# Graph Neural Networks for Routing Optimization: Challenges and Opportunities
## 1 Introduction  
Routing optimization can be expressed as a combinatorial optimization problem that selects packet forwarding paths with different optimization objectives and constraints under various scenarios [1]. Routing optimization has been considered in multiple disciplines, including operation research, transportation research, and computer science, for problems such as vehicle routing [2] and data packet routing [3]. Some classical optimization algorithms have been successfully applied in these domains, such as [PERSON]'s algorithm for finding the shortest path in a graph [4]. Powered by these optimization algorithms, a large family of routing protocols has been designed and deployed in communication networks, e.g., the Open Shortest Path Protocol (OSPF) [5]. Routing optimization has been a pivotal research area in communication networks due to its significant application potential and the inherent challenges it poses [6]. Incommunication networks, it refers to the process of identifying the most efficient paths for data packets to traverse from a source to a destination within a network, based on inputs including network topology, traffic load, and other key variables. The primary objectives of routing optimization are to reduce latency, increase throughput, and ensure dependable communication while maximizing the efficiency of network resources. These optimizations are critical for enhancing network performance, scalability, and resilience across various applications, including the Internet, cloud computing, and large-scale enterprise systems. However, distinct challenges emerge across different network environments, especially in next-generation and specialized networks. For example, in unmanned aerial vehicle (UAV) networks, the primary obstacles include high mobility, frequent topology changes, energy constraints, and limited transmission range [7; 8]. Similarly, satellite networks face difficulties stemming from satellite mobility, including dynamic constellation topologies and frequent inter-satellite link switching [9]. These challenges highlight the need for advanced routing solutions that can adapt to the unique demands of each network scenario. Existing routing techniques fall short of meeting the demands of future networks, which are characterized by the need for extremely large bandwidth, ultra-low latency, deterministic delay, high reliability, and massive connectivity. To address these requirements, machine learning (ML) and artificial intelligence (AI) techniques have been introduced for routing optimization. These approaches can effectively learn optimized routing strategies by leveraging historical traffic patterns, allowing them to adapt to future conditions [1]. Compared to traditional routing algorithms and protocols, ML- and AI-based schemes have shown superior performance, as demonstrated in numerous studies [10; 11]. ML paradigms can be more concisely and clearly related to the inputs that make up network topologies, traffic network matrices, routing schemes, and the output of routing optimization performance metrics. The testing of the trained models demonstrated that ML-based routing solutions significantly outperform traditional algorithms in terms of key performance metrics such as reduced latency and improved throughput, effectively adapting to dynamic network conditions and optimizing routing decisions. However, applying these ML-based routing methods in real-world network environments remains a challenge. This difficulty stems from the limitations in accurately modeling dynamic network topologies and the complexities involved in optimizing routing policies in real time, where adaptability and low-latency decision-making are crucial. These factors continue to pose significant barriers to the practical deployment of AI-driven routing solutions in modern communication systems.