The improved GM(1,1) based on PSO with stochastic weight

Abstract

In order to improve the prediction accuracy of GM(1,1) this paper points out the disadvantages of using least square method to solve the parameters of model, attempts to use particle swarm optimization algorithm (PSO) to calculate the parameter of GM(1,1), introduces the stochastic strategy into PSO to endow the inertia weight of particle randomly, and then selects high-rising exponential sequence and low-rising exponential sequence to establish the improved GM(1,1), traditional GM(1,1) and DGM(1,1) to compare the fitting accuracy. In addition, the grey correlation analysis is used to measure the similarity between the fitting sequence and the original sequence of three models. The results show that: for the low-rising exponential sequence, the improved GM(1,1) is slightly better than traditional GM(1,1) and DGM(1,1); for the high-rising exponential sequence, the superiority of improved GM(1,1) is obviously higher than the other two models, especially the traditional GM(1,1); for these two types of sequences, the geometry of fitting sequence based on improved GM(1,1) is closer to the geometry of original sequence.