## 1 Introduction
[PERSON] [20] raised a prediction model based on the improved fruit fly algorithm to optimize the parameters of SVM so that the accuracy of forecasting can be enhanced. [PERSON] _et al._[21] used a modified PSO combined with simulated annealing algorithm (SA) to optimize SVM. [PERSON] _et al._[22] used genetic algorithms to obtain the best-optimized parameter values of SVM model to enhance the precision of forecasting. [PERSON] _et al._[23] used support vector regression optimized by differential evolution algorithm to predict electricity consumption. [PERSON] _et al._[24] employed fruit fly optimization algorithm to obtain the weights of combination forecasting model for urban saturated power load analysis. The grey system theory proposed by Chinese professor [PERSON] is a theory that deals with uncertainty issues with the characteristics of less data and imperfect information [25]. Grey model (1,1) (GM (1,1)), which is a kind of grey forecasting model, has been employed in many forecasting problems, such as the prediction of short term and long term electric load [26,27], tourism flow [28], airline industry [29], automobile production [30], wave [31], wind speed and wind power [32], per capita annual net income forecast of rural households [33], fuel production [34], and carbon emissions, energy demand and economic growth [35]. Since the power system also has the characteristics of grey system, GM (1,1) has been used in electric energy demand forecasting [36,37,38,39]. However, the accuracy of electricity demand prediction is affected by many factors, such as political environment, economic development and social status. Therefore, the exponentially growing rule of GM (1,1) may not show a good forecasting performance in electricity demand prediction. Under this circumstance, the optimization of GM (1,1) is widely discussed. Recently, several studies have made valuable progress, for example, GM (1,1) with rolling mechanism was employed to predict annual peak load [40] and the chaotic co-evolutionary PSO algorithm was employed to determine the parameters of GM (1,1) [41]. [PERSON] and [PERSON] [42] utilized grey model with rolling mechanism to predict electricity and coal demand. [PERSON] and [PERSON] [43] presented a load forecasting model on the basis of the improved GM (1,1) Euler model, which uses the Euler formula to modify the whithenization equation with the aim of weakening the effect of the equation on the predicting results. Case analysis shows that the forecasting precision of improved GM (1,1) Euler model is better than that of the general grey model. In the past few years, many swarm intelligence algorithms have also been proposed to solve practical optimization issues, such as particle swarm optimization (PSO) [44], genetic algorithm (GA) [45], ant colony optimization (ACO) [46], differential evolution algorithm (DE) [47], evolutionary strategy (ES) [48], evolutionary programming (EP) [49; 50] and fruit fly optimization algorithm (FOA) [51; 52; 53]. Both-flame optimization (MFO) is a novel nature-enlightenment algorithm, which was proposed by [PERSON] in 2015 to compete with the current optimization algorithms [54]. In this paper, the parameters of GM (1,1) would be optimized by employing MFO. Moreover, as the data may be used to perform diverse tendencies or features at different times, a rolling mechanism is also applied to address these differences in this paper [33; 40; 42]. _PE_, _MAPE_ and _RMSE_ are employed to compare the forecasting performances of LSR, GM (1,1), FOA-GM (1,1), MFO-GM (1,1), Rolling-LSR, Rolling-GM (1,1), Rolling-FOA-GM (1,1), and Rolling-MFO-GM (1,1). The main contributions of this paper include:  
1. A new intelligent optimization algorithm named MFO is utilized to optimize the parameters of GM (1,1) model, and it is verified that it can increase the precision of annual electricity demand prediction. 2. Currently, most literature only study the combination of optimization algorithm or rolling mechanism with grey model for annual electricity consumption forecasting.