## 5 Conclusions  
This paper studies the energy consumption algorithm of high-speed train operations and proposes a graph optimization algorithm based on the VGAE, which can fully consider the complex relationship between nodes in the operation of trains. Through a simulation and comparative tests, under the premise of ensuring safe, on-time, and accurate parking, the control method in this study shows increased energy savings.  
In the process of solving the driving strategy, this study balanced the sample size of each class of the training set and considered some special cases. A algorithm based on the KNN and undersampling is used to balance the negative impact of the number imbalance between the data sets, and the braking problem of the high-speed train is transformed into the link prediction problem of the implicit graph. The variational graph autoencoder is used to solve the initial strategy of train braking, and the time of intermediate trips is adjusted to ensure that the driving distance is consistent with the length of the route. The actual feasible braking application time and brake handling operation are obtained. However, the training data are based on relatively safe driving conditions, which makes the actual driving situation, especially in the face of a complex or dangerous driving environment, too idealistic. Therefore, for future research, we suggest inputting more train operation factors and real-time data into the VGAE model to obtain a more optimized strategy.  
In detail, in order to further evaluate the proximity between research and practical applications, the following aspects need to be considered. First of all, the simulation data used in this study may not be able to fully simulate the various complex situations and changes during the operation of actual trains. The actual train operation environment may be affected by many factors, such as the weather, road conditions, traffic conditions, etc. These factors may have an important impact on the energy consumption of trains and the driving strategy of their drivers. Secondly, our research focuses on the safety, punctuality, and accuracy of trains, but in practical applications, safety is always the primary consideration. Therefore, any control method that optimizes energy consumption must ensure that the safety of the train is not sacrificed. Finally, the training data in the study are relatively restricted, which may limit the generalizability of the algorithm to actual driving environments. Therefore, incorporating more actual operating data and factors into the model should be the focus of future research to ensure the effectiveness and reliability of the algorithm in practical applications.  
Conceptualization, W.M.; Methodology, W.M.; Validation, L.Z.; Formal analysis, W.J.; Writing--original draft, J.W.; Writing--review & editing, Q.J.; Visualization, C.Z.; Supervision, Z.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China, grant number U1734210.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflict of interest.