  Evolutionary algorithms (EAs) are population-based general-purpose
optimization algorithms, and have been successfully applied in various
real-world optimization tasks. However, previous theoretical studies often
employ EAs with only a parent or offspring population and focus on specific
problems. Furthermore, they often only show upper bounds on the running time,
while lower bounds are also necessary to get a complete understanding of an
algorithm. In this paper, we analyze the running time of the
($\mu$+$\lambda$)-EA (a general population-based EA with mutation only) on the
class of pseudo-Boolean functions with a unique global optimum. By applying the
recently proposed switch analysis approach, we prove the lower bound $\Omega(n
\ln n+ \mu + \lambda n\ln\ln n/ \ln n)$ for the first time. Particularly on the
two widely-studied problems, OneMax and LeadingOnes, the derived lower bound
discloses that the ($\mu$+$\lambda$)-EA will be strictly slower than the
(1+1)-EA when the population size $\mu$ or $\lambda$ is above a moderate order.
Our results imply that the increase of population size, while usually desired
in practice, bears the risk of increasing the lower bound of the running time
and thus should be carefully considered.
