Genetic algorithms: bridging the convergence gap
Theoretical Computer Science - Special issue on evolutionary computation
On the convergence rates of genetic algorithms
Theoretical Computer Science - Special issue on evolutionary computation
Theoretical Computer Science
The Simple Genetic Algorithm: Foundations and Theory
The Simple Genetic Algorithm: Foundations and Theory
Genetic Programming and Evolvable Machines
Theoretical Analysis of Mutation-Adaptive Evolutionary Algorithms
Evolutionary Computation
Schema theory for genetic programming with one-point crossover and point mutation
Evolutionary Computation
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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This paper focuses on the limit behaviors of evolutionary algorithms based on finite search space by using the properties of Markov chains and Perron-Frobenius Theorem. Some convergence results of general square matrices are given, and some useful properties of homogeneous Markov chains with finite states are investigated. The geometric convergence rates of the transition operators, which is determined by the revised spectral of the corresponding transition matrix of a Markov chain associated with the EA considered here, are estimated. Some applications of the theoretical results in this paper are also discussed.