The Simple Genetic Algorithm: Foundations and Theory
The Simple Genetic Algorithm: Foundations and Theory
Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory
Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory
EA models and population fixed-points versus mutation rates for functions of unitation
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Strong recombination, weak selection, and mutation
Proceedings of the 8th annual conference on Genetic and evolutionary computation
The simple genetic algorithm and the walsh transform: Part i, theory
Evolutionary Computation
Crossover accelerates evolution in gas with a babel-like fitness landscape: Mathematical analyses
Evolutionary Computation
Genericity of the fixed point set for the infinite population genetic algorithm
FOGA'07 Proceedings of the 9th international conference on Foundations of genetic algorithms
Hyperbolicity of the fixed point set for the simple genetic algorithm
Theoretical Computer Science
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The Vose dynamical system model of the simple genetic algorithm models the behavior of this algorithm for large population sizes and is the basis of the exact Markov chain model. Populations consisting of multiple copies of one individual correspond to vertices of the simplex. For zero mutation, these are fixed points of the dynamical system and absorbing states of the Markov chain. For proportional selection, the asymptotic stability of vertex fixed points is understood from previous work. We derive the eigenvalues of the differential at vertex fixed points of the dynamical system model for tournament selection. We show that as mutation increases from zero, hyperbolic asymptotically stable fixed points move into the simplex, and hyperbolic asymptotically unstable fixed points move outside of the simplex. We calculate the derivative of local path of the fixed point with respect to the mutation rate for proportional selection. Simulation analysis shows how fixed points bifurcate with larger changes in the mutation rate and changes in the crossover rate.