Abstract
The infinite population model 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.
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Gedeon, T., Hayes, C., Swanson, R. (2007). Genericity of the Fixed Point Set for the Infinite Population Genetic Algorithm. In: Stephens, C.R., Toussaint, M., Whitley, D., Stadler, P.F. (eds) Foundations of Genetic Algorithms. FOGA 2007. Lecture Notes in Computer Science, vol 4436. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73482-6_6
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DOI: https://doi.org/10.1007/978-3-540-73482-6_6
Publisher Name: Springer, Berlin, Heidelberg
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