Kramers problem in evolutionary strategies

Abstract

We calculate the escape rates of different dynamical processes for the case of a one-dimensional symmetric double-well potential. In particular, we compare the escape rates of a Smoluchowski process, i.e., a corresponding overdamped Brownian motion dynamics in a metastable potential landscape, with the escape rates obtained for a biologically motivated model known as the Fisher-Eigen process. The main difference between the two models is that the dynamics of the Smoluchowski process is determined by local quantities, whereas the Fisher-Eigen process is based on a global coupling (nonlocal interaction). If considered in the context of numerical optimization algorithms, both processes can be interpreted as archetypes of physically or biologically inspired evolutionary strategies. In this sense, the results discussed in this work are utile in order to evaluate the efficiency of such strategies with regard to the problem of surmounting various barriers. We find that a combination of both scenarios, starting with the Fisher-Eigen strategy, provides a most effective evolutionary strategy. © 2003 The American Physical Society.