The Simple Genetic Algorithm: Foundations and Theory
The Simple Genetic Algorithm: Foundations and Theory
Group properties of crossover and mutation
Evolutionary Computation
Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory
Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory
A Normed Space of Genetic Operators with Applications to Scalability Issues
Evolutionary Computation
Finiteness of the fixed point set for the simple genetic algorithm
Evolutionary Computation
On the movement of vertex fixed points in the simple GA
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
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The infinite populationmodel for the genetic algorithm,where the iteration of the genetic algorithm corresponds to an iteration of a map G, is a discrete dynamical system. The map G is a composition of a selection operator and a mixing operator, where the latter models the effects of both mutation and crossover. This paper shows that for a typical mixing operator, the fixed point set of G is finite. That is, an arbitrarily small perturbation of the mixing operator will result in a map G with finitely many fixed points. Further, any sufficiently small perturbation of the mixing operator preserves the finiteness of the fixed point set.