Continuous Dynamical System Models of Steady-State Genetic Algorithms

posted 2/16/00

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
(406) 243-4790

Jonathon E. Rowe
Artificial Intelligence Group
Dept. Computer & Information Science
De Montfort University
Milton Keynes MK7 6HP
Great Britain

Abstract

This paper constructs discrete-time and continuous-time dynamical system
expected value and infinite population models for steady-state 
genetic and evolutionary search algorithms.  Conditions are given under 
which the discrete-time expected value models converge to the
continuous-time models as the population size goes to infinity.
Existence and uniqueness theorems are proved for solutions of
the continuous-time models.
The fixed points of these models and their asymptotic stability
are compared.