  It is known that the $(1+(\lambda,\lambda))$~Genetic Algorithm (GA) with
self-adjusting parameter choices achieves a linear expected optimization time
on OneMax if its hyper-parameters are suitably chosen. However, it is not very
well understood how the hyper-parameter settings influences the overall
performance of the $(1+(\lambda,\lambda))$~GA. Analyzing such multi-dimensional
dependencies precisely is at the edge of what running time analysis can offer.
To make a step forward on this question, we present an in-depth empirical study
of the self-adjusting $(1+(\lambda,\lambda))$~GA and its hyper-parameters. We
show, among many other results, that a 15\% reduction of the average running
time is possible by a slightly different setup, which allows non-identical
offspring population sizes of mutation and crossover phase, and more
flexibility in the choice of mutation rate and crossover bias --a
generalization which may be of independent interest. We also show indication
that the parametrization of mutation rate and crossover bias derived by
theoretical means for the static variant of the $(1+(\lambda,\lambda))$~GA
extends to the non-static case.
