Paper Info
Title
On the movement of vertex fixed points in the simple GA
Abstract
The Vose dynamical system model of the simple genetic algorithm models the behavior of this algorithm for large population sizes and is the basis of the exact Markov chain model. Populations consisting of multiple copies of one individual correspond to vertices of the simplex. For zero mutation, these are fixed points of the dynamical system and absorbing states of the Markov chain. For proportional selection, the asymptotic stability of vertex fixed points is understood from previous work. We derive the eigenvalues of the differential at vertex fixed points of the dynamical system model for tournament selection. We show that as mutation increases from zero, hyperbolic asymptotically stable fixed points move into the simplex, and hyperbolic asymptotically unstable fixed points move outside of the simplex. We calculate the derivative of local path of the fixed point with respect to the mutation rate for proportional selection. Simulation analysis shows how fixed points bifurcate with larger changes in the mutation rate and changes in the crossover rate.
Year
DOI
Venue
2011
10.1145/1967654.1967672
FOGA
Keywords
Field
DocType
vose dynamical system model,fixed point,mutation rate,simple ga,asymptotically stable fixed point,zero mutation,fixed points bifurcate,asymptotically unstable fixed point,proportional selection,mutation increase,vertex fixed point,bifurcation,tournament selection,dynamical systems,crossover,markov chain model,markov chain,genetic algorithms,selection,fixed points,dynamic system,asymptotic stability,theory,genetic algorithm,population size
Population,Mathematical optimization,Vertex (geometry),Markov chain,Fixed-point iteration,Simplex,Dynamical systems theory,Fixed point,Dynamical system,Mathematics
Conference
Citations 
PageRank 
References 
0
0.34
13
Authors
3
Name
Order
Citations
PageRank
Alden H. Wright133045.58
Tomas Gedeon2298.71
J. Neal Richter3254.38