# Inverse Coupled Simulated Annealing for Enhanced OSPF Convergence in IoT Networks
## 1 Introduction
To reduce routing overhead, [PERSON] et al. developed a tool based on an enhanced simulated annealing algorithm, aimed at automatically optimizing OSPF area partitioning to balance multi-objective performance requirements. This tool effectively reduces routing overhead, convergence time, and latency while improving bandwidth utilization [19]. However, its applicability is limited, primarily targeting network environments with minimal topological changes. Considering the dynamic characteristics of network topology in the IoT, this limitation affects the tool's feasibility in practical deployment. In response to time-varying network topologies, the IETF has introduced the OSPF-MPR [20; 21], OSPF-MDR [22], and OSPF-OR [23] protocols to address topological changes in MANETs. These protocols introduce specific mechanisms to meet the demand for routing convergence in MANET topologies; however, their effectiveness in improving convergence speed is not significant. To address this gap, researchers have introduced centrality into the routing convergence process to enhance convergence speed while optimizing routing overhead to some extent. References [24; 25] discuss the placement problem of Designated Routers (DRs) and propose optimizing DR layouts using betweenness centrality, closeness centrality, and degree centrality to shorten routing convergence time. References [26; 27] adjust the sending frequency of Hello packets based on betweenness centrality, increasing the frequency for nodes with higher intermediary centrality to expedite fault detection and reduce routing overhead. References [28; 29; 30] optimize the sending of Hello packets based on load centrality, running the load centrality algorithm directly in distributed routers to reduce computational complexity, significantly improving routing convergence efficiency. Although centrality-based algorithms have achieved success in accelerating fault detection and controlling routing overhead, nodes with lower centrality can still become critical routing nodes. Their failures can delay link fault detection and convergence, leading to data loss. Furthermore, nodes with higher centrality may waste network resources due to the frequent sending of Hello messages. To address this, this paper proposes an inverse coupled simulated annealing for enhanced OSPF route convergence (OSPF-ICSA), aimed at resolving the issues of time-varying topology in IoT backbone nodes, slow fault detection, and inadequate topological awareness, which result in shorter effective transmission times for services. This method integrates the OSPF protocol into the Internet of Things and improves upon the traditional OSPF protocol. This method first utilizes the statistical characteristics of Hello packets to assess the link state and characterizes the node state through aggregated link state features, dynamically reflecting the topological changes of nodes in the IoT. This process effectively captures the dynamic characteristics of connection relationships, providing real-time network state data support for the inverse coupled annealing algorithm. Secondly, based on the improvement of Hello packets, a mechanism for OSPF interval synchronization and node state transmission is designed to ensure that the sending intervals and fault detection times of all nodes within the same subnet are synchronized, facilitating the effective transmission of node status messages and laying the foundation for the efficient application of the inverse coupled annealing algorithm. Finally, based on this foundation, the inverse coupled annealing algorithm is introduced to collaboratively optimize the sending intervals of Hello packets and fault detection times through two coupled annealing algorithms, dynamically adjusting the sending frequency of Hello packets and fault detection times. In poor link states, this accelerates fault detection so that nodes can more swiftly and flexibly identify and respond to link failures, thus shortening overall routing convergence time.