Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
Convergence rates for Markov chains
SIAM Review
A computational view of population genetics
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Theoretical Computer Science
The Simple Genetic Algorithm: Foundations and Theory
The Simple Genetic Algorithm: Foundations and Theory
Group properties of crossover and mutation
Evolutionary Computation
Proceedings of the European Conference on Genetic Programming
A mathematical model of evolutionary computation and some consequences
A mathematical model of evolutionary computation and some consequences
Structural Search Spaces and Genetic Operators
Evolutionary Computation
Crossover Invariant Subsets of the Search Space for Evolutionary Algorithms
Evolutionary Computation
Some results about the Markov chains associated to GPs and general EAs
Theoretical Computer Science - Foundations of genetic algorithms
Comparing evolutionary computation techniques via their representation
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartI
Proceedings of the twelfth workshop on Foundations of genetic algorithms XII
Natural Computing: an international journal
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The frequency with which various elements of the search space of a given evolutionary algorithm are sampled is affected by the family of recombination reproduction operators. The original Geiringer theorem tells us the limiting frequency of occurrence of a given individual under repeated application of crossover alone for the classical genetic algorithm. Recently, Geiringer's theorem has been generalized to include the case of linear GP with homologous crossover which can also be thought of as a variable length GA. In the current paper we prove a general theorem which tells us that under rather mild conditions on a given evolutionary algorithm, call it A, the stationary distribution of a certain Markov chain of populations in the absence of selection is unique and uniform. This theorem not only implies the already existing versions of Geiringer's theorem, but also provides a recipe of how to obtain similar facts for a rather wide class of evolutionary algorithms. The techniques which are used to prove this theorem involve a classical fact about random walks on a group and may allow us to compute and/or estimate the eigenvalues of the corresponding Markov transition matrix which is directly related to the rate of convergence towards the unique limiting distribution.