Growth curves and takeover time in distributed evolutionary algorithms

Abstract

This paper presents a study of different models for the growth curves and takeover time in a distributed EA (dEA). The calculation of the takeover time and the dynamical growth curves is a common analytical approach to measure the selection pressure of an EA. This work is a first step to mathematically unify and describe the roles of the migration rate and the migration frequency in the selection pressure induced by the dynamics of dEAs. In order to achieve these goals we evaluate the appropriateness of the well-known logistic model and of a hypergraph model for dEAs. After that, we propose a corrected hypergraph model and two new models based in an extension of the logistic one. Our results show that accurate models for growth curves can be defined for dEAs, and explain analytically the migration rate and frequency effects. © Springer-Verlag Berlin Heidelberg 2004.