The heavy-tailed mutation operator proposed in Doerr, Le, Makhmara, and
Nguyen (GECCO 2017), called \emph{fast mutation} to agree with the previously
used language, so far was proven to be advantageous only in mutation-based
algorithms. There, it can relieve the algorithm designer from finding the
optimal mutation rate and nevertheless obtain a performance close to the one
that the optimal mutation rate gives.
In this first runtime analysis of a crossover-based algorithm using a
heavy-tailed choice of the mutation rate, we show an even stronger impact. For
the (1+(λ,λ)) genetic algorithm optimizing the OneMax benchmark
function, we show that with a heavy-tailed mutation rate a linear runtime can
be achieved. This is asymptotically faster than what can be obtained with any
static mutation rate, and is asymptotically equivalent to the runtime of the
self-adjusting version of the parameters choice of the (1+(λ,λ))
genetic algorithm. This result is complemented by an empirical study which
shows the effectiveness of the fast mutation also on random satisfiable
Max-3SAT instances.Comment: This is a version of the same paper presented at GECCO 2020 completed
with the proofs which were missing because of the page limi