  We analyse the impact of the selective pressure for the global optimisation
capabilities of steady-state EAs. For the standard bimodal benchmark function
\twomax we rigorously prove that using uniform parent selection leads to
exponential runtimes with high probability to locate both optima for the
standard ($\mu$+1)~EA and ($\mu$+1)~RLS with any polynomial population sizes.
On the other hand, we prove that selecting the worst individual as parent leads
to efficient global optimisation with overwhelming probability for reasonable
population sizes. Since always selecting the worst individual may have
detrimental effects for escaping from local optima, we consider the performance
of stochastic parent selection operators with low selective pressure for a
function class called \textsc{TruncatedTwoMax} where one slope is shorter than
the other. An experimental analysis shows that the EAs equipped with inverse
tournament selection, where the loser is selected for reproduction and small
tournament sizes, globally optimise \textsc{TwoMax} efficiently and effectively
escape from local optima of \textsc{TruncatedTwoMax} with high probability.
Thus they identify both optima efficiently while uniform (or stronger)
selection fails in theory and in practice. We then show the power of inverse
selection on function classes from the literature where populations are
essential by providing rigorous proofs or experimental evidence that it
outperforms uniform selection equipped with or without a restart strategy. We
conclude the paper by confirming our theoretical insights with an empirical
analysis of the different selective pressures on standard benchmarks of the
classical MaxSat and Multidimensional Knapsack Problems.
