Continuous Dynamical System Models of Steady-State Genetic Algorithms

Continuous Dynamical System Models of Steady-State Genetic
Algorithms

Alden H. Wright
Computer Science Dept.
Univ. of Montana
Missoula, MT 59812
wright@cs.umt.edu
http://www.cs.umt.edu/u/wright/wright.htm

Jonathan E. Rowe
School of Computer Science
University of Birmingham
Birmingham B15 2TT
Great Britain
J.E.Rowe@cs.bham.ac.uk


Abstract

Discrete-time dynamical system expected value models for a
general steady state genetic algorithm were constructed.
These lead to a continuous-time dynamical system
infinite population model by a process of letting the population
size go to infinity while the time step goes to zero.
Conditions were given that imply existence and uniqueness of
solutions to this model.

For the random deletion version of the steady state genetic algorithm,
the set of fixed points for the continuous-time model, the
discrete-time models, and the
infinite population model of the corresponding generational genetic
algorithm, are all the same.  An example was given that showed that
a fixed point may be stable for the continuous-time model, but unstable
for the generational GA model.