## 1 Introduction
There are also studies on improving the structure of GMDH to better adapt to the characteristics of the model, such as in a past paper [33], in which five diversity metrics were used as external criteria to construct a new type of GMDH forecasting model called diversity group method of data handling (D-GMDH). Research shows that GMDH is also suitable for short-term load forecasting. However, through an actual measurement, we found that the model output is unstable and that the prediction accuracy is quite different when GMDH is used for short-term load forecasting. This is because the GMDH algorithm uses least square estimates to fit polynomials. However, the input variables used in load forecasting are prone to severe multicollinearity, which will invalidate the least square estimates and lead to distortion of the model evaluation [34]. Moreover, it is easy for the overfitting problem to occur when the least square estimate deals with complicated characteristic variables; this leads to the reduction of the model's generalization ability and increases the error of the coefficient estimation. To solve this problem, the elastic net is proposed to replace the least square fitting polynomial. Elastic net is an improved regression algorithm based on the lasso algorithm. Its regular terms apply the Gaussian prior distribution and Laplace prior distribution principles to remove the noise and redundancy of data, enhance robustness, and reduce model complexity and thus have good variable selectivity [35; 36; 37; 38]. These properties of elastic net can compensate for the deficiencies caused by GMDH due to the least-squares method. In this paper, GMDH is revised to use the elastic net. The GMDH algorithm, based on the elastic net regression, is proposed as a short-term load forecasting model to improve the accuracy of load forecasting and ensure the smooth operation of power systems. Short-term load forecasting needs to refer to historical data such as load and characteristic factors in the days before the forecast. However, equipment failure emergencies, important activities, and vagaries of the weather may abruptly change the load law, and this change will continue for at least a few days. Thus, the law between load and characteristic factors fitted before the occurrence of mutation factors will be different from the new load law. This will make the conventional load forecasting algorithm produce a certain amount of error. The simple principle of \"near is larger and far is small\" cannot distinguish the influence degree of different historical data on the load forecasting effectively. Therefore, according to the difference degree of historical data, this paper carries out variable weight processing on the input data, so as to measure the difference between the load law of the old date and the load law of the new date and reflect this difference in the load forecast. In terms of short-term load forecasting, although there have been many studies on the processing of input data and the improvement of the prediction algorithm, it is of great significance to the improvement of GMDH in face of the larger short-term load forecasting data and higher requirements for prediction accuracy, which are widely used in big data analysis in many fields. Meanwhile, in face of the problem that the mutation of load law affects the prediction accuracy, the new idea of variable weight processing of the input data based on the difference degree of historical data has the opportunity for broad application. In addition, when selecting the input variables of the model, this paper selects the characteristic variables of three dimensions, and uses the temperature and humidity index (THI) to calculate the cumulative effect of meteorological factors. This paper proposes a short-term load forecasting model based on elastic net regression, which is EN-GMDH. Among them, it is proposed to address the overfitting and multicollinearity issuers using elastic net.