrier surmounting.
  • To identify optimal strategies for navigating metastable landscapes.

Main Methods:

  • Calculation of escape rates for a one-dimensional symmetric double-well potential.
  • Modeling dynamics using the Smoluchowski process (overdamped Brownian motion).

Related Experiment Videos

  • Modeling dynamics using the Fisher-Eigen process (global coupling).

    • Main Results:

    • The Smoluchowski process relies on local dynamics, while the Fisher-Eigen process uses global coupling.
    • Both processes serve as archetypes for evolutionary strategies in numerical optimization.
    • A combined strategy, initiating with the Fisher-Eigen process, demonstrated superior effectiveness.

    Conclusions:

    • The Fisher-Eigen process offers a distinct approach to barrier surmounting compared to local dynamics.
    • Hybrid strategies combining global and local dynamics can enhance efficiency.
    • The findings provide insights into optimizing evolutionary strategies for complex potential landscapes.