Sequential sampling in noisy environments

Abstract

In an environment where fitness evaluations are disturbed by noise, the selection operator is prone to errors, occasionally and intendedly selecting the worse individual. A common method to reduce the noise is to sample an individual's fitness several times, and use the average as an estimate of the true fitness. Unfortunately, such a noise reduction is computationally rather expensive. Sequential sampling does not fix the number of samples in advance for all individuals, but instead selects samples one at a time, until a certain level of confidence is achieved. This allows to reduce the number of samples, because individuals with very different true fitness values can be compared on the basis of only few samples (as the signal-to-noise ratio is rather high in this case) while very similar individuals are evaluated often enough to guarantee the desired level of confidence. In this paper, for the case of tournament selection, we show that the use of a state-of-the-art sequential sampling procedure may save a significant portion of the fitness evaluations, without increasing the selection error. Furthermore, we design a new sequential sampling procedure and show that it saves an even larger portion of the fitness evaluations. Finally, we compare the three methods also empirically on a simple onemax function. © Springer-Verlag 2004.