MILPnet: A Multi-Scale Architecture with Geometric Feature Sequence Representations for Advancing MILP Problems

We propose MILPnet, a multi-scale hybrid attention framework that models Mixed Integer Linear Programming (MILP) problems as geometric sequences rather than graphs. This approach directly addresses the challenge of Foldable MILP instances, a class of problems that graph-based models, specifically Graph Neural Networks (GNNs), fail to distinguish due to expressiveness limits imposed by the Weisfeiler-Lehman test. By representing MILPs through sequences of constraint and objective features, MILPnet captures both local and global geometric structure using a theoretically grounded multi-scale attention mechanism. We theoretically prove that MILPnet can approximate feasibility, optimal objective value, and optimal solution mappings over a measurable topological space with arbitrarily small error. Empirically, MILPnet outperforms graph-based methods by multiple orders of magnitude in feasibility prediction accuracy and convergence speed on Foldable MILPs, while using significantly fewer parameters. It also generalizes effectively across problem scales and demonstrates strong performance on real-world MILP benchmarks when integrated into an end-to-end solver pipeline.Our code is available with the https://anonymous.4open.science/r/MILPnet-2BD1/