Sorting by Swaps with Noisy Comparisons

We study sorting of permutations by random swaps if the comparison operator is noisy. The noise is not associated with the underlying fitness but is inherent to the comparison operator. This type of fitness-independent noise has not been studied before in the community but is prototypical for comparison-based evolutionary algorithms, which often do not need to compute or approximate explicit fitness values. As quality measure, we compute the average fitness of the stationary distribution. To measure runtime, we compute the minimal number of steps after which the expected fitness approximates the average fitness of the stationary distribution. As mutations, we allow swaps of any two elements which have distance at most r. We give theoretical results for the extreme cases r = 1 and r = n, and experimental results for intermediate cases. We find a trade-off, between faster convergence (for large r) and better average quality of the solution after convergence (for small r).