Name
Abstract | ||
|---|---|---|
The infinite population simple genetic algorithm is a discrete dynamical system model of a genetic algorithm. It is conjectured that trajectories in the model always converge to fixed points. This paper shows that an arbitrarily small perturbation of the fitness will result in a model with a finite number of fixed points. Moreover, every sufficiently small perturbation of fimess preserves the finiteness of the fixed point set. These results allow proofs and constructions that require finiteness of the fixed point set. For example, applying the stable manifold theorem to a fixed point requires the hyperbolicity of the differential of the transition map of the genetic algorithm, which requires (among other things) that the fixed point be isolated. |
Year | DOI | Venue |
|---|---|---|
1995 | 10.1162/evco.1995.3.3.299 | Evolutionary Computation |
Keywords | Field | DocType |
discrete dynamical system model,fixed point,finite number,small perturbation,simple genetic algorithm,infinite population,genetic algorithm,stable manifold theorem,fixed point set,transition map,dynamical system,transversality,population model,genetic algorithms,dynamic system | Schauder fixed point theorem,Mathematical optimization,Fixed-point iteration,Stable manifold theorem,Fixed-point property,Least fixed point,Hyperbolic equilibrium point,Fixed point,Fixed-point theorem,Mathematics | Journal |
Volume | Issue | ISSN |
3 | 3 | 1063-6560 |
Citations | PageRank | References |
6 | 0.77 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alden H. Wright | 1 | 330 | 45.58 |
| Michael D. Vose | 2 | 752 | 215.67 |