Cross-Problem Solving for Network Optimization: Is Problem-Aware Learning the Key?

As intelligent network services continue to diversify, ensuring efficient and adaptive resource allocation in edge networks has become increasingly critical. Yet the wide functional variations across services often give rise to new and unforeseen optimization problems, rendering traditional manual modeling and solver design both time-consuming and inflexible. This limitation reveals a key gap between current methods and human solving - the inability to recognize and understand problem characteristics. It raises the question of whether problem-aware learning can bridge this gap and support effective cross-problem generalization. To answer this question, we propose a problem-aware diffusion (PAD) model, which leverages a problem-aware learning framework to enable cross-problem generalization. By explicitly encoding the mathematical formulations of optimization problems into token-level embeddings, PAD empowers the model to understand and adapt to problem structures. Extensive experiments across ten representative network optimization problems show that PAD generalizes well to unseen problems while avoiding the inefficiency of building new solvers from scratch, yet still delivering competitive solution quality. Meanwhile, an auxiliary constraint-aware module is designed to enforce solution validity further. The experiments indicate that problem-aware learning opens a promising direction toward general-purpose solvers for intelligent network operation and resource management. Our code is open source at https://github.com/qiyu3816/PAD.