  We investigate a family of $(\mu+\lambda)$ Genetic Algorithms (GAs) which
creates offspring either from mutation or by recombining two randomly chosen
parents. By scaling the crossover probability, we can thus interpolate from a
fully mutation-only algorithm towards a fully crossover-based GA. We analyze,
by empirical means, how the performance depends on the interplay of population
size and the crossover probability.
  Our comparison on 25 pseudo-Boolean optimization problems reveals an
advantage of crossover-based configurations on several easy optimization tasks,
whereas the picture for more complex optimization problems is rather mixed.
Moreover, we observe that the ``fast'' mutation scheme with its are power-law
distributed mutation strengths outperforms standard bit mutation on complex
optimization tasks when it is combined with crossover, but performs worse in
the absence of crossover.
  We then take a closer look at the surprisingly good performance of the
crossover-based $(\mu+\lambda)$ GAs on the well-known LeadingOnes benchmark
problem. We observe that the optimal crossover probability increases with
increasing population size $\mu$. At the same time, it decreases with
increasing problem dimension, indicating that the advantages of the crossover
are not visible in the asymptotic view classically applied in runtime analysis.
We therefore argue that a mathematical investigation for fixed dimensions might
help us observe effects which are not visible when focusing exclusively on
asymptotic performance bounds.
