Theoretical Computer Science
The Simple Genetic Algorithm: Foundations and Theory
The Simple Genetic Algorithm: Foundations and Theory
A New Interpretation of Schema Notation that Overtums the Binary Encoding Constraint
Proceedings of the 3rd International Conference on Genetic Algorithms
Population aggregation based on fitness
Natural Computing: an international journal
Crossover Invariant Subsets of the Search Space for Evolutionary Algorithms
Evolutionary Computation
An Extension of Geiringer's Theorem for a Wide Class of Evolutionary Search Algorithms.
Evolutionary Computation
Some results about the Markov chains associated to GPs and general EAs
Theoretical Computer Science - Foundations of genetic algorithms
Differentiable coarse graining
Theoretical Computer Science - Foundations of genetic algorithms
SEAL'06 Proceedings of the 6th international conference on Simulated Evolution And Learning
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Using markov-chain mixing time estimates for the analysis of ant colony optimization
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Natural Computing: an international journal
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In this work, a method is presented for analysis of Markov chains modeling evolutionary algorithms through use of a suitable quotient construction. Such a notion of quotient of a Markov chain is frequently referred to as "coarse graining" in the evolutionary computation literature. We shall discuss the construction of a quotient of an irreducible Markov chain with respect to an arbitrary equivalence relation on the state space. The stationary distribution of the quotient chain is "coherent" with the stationary distribution of the original chain. Although the transition probabilities of the quotient chain depend on the stationary distribution of the original chain, we can still exploit the quotient construction to deduce some relevant properties of the stationary distribution of the original chain. As one application, we shall establish inequalities that describe how fast the stationary distribution of Markov chains modeling evolutionary algorithms concentrates on the uniform populations as the mutation rate converges to 0. Further applications are discussed. One of the results related to the quotient construction method is a significant improvement of the corresponding result of the authors' previous conference paper [Mitavskiy et al. (2006) In: Simulated Evolution and Learning, Proceedings of SEAL 2006, Lecture Notes in Computer Science v. 4247, Springer Verlag, pp 726---733]. This papers implications are all strengthened accordingly.