Sorting by Swaps with Noisy Comparisons

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 $r$).Comment: An extended abstract of this paper has been presented at Genetic and Evolutionary Computation Conference (GECCO 2017

A mathematically derived number of resamplings for noisy optimization

International audienceIn Noisy Optimization, one of the most common way to deal with noise is through resampling. In this paper, we compare various resampling rules applied to Evolution Strategy (ES). The goal is to provide a conclusive answer for resampling rules in simple settings. We use a variant of ES as our main algorithm: Self-Adaptive (μ/μ,λ)-Evolution Strategy. We focus our attention on local noisy optimization. In other words, we are interested in situation where reducing the noise is more important than avoiding local minima. We study different sampling rules on the noisy sphere function and compare them experimentally. We conclude that there exists parameter-free formulas that provide adequate resampling rules