  The $(1+(\lambda,\lambda))$ genetic algorithm, first proposed at GECCO 2013,
showed a surprisingly good performance on so me optimization problems. The
theoretical analysis so far was restricted to the OneMax test function, where
this GA profited from the perfect fitness-distance correlation. In this work,
we conduct a rigorous runtime analysis of this GA on random 3-SAT instances in
the planted solution model having at least logarithmic average degree, which
are known to have a weaker fitness distance correlation.
  We prove that this GA with fixed not too large population size again obtains
runtimes better than $\Theta(n \log n)$, which is a lower bound for most
evolutionary algorithms on pseudo-Boolean problems with unique optimum.
However, the self-adjusting version of the GA risks reaching population sizes
at which the intermediate selection of the GA, due to the weaker
fitness-distance correlation, is not able to distinguish a profitable offspring
from others. We show that this problem can be overcome by equipping the
self-adjusting GA with an upper limit for the population size. Apart from
sparse instances, this limit can be chosen in a way that the asymptotic
performance does not worsen compared to the idealistic OneMax case. Overall,
this work shows that the $(1+(\lambda,\lambda))$ GA can provably have a good
performance on combinatorial search and optimization problems also in the
presence of a weaker fitness-distance correlation.
