Differential Evolution for Strongly Noisy Optimization: Use 1.01n Resamplings at Iteration n and Reach the −12 Slope

Abstract—This paper is devoted to noisy optimization in case of a noise with standard deviation as large as variations of the fitness values, specifically when the variance does not decrease to zero around the optimum. We focus on comparing methods for choosing the number of resamplings. Experiments are performed on the differential evolution algorithm. By mathematical analysis, we design a new rule for choosing the number of resamplings for noisy optimization, as a function of the dimension, and validate its efficiency compared to existing heuristics