# Sequence-Structured Decision Learning for Branch-and-Bound in Mixed-Integer Linear Programming

arXiv: https://arxiv.org/abs/2610.14835 · HTML: https://mlsanity.com/paper/2610.14835/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 41 references that are in the map.
- First posted on arXiv 10 Oct 2026.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies](https://mlsanity.com/paper/2002.05120/) (2020)
- [Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learning](https://mlsanity.com/paper/2206.13414/) (2022)
- [Learning to Schedule Heuristics in Branch-and-Bound](https://mlsanity.com/paper/2103.10294/) (2021)
- [Learning a Large Neighborhood Search Algorithm for Mixed Integer Programs](https://mlsanity.com/paper/2107.10201/) (2021)
- [Learning to Compare Nodes in Branch and Bound with Graph Neural Networks](https://mlsanity.com/paper/2210.16934/) (2022)
- [Towards Foundation Models for Mixed Integer Linear Programming](https://mlsanity.com/paper/2410.08288/) (2024)
- [Reinforcement Learning for Variable Selection in a Branch and Bound Algorithm](https://mlsanity.com/paper/2005.10026/) (2020)
- [Lookback for Learning to Branch](https://mlsanity.com/paper/2206.14987/) (2022)
- [Adaptive Cut Selection in Mixed-Integer Linear Programming](https://mlsanity.com/paper/2202.10962/) (2022)
- [Reinforcement Learning for Branch-and-Bound Optimisation using Retrospective Trajectories](https://mlsanity.com/paper/2205.14345/) (2022)
- [Machine Learning for Cutting Planes in Integer Programming: A Survey](https://mlsanity.com/paper/2302.09166/) (2023)
- [Learning to Search via Retrospective Imitation](https://mlsanity.com/paper/1804.00846/) (2018)
- [Multi-task Representation Learning for Mixed Integer Linear Programming](https://mlsanity.com/paper/2412.14409/) (2024)

## Abstract (arXiv)

Branch-and-bound (BnB) solves mixed-integer linear programs by constructing and exploring a search tree. Node selection and branching are two recurrent decisions that directly determine the tree. Learning-based approaches typically optimize either decision in isolation and condition on a mostly local view, leaving the coupled evolution of the search tree insufficiently modeled. This paper proposes Seq-BnB, a sequence-structured framework that learns branching and node selection from a shared global representation of the evolving BnB process. Seq-BnB serializes node creations, node updates, node-selection events, and branching events into typed tokens, producing a causal event sequence of the search trajectory. A self-attention encoder summarizes this global search history, a bipartite graph neural network encodes the current LP relaxation, and context-conditioned decision heads score branching variables and open nodes. To reduce distribution shift between expert demonstrations and learned policies, Seq-BnB is trained with DAgger-style data aggregation. On four MILP benchmark families, Seq-BnB consistently processes fewer BnB nodes than heuristic and learning-based baselines, with strong solution times on both standard and larger transfer instances. While this paper evaluates Seq-BnB instantiation for branching and node selection, it accommodates additional solver decisions, such as cut selection, by introducing new action tokens and decision heads.