We investigate the effect of restricting the mutation operator in
evolutionary algorithms with respect to the runtime behavior.
Considering the Eulerian cycle problem we present runtime bounds on
evolutionary algorithms with a restricted operator that are much
smaller than the best upper bounds for the general case. In our
analysis it turns out that a plateau which has to be coped with for
both algorithms changes its structure in a way that allows the
algorithms to obtain an improvement much faster. In addition, we
present a lower bound for the general case which shows that the
restricted operator speeds up computation by at least a linear
factor.