A Differential Evolution for Optimisation in Noisy Environment

This paper proposes a novel variant of differential evolution (DE) tailored to the optimisation of noisy fitness functions. The proposed algorithm, namely noise analysis differential evolution (NADE), combines the stochastic properties of a randomised scale factor and a statistically rigorous test which supports one-to-one spawning survivor selection that automatically selects a proper sample size and then selects, among parent and offspring, the most promising solution. The actions of these components are separately analysed and their combined effect on the algorithmic performance is studied by means of a set of numerous and various test functions perturbed by Gaussian noise. Various noise amplitudes are considered in the result section. The performance of the NADE has been extensively compared with a classical algorithm and two modern metaheuristics designed for optimisation in the presence of noise. Numerical results show that the proposed NADE has very good performance with most of the problems considered in the benchmark set. The NADE seems to be able to detect high quality solutions despite the noise and display high performance in terms of robustness.