Finiteness of the Fixed Point Set for the Simple Genetic Algorithm

Author:

Wright Alden H.1,Vose Michael D.2

Affiliation:

1. Department of Computer Science The University of Montana Missoula, MT 59812-1008

2. Department of Computer Science The University of Tennessee Knoxville, TN 37996-1301

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.

Publisher

MIT Press - Journals

Subject

Computational Mathematics

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A Special Mutation Operator in the Genetic Algorithm for Fixed Point Problems;Journal of Function Spaces;2023-04-17

2. The Convergence Mechanism and Strategies for Non-Elitist Genetic Programming;Applied Mechanics and Materials;2013-08

3. A discipline of evolutionary programming;Theoretical Computer Science;2000-06

4. Random heuristic search;Theoretical Computer Science;1999-11

5. Genericity of the Fixed Point Set for the Infinite Population Genetic Algorithm;Foundations of Genetic Algorithms

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