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We analyse the performance of well-known evolutionary algorithms (1+1)EA and(1+$\lambda$)EA in the prior noise model, where in each fitness evaluation thesearch point is altered before evaluation with probability $p$. We presentrefined results for the expected optimisation time of the (1+1)EA and the(1+$\lambda$)EA on the function LeadingOnes, where bits have to be optimised insequence. Previous work showed that the (1+1)EA on LeadingOnes runs inpolynomial expected time if $p = O((\log n)/n^2)$ and needs superpolynomialexpected time if $p = \omega((\log n)/n)$, leaving a huge gap for which noresults were known. We close this gap by showing that the expected optimisationtime is $\Theta(n^2) \cdot \exp(\Theta(\min\{pn^2, n\}))$ for all $p \le 1/2$,allowing for the first time to locate the threshold between polynomial andsuperpolynomial expected times at $p = \Theta((\log n)/n^2)$. Hence the (1+1)EAon LeadingOnes is much more sensitive to noise than previously thought. We alsoshow that offspring populations of size $\lambda \ge 3.42\log n$ caneffectively deal with much higher noise than known before.  Finally, we present an example of a rugged landscape where prior noise canhelp to escape from local optima by blurring the landscape and allowing a hillclimber to see the underlying gradient. We prove that in this particularsetting noise can have a highly beneficial effect on performance.

Analysing the Robustness of Evolutionary Algorithms to Noise: Refined Runtime Bounds and an Example Where Noise is Beneficial