# Inverse Coupled Simulated Annealing for Enhanced OSPF Convergence in IoT Networks
## 1 Introduction  
With the rapid development of the Internet of Things (IoT), the interconnectivity of smart devices through the internet has experienced explosive growth, resulting in an unprecedented scale of networks [1; 2; 3]. Correspondingly, the IoT network structure has gradually evolved from small-scale distributed systems to a large-scale hierarchical layout characterized by tight collaboration between backbone and access networks, showcasing strong cross-domain communication potential [4; 5; 6]. In this context, the dynamic characteristic of backbone node connections and the surge in service demands pose a pressing challenge: how to achieve rapid fault detection of backbone node links and real-time awareness of topological changes, thereby increasing the effective transmission time of services. In the process of service transmission, the role of routing protocols becomes increasingly critical, especially in the Internet of Things (IoT), where the on-demand routing protocol AODV is widely used [7; 8]. However, the path selection of AODV is often relatively singular, which can lead to route contention and result in network congestion issues. Furthermore, the delays associated with AODV's path discovery process conflict with the real-time awareness requirements of backbone network nodes regarding topological changes, thereby limiting the application of AODV within backbone networks. To optimize the issue of routing contention in the Internet of Things, [PERSON] et al. proposeda congestion- and interference-aware energy efficient routing technique for the IoT. This approach is based on the signal-to-noise ratio and noise ratio of links. By evaluating the survivability factor of the path from the next-hop node to the destination and its current congestion level, it effectively meets the data routing demands in high-load network environments [9]. [PERSON] et al. introduced a routing algorithm based on reinforcement learning, which constructs a reward function using remaining energy and hop count, optimizing routing in wireless sensor networks (WSNs), extending network lifespan, and ensuring a good data flow transmission rate [10]. [PERSON] et al. utilized reinforcement learning to optimize routing in software-defined networking (SDN) wireless sensor networks, proposing a reward function based on energy utilization and QoS requirements, significantly improving data flow transmission efficiency [11]. Although these algorithms have reduced routing contention and improved data transmission efficiency to some extent, they primarily avoid routing contention by optimizing paths. When link failures occur between nodes and fault detection is not timely, even the best routing algorithms struggle to mitigate the impact of faulty links, leading to packet loss and reduced transmission efficiency. Open Shortest Path First (OSPF) is a proactive routing protocol that possesses a comprehensive network topology view of all nodes within the area [12; 13; 14]. In the event of a link failure, it can swiftly disseminate information to all nodes and update routing, ensuring rapid route convergence across all nodes simultaneously. This mechanism is particularly suitable for backbone nodes in the Internet of Things, as it avoids the delays associated with path discovery in AODV. However, its fault detection process is mechanical and slow, making it difficult to quickly identify failures, which severely impacts service transmission in the IoT and hinders its deployment. To accelerate fault detection speed, the literature [15; 16; 17] has introduced the BFD protocol. BFD establishes independent sessions between OSPF neighbors to send probe messages at millisecond intervals, allowing for real-time monitoring of link status and rapid detection of link failures. However, this high-frequency probing also results in increased routing overhead. Particularly in cases of link congestion or interference, BFD is prone to false alarms, leading to unnecessary route convergence and further exacerbating routing overhead in the network [18].