On the Robustness of Evolutionary Algorithms to Noise: Refined Results and an Example Where Noise Helps

We present reined results for the expected optimisation time of the (1+1) EA and the (1+λ) EA on LeadingOnes in the prior noise model, where in each itness evaluation the search point is altered before evaluation with probability p. Previous work showed that the (1+1) EA runs in polynomial time if p = O((logn)/n 2 ) and needs superpolynomial time if p = Ω((logn)/n), leaving a huge gap for which no results were known. We close this gap by showing that the expected optimisation time is Θ(n 2 ) · exp(Θ(pn2 )), allowing for the irst time to locate the threshold between polynomial and superpolynomial expected times at p = Θ((logn)/n 2 ). Hence the (1+1) EA on LeadingOnes is much more sensitive to noise than previously thought. We also show that ofspring populations of size λ ≥ 3.42 logn can efectively deal with much higher noise than known before. Finally, we present an example of a rugged landscape where prior noise can help to escape from local optima by blurring the landscape and allowing a hill climber to see the underlying gradient.