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 in feasibility prediction accuracy and convergence speed on Foldable MILPs, while using significantly fewer parameters. It also generalizes effectively among problem scales and demonstrates strong performance on real-world MILP benchmarks when integrated into an end-to-end solver pipeline. Our code is available.