It is an ongoing debate whether and how comma selection in evolutionary
algorithms helps to escape local optima. We propose a new benchmark function to
investigate the benefits of comma selection: OneMax with randomly planted local
optima, generated by frozen noise. We show that comma selection (the
(1,λ) EA) is faster than plus selection (the (1+λ) EA) on this
benchmark, in a fixed-target scenario, and for offspring population sizes
λ for which both algorithms behave differently. For certain parameters,
the (1,λ) EA finds the target in Θ(nlnn) evaluations, with
high probability (w.h.p.), while the (1+λ) EA) w.h.p. requires almost
Θ((nlnn)2) evaluations.
We further show that the advantage of comma selection is not arbitrarily
large: w.h.p. comma selection outperforms plus selection at most by a factor of
O(nlnn) for most reasonable parameter choices. We develop novel methods
for analysing frozen noise and give powerful and general fixed-target results
with tail bounds that are of independent interest.Comment: An extended abstract will be published at GECCO 202