Statistical dynamics of the Royal Road genetic algorithm
Theoretical Computer Science - Special issue on evolutionary computation
Theoretical Computer Science - Special issue on evolutionary computation
The Simple Genetic Algorithm: Foundations and Theory
The Simple Genetic Algorithm: Foundations and Theory
Simple genetic algorithms with linear fitness
Evolutionary Computation
Group properties of crossover and mutation
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
Schema analysis of average fitness in multiplicative landscape
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartI
Hyperbolicity of the fixed point set for the simple genetic algorithm
Theoretical Computer Science
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We define an abstract normed vector space where the genetic operators are elements. This is used to define the disturbance of the generational operator G as the distance between the crossover and mutation operator (combined) and the identity. This quantity appears in a bound on the variance of fixed-point populations, and in a bound on the force ||v - G(v)|| that applies to the optimal population v. When analyzed for the case of fixed-length binary strings, a connection is shown between these measures and the size of the search space. Guides for parameter settings are given, if population convergence is required as the string length tends to infinity.