Evolutionary Algorithms in the Presence of Noise: To Sample or Not to Sample

In this paper, we empirically analyze the convergence behavior of evolutionary algorithms (evolution strategies - ES and genetic algorithms A) for two noisy optimization problems which belong to the class of functions with noise induced multi-modality (FNIMs). Although, both functions are qualitatively very similar, the ES is only able to converge to the global optimizer state for one of them. Additionally, we observe that canonical GA exhibits similar problems. We present a theoretical analysis which explains the different behaviors for the two functions and which suggests to resort to resampling strategies to solve the problem. Although, resampling is an inefficient way to cope with noisy optimization problems, it turns out that depending on the properties of the problem, (moderate) resampling might be necessary to guarantee convergence to the robust optimizer