GNN-based bounded maximum flow approximation for routing and wavelength assignment in dynamic optical networks

The growing global demand for data traffic necessitates continuous capacity expansion in optical networks. Maximizing the utilization of enhanced physical infrastructure critically depends on efficient routing and wavelength assignment (RWA), especially under dynamic optical path controls. While machine learning (ML) approaches have shown promise for RWA, many proposals still struggle to consistently outperform traditional heuristics. A key limitation is their lack of explicit awareness of global residual capacity of the network, often resulting in suboptimal resource allocation. Effective capacity-aware routing requires evaluating global metrics such as maximum flow between node pairs. However, constrained variants of the maximum flow problem involving bounded maximum flows with physical transmission constraints are NP-complete or NP-hard. In this work, we propose a graph neural network (GNN)-based framework for RWA in optical networks, leveraging approximate bounded maximum flows across all node pairs to guide routing decisions. Our method introduces a deterministic global metric that quantifies residual capacity and enables capacity-aware routing under dynamic conditions. To ensure real-time applicability, we develop a GNN-based approximator with low inference overhead, making it suitable for integration into online network management systems. Simulations show that our approach significantly outperforms heuristic baselines in terms of achievable network capacity. Notably, our method reaches up to 98.8% of an upper bound given in our previous study, highlighting the effectiveness of incorporating global capacity metrics through GNN approximation. This work demonstrates the practical benefits of global metric approximation for robust and scalable optical network control.