# Exact Combinatorial Optimization with Temporo-Attentional Graph Neural Networks

arXiv: https://arxiv.org/abs/2311.13843 · HTML: https://mlsanity.com/paper/2311.13843/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 51 references that are in the map.
- First posted on arXiv 23 Nov 2023.

## Builds on (most cited first, 18 of 18)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [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)
- [Hybrid Models for Learning to Branch](https://mlsanity.com/paper/2006.15212/) (2020)
- [Ecole: A Gym-like Library for Machine Learning in Combinatorial Optimization Solvers](https://mlsanity.com/paper/2011.06069/) (2020)
- [The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insights](https://mlsanity.com/paper/2203.02433/) (2022)
- [Learning to Search via Retrospective Imitation](https://mlsanity.com/paper/1804.00846/) (2018)
- [Learning Primal Heuristics for Mixed Integer Programs](https://mlsanity.com/paper/2107.00866/) (2021)
- [Deep Reinforcement Learning for Exact Combinatorial Optimization: Learning to Branch](https://mlsanity.com/paper/2206.06965/) (2022)
- [ML4CO-KIDA: Knowledge Inheritance in Dataset Aggregation](https://mlsanity.com/paper/2201.10328/) (2022)
- [ML4CO: Is GCNN All You Need? Graph Convolutional Neural Networks Produce Strong Baselines For Combinatorial Optimization Problems, If Tuned and Trained Properly, on Appropriate Data](https://mlsanity.com/paper/2112.12251/) (2021)
- [PENLAB: A MATLAB solver for nonlinear semidefinite optimization](https://mlsanity.com/paper/1311.5240/) (2013)
- [Yordle: An Efficient Imitation Learning for Branch and Bound](https://mlsanity.com/paper/2202.01896/) (2022)

## Built on by (most cited first, 3 of 3)

- [Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programming](https://mlsanity.com/paper/2402.05501/) (2024)
- [Dynamic Stratified Contrastive Learning with Upstream Augmentation for MILP Branching](https://mlsanity.com/paper/2511.21107/) (2025)
- [A Markov Decision Process for Variable Selection in Branch & Bound](https://mlsanity.com/paper/2510.19348/) (2025)

## Abstract (arXiv)

Combinatorial optimization finds an optimal solution within a discrete set of variables and constraints. The field has seen tremendous progress both in research and industry. With the success of deep learning in the past decade, a recent trend in combinatorial optimization has been to improve state-of-the-art combinatorial optimization solvers by replacing key heuristic components with machine learning (ML) models. In this paper, we investigate two essential aspects of machine learning algorithms for combinatorial optimization: temporal characteristics and attention. We argue that for the task of variable selection in the branch-and-bound (B&B) algorithm, incorporating the temporal information as well as the bipartite graph attention improves the solver's performance. We support our claims with intuitions and numerical results over several standard datasets used in the literature and competitions. Code is available at: https://developer.huaweicloud.com/develop/aigallery/notebook/detail?id=047c6cf2-8463-40d7-b92f-7b2ca998e935