  We study sorting of permutations by random swaps if each comparison gives the
wrong result with some fixed probability $p<1/2$. We use this process as
prototype for the behaviour of randomized, comparison-based optimization
heuristics in the presence of noisy comparisons. As quality measure, we compute
the expected fitness of the stationary distribution. To measure the runtime, we
compute the minimal number of steps after which the average fitness
approximates the expected fitness of the stationary distribution.
  We study the process where in each round a random pair of elements at
distance at most $r$ are compared. We give theoretical results for the extreme
cases $r=1$ and $r=n$, and experimental results for the intermediate cases. We
find a trade-off between faster convergence (for large $r$) and better quality
of the solution after convergence (for small $r$).
