  We analyze the performance of the 2-rate $(1+\lambda)$ Evolutionary Algorithm
(EA) with self-adjusting mutation rate control, its 3-rate counterpart, and a
$(1+\lambda)$~EA variant using multiplicative update rules on the OneMax
problem. We compare their efficiency for offspring population sizes ranging up
to $\lambda=3,200$ and problem sizes up to $n=100,000$.
  Our empirical results show that the ranking of the algorithms is very
consistent across all tested dimensions, but strongly depends on the population
size. While for small values of $\lambda$ the 2-rate EA performs best, the
multiplicative updates become superior for starting for some threshold value of
$\lambda$ between 50 and 100. Interestingly, for population sizes around 50,
the $(1+\lambda)$~EA with static mutation rates performs on par with the best
of the self-adjusting algorithms.
  We also consider how the lower bound $p_{\min}$ for the mutation rate
influences the efficiency of the algorithms. We observe that for the 2-rate EA
and the EA with multiplicative update rules the more generous bound
$p_{\min}=1/n^2$ gives better results than $p_{\min}=1/n$ when $\lambda$ is
small. For both algorithms the situation reverses for large~$\lambda$.
