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A General Neural Backbone for Mixed-Integer Linear Optimization via Dual Attention

Year: 2026

Type: preprint

Abstract: Mixed-integer linear programming (MILP) is a foundational framework for combinatorial optimization across science and engineering, but remains hard to solve at scale due to NP-hardness. Recent learning-based methods typically model MILP instances as variable-constraint bipartite graphs and use Graph Neural Networks (GNNs) for representation learning, yet their locality limits representation power. We propose an attention-driven neural backbone that adopts an element-centric view of variables and constraints, with dual attention performing parallel intra-type self-attention and inter-type cross-attention. Across three representative tasks at the instance, element, and solving-state levels, our model consistently outperforms conventional GNN-based architectures, highlighting attention-based, element-centric modeling as a powerful foundation for learning-enhanced combinatorial optimization.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2601.04509

Authors: Huang, Peixin, Wu, Yaoxin, Ma, Yining, Wu, Cathy, Zhang, Wei, Song, Wen

Institutions: Eindhoven University of Technology, Massachusetts Institute of Technology, Qingdao Binhai University

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7119938225

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