# Graph Neural Networks for Routing Optimization: Challenges and Opportunities
## 1 Introduction
Energy-efficient routing and load balancing in SDN is reviewed in [26] and a deep reinforcement learning (DRL)-based predictive and rate-adaptive energy-efficient routing scheme is proposed with guaranteed QoS. Three types of ML techniques for routing optimization in SDN, namely supervised learning, unsupervised learning, and reinforcement learning, are summarized and discussed in [25]. Several surveys have focused on ML-based techniques for network routing. ML-based intelligent routing algorithms are reviewed in [10], with the key concepts and applications, training and deployment strategies, and future development directions. Reinforcement learning (RL)-based routing protocols for vehicular ad hoc networks are reviewed in [11], with the introduction of their working procedure, advantages, disadvantages, and applications, and a qualitative comparison of their key features. ML-based routing optimization techniques for future communication networks have been reviewed in [1]. AI-enabled routing protocols for UAV networks are summarized and discussed in [7], including topology-predictive and self-adaptive learning-based routing algorithms. Q-learning-based position-aware routing protocols for flying ad hoc networks (FANETs) are reviewed in [8], with a focus on the relationship between Q-learning and routing when dealing with high-mobility and dynamic topology challenges. However, the discussion of GNN-based solutions is insufficient in the existing surveys of ML-based solutions. There have also been surveys from the perspective of GNN-based methodologies. However, their focus was not on the specific field of network routing. Some existing surveys have focused on the application of graph-based methods in communications and networking domains [27]. The application of graph-based deep learning methods in three different scenarios is considered in [28], namely, wireless networks, wired networks, and software-defined networks, with a wide range of applications including routing, traffic prediction, resource allocation, and wireless link scheduling [29]. GNN is seen as a key enabler for the modeling, control and management of communication networks with strong generalization capabilities over traditional neural network solutions in [19]. Two example use cases, RouteNet [30] for performance evaluation in wired networks and WCGCN [31] for radio resource management in wireless networks, are further implemented and discussed in [19] to demonstrate the superiority of GNN-based solutions. Another survey of combinatorial optimization on graphs is presented in [32], where the focus is on the machine learning structures used for solving combinatorial optimization problems on graphs, while these problems are from the telecommunications field. Routing is one of the networking applications discussed in [32]. Some surveys have discussed the application of graph-based deep learning to a specific network domain. The construction method for various wireless communication graphs is introduced in [33], with several GNN-based solutions for resource allocation, routing, and other applications in wireless networks. Graph-based solutions are discussed in [34] for resource allocation in integrated space and terrestrial communications, whereas routing optimization is not mentioned. A comparison of this survey and other existing surveys is summarized in Table 1. Compared with existing surveys, this survey serves the specific purpose of providing an up-to-date literature review of GNN techniques for routing optimization. In existing surveys, GNN-based network routing solutions are not mentioned or the discussion of GNN-based solutions for routing optimization applications is not thorough. This paper is a comprehensive guide for newcomers with a full picture of existing studies. This paper is also insightful for experienced researchers with the collection of dataset and tool resources and the inspiring discussion of research challenges and opportunities.