  In noisy evolutionary optimization, sampling is a common strategy to deal
with noise. By the sampling strategy, the fitness of a solution is evaluated
multiple times (called \emph{sample size}) independently, and its true fitness
is then approximated by the average of these evaluations. Most previous studies
on sampling are empirical, and the few theoretical studies mainly showed the
effectiveness of sampling with a sufficiently large sample size. In this paper,
we theoretically examine what strategies can work when sampling with any fixed
sample size fails. By constructing a family of artificial noisy examples, we
prove that sampling is always ineffective, while using parent or offspring
populations can be helpful on some examples. We also construct an artificial
noisy example to show that when using neither sampling nor populations is
effective, a tailored adaptive sampling (i.e., sampling with an adaptive sample
size) strategy can work. These findings may enhance our understanding of
sampling to some extent, but future work is required to validate them in
natural situations.
