  We propose a new way to self-adjust the mutation rate in population-based
evolutionary algorithms in discrete search spaces. Roughly speaking, it
consists of creating half the offspring with a mutation rate that is twice the
current mutation rate and the other half with half the current rate. The
mutation rate is then updated to the rate used in that subpopulation which
contains the best offspring.
  We analyze how the $(1+\lambda)$ evolutionary algorithm with this
self-adjusting mutation rate optimizes the OneMax test function. We prove that
this dynamic version of the $(1+\lambda)$ EA finds the optimum in an expected
optimization time (number of fitness evaluations) of
$O(n\lambda/\log\lambda+n\log n)$. This time is asymptotically smaller than the
optimization time of the classic $(1+\lambda)$ EA. Previous work shows that
this performance is best-possible among all $\lambda$-parallel mutation-based
unbiased black-box algorithms.
  This result shows that the new way of adjusting the mutation rate can find
optimal dynamic parameter values on the fly. Since our adjustment mechanism is
simpler than the ones previously used for adjusting the mutation rate and does
not have parameters itself, we are optimistic that it will find other
applications.
