Application of Limit Theorems to Runtime Analysis of the (1 + ( <i>λ, λ</i> )) Genetic Algorithm

Using a limit theorem describing the maximum of independent identically distributed random variables (hereinafter r.v.). in terms of Gumbel distribution, we obtain two claims about the runtime of the (1 + (λ,λ)) GAμ, which is a modification of the (1 + (λ,λ)) GA from (Doerr, Doerr, Ebel, 2015). The modification consists in starting the (1 + (λ,λ)) GA from a best individual out of μ = n/ln n randomly sampled individuals. The population size λ = ω(1) is deterministic.