  Evolutionary Algorithms (EAs) and other randomized search heuristics are
often considered as unbiased algorithms that are invariant with respect to
different transformations of the underlying search space. However, if a certain
amount of domain knowledge is available the use of biased search operators in
EAs becomes viable. We consider a simple (1+1) EA for binary search spaces and
analyze an asymmetric mutation operator that can treat zero- and one-bits
differently. This operator extends previous work by Jansen and Sudholt (ECJ
18(1), 2010) by allowing the operator asymmetry to vary according to the
success rate of the algorithm. Using a self-adjusting scheme that learns an
appropriate degree of asymmetry, we show improved runtime results on the class
of functions OneMax$_a$ describing the number of matching bits with a fixed
target $a\in\{0,1\}^n$.
