  Despite significant progress in the theory of evolutionary algorithms, the
theoretical understanding of evolutionary algorithms which use non-trivial
populations remains challenging and only few rigorous results exist. Already
for the most basic problem, the determination of the asymptotic runtime of the
$(\mu+\lambda)$ evolutionary algorithm on the simple OneMax benchmark function,
only the special cases $\mu=1$ and $\lambda=1$ have been solved.
  In this work, we analyze this long-standing problem and show the
asymptotically tight result that the runtime $T$, the number of iterations
until the optimum is found, satisfies \[E[T] = \Theta\bigg(\frac{n\log
n}{\lambda}+\frac{n}{\lambda / \mu} + \frac{n\log^+\log^+ \lambda/ \mu}{\log^+
\lambda / \mu}\bigg),\] where $\log^+ x := \max\{1, \log x\}$ for all $x > 0$.
  The same methods allow to improve the previous-best $O(\frac{n \log
n}{\lambda} + n \log \lambda)$ runtime guarantee for the $(\lambda+\lambda)$~EA
with fair parent selection to a tight $\Theta(\frac{n \log n}{\lambda} + n)$
runtime result.
