## 6 Conclusions and Future Research Directions  
This paper presents a comprehensive overview of routing algorithms in WSNs. We elaborate on traditional and ML approaches of green routing algorithm design in WSNs. Based on detailed comparisons and analysis, we propose a mathematical hypothesis model of an ML-based routing algorithm for extending the lifetime of WSNs. In addition, this study reviews the basic principles and characteristics of various routing algorithms in WSNs. We also discuss the merits and demerits of the different techniques that can be used to improve the performance of routing algorithms in WSN. Finally, this study presents the challenges of implementing ML for routing algorithms design in WSNs and identifies future research directions to be addressed and worthy of exploration with ML. This discussion will be of interest to a broad audience in ML and WSNs.  
Future research work may include the following: Due to the arithmetic bottleneck and energy consumption limitation of WSNs, ML algorithms cannot be deployed at scale in sensors with small computational power and limited energy. However, distributed learning methods require less computational capacity, energy consumption, and smaller memory footprints than centralized learning algorithms (i.e., they do not need to consider the entire network information). Distributed cooperative learning breaks the arithmetic bottleneck and achieves ML-based green routing with less energy consumption, which is very suitable for WSNs.  
On the other hand, ML algorithms require a lot of computation and energy for proper parameter learning in the training learning phase, which makes their deployment in WSNs extremely difficult. Additionally, nodes have very different computational capabilities (e.g., the sink has a strong computational capability, while the rest of the nodes are weak), which provides us with ideas for how to apply transfer learning in WSNs. Since sink nodes have more power and computing capacity, they can train the model in a distributed manner with other sensor nodes. Then, sink nodes can transmit the trained model parameters to the sensor nodes. After receiving the model parameters from different nodes, the sensor nodes multiply these parameters by the corresponding weights and perform a weighted average to obtain their final model parameters, which will reduce the training consumption of the sensor nodes and improve the accuracy of the model in WSNs. Meanwhile, addressing the QoS-aware routing is quite a challenging task. Satisfying the delay constraints, bandwidth constraints, and incorporating machine learning techniques to develop a routing protocol is quite exciting research, especially utilizing the hybrid ML techniques in WSNs.  
Conceptualization, Q.D. and R.Z.; formal analysis, R.Z.; investigation, Q.D. and H.L.; methodology, R.Z. and M.M.; supervision, R.Z.; writing--original-draft preparation, Q.D. and H.L.; writing--review and editing, R.Z. and M.M. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (No. 61772562), the Key Project of Hubei Provincial Science and Technology Innovation Foundation of China (No. 2018 ABB1485), and the Youth Elite Project of State Ethnic Affairs Commission of China (No. 2016-3-08).  
The authors declare no conflict of interest.