Investigation of the (μ, λ)-ES in the presence of noise

While in the absence of noise no improvement in local performance can be gained from retaining but the best candidate solution found so far, it has been shown experimentally that, in the presence of noise, operating with a non-trivial population of candidate solutions can have a marked and positive effect on the local performance of evolution strategies (ES). In this paper, we attempt to shed some light on the reasons for the potential performance improvement. In particular, we derive a progress law for the (μ, λ)-ES on a noisy linear fitness function and both numerically and empirically study its implications. We then discuss the significance of the progress coefficients that have been obtained on the linear function for the quadratic sphere, Comparisons of the local performance of the (μ, λ)-ES and of the (1+1)-ES and the (1, λ)-ES are presented