A Probabilistic Multimodal Optimization Algorithm Based on Buffon Principle and Nyquist Sampling Theorem for Noisy Environment

A novel method named probabilistic multimodal optimization (PMO) algorithm is proposed in this paper to competently optimize noisy objective function. In the PMO algorithm, we propose two new strategies to make the algorithm have the capability of probability prediction and multiple extreme points optimization. The first strategy is concerned with the partition strategy of search space based on Buffon principle, which provides the probability prediction of peak detection ratio according to the Buffon distance and extrema resolution. At the same time, several local scopes where multiple extreme points are located can be retained by the partition strategy. The second strategy deals with a same-peak detection method based on Nyquist sampling theorem to identify the position of the extreme point. Based on 12 benchmark functions, experiments are carried out from three aspects, including probabilistic property verification, analysis of the influence of sampling frequency on the same-peak detection method, and multiple extreme points optimization. The validity of PMO algorithm theory and the probabilistic characteristic of global optimization under noise interference are proved, and it is denoted that PMO algorithm can locate more optima and gain higher location precision.