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- W4300566512 abstract "We study the simple genetic algorithm with a ranking selection mechanism (linear ranking or tournament). We denote by $ell$ the length of the chromosomes, by $m$ the population size, by $p_C$ the crossover probability and by $p_M$ the mutation probability. We introduce a parameter $sigma$, called the selection drift, which measures the selection intensity of the fittest chromosome. We show that the dynamics of the genetic algorithm depend in a critical way on the parameter $$pi ,=,sigma(1-p_C)(1-p_M)^ell,.$$ If $pi<1$, then the genetic algorithm operates in a disordered regime: an advantageous mutant disappears with probability larger than $1-1/m^beta$, where $beta$ is a positive exponent. If $pi>1$, then the genetic algorithm operates in a quasispecies regime: an advantageous mutant invades a positive fraction of the population with probability larger than a constant $p^*$ (which does not depend on $m$). We estimate next the probability of the occurrence of a catastrophe (the whole population falls below a fitness level which was previously reached by a positive fraction of the population). The asymptotic results suggest the following rules: $pi=sigma(1-p_C)(1-p_M)^ell$ should be slightly larger than $1$; $p_M$ should be of order $1/ell$; $m$ should be larger than $elllnell$; the running time should be of exponential order in $m$. The first condition requires that $ ell p_M +p_C< lnsigma$. These conclusions must be taken with great care: they come from an asymptotic regime, and it is a formidable task to understand the relevance of this regime for a real-world problem. At least, we hope that these conclusions provide interesting guidelines for the practical implementation of the simple genetic algorithm." @default.
- W4300566512 created "2022-10-03" @default.
- W4300566512 creator A5013447678 @default.
- W4300566512 date "2014-03-21" @default.
- W4300566512 modified "2023-10-17" @default.
- W4300566512 title "The quasispecies regime for the simple genetic algorithm with ranking selection" @default.
- W4300566512 doi "https://doi.org/10.48550/arxiv.1403.5427" @default.
- W4300566512 hasPublicationYear "2014" @default.
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