  It is generally accepted that populations are useful for the global
exploration of multi-modal optimisation problems. Indeed, several theoretical
results are available showing such advantages over single-trajectory search
heuristics. In this paper we provide evidence that evolving populations via
crossover and mutation may also benefit the optimisation time for hillclimbing
unimodal functions. In particular, we prove bounds on the expected runtime of
the standard ($\mu$+1)~GA for OneMax that are lower than its unary black box
complexity and decrease in the leading constant with the population size up to
$\mu=O(\sqrt{\log n})$. Our analysis suggests that the optimal mutation
strategy is to flip two bits most of the time. To achieve the results we
provide two interesting contributions to the theory of randomised search
heuristics: 1) A novel application of drift analysis which compares absorption
times of different Markov chains without defining an explicit potential
function. 2) The inversion of fundamental matrices to calculate the absorption
times of the Markov chains. The latter strategy was previously proposed in the
literature but to the best of our knowledge this is the first time is has been
used to show non-trivial bounds on expected runtimes.
