Exploring the power of graph neural networks in solving linear optimization problems

C Qian, D Chételat, C Morris - International Conference on …, 2024 - proceedings.mlr.press
Recently, machine learning, particularly message-passing graph neural networks (MPNNs),
has gained traction in enhancing exact optimization algorithms. For example, MPNNs speed …

On representing linear programs by graph neural networks

Z Chen, J Liu, X Wang, J Lu, W Yin - arXiv preprint arXiv:2209.12288, 2022 - arxiv.org
Learning to optimize is a rapidly growing area that aims to solve optimization problems or
improve existing optimization algorithms using machine learning (ML). In particular, the …

Learning cut selection for mixed-integer linear programming via hierarchical sequence model

Z Wang, X Li, J Wang, Y Kuang, M Yuan, J Zeng… - arXiv preprint arXiv …, 2023 - arxiv.org
Cutting planes (cuts) are important for solving mixed-integer linear programs (MILPs), which
formulate a wide range of important real-world applications. Cut selection--which aims to …

Taking the human out of decomposition-based optimization via artificial intelligence, Part I: Learning when to decompose

I Mitrai, P Daoutidis - Computers & Chemical Engineering, 2024 - Elsevier
In this paper, we propose a graph classification approach for automatically determining
whether to use a monolithic or a decomposition-based solution method. In this approach, an …

Machine learning insides optverse ai solver: Design principles and applications

X Li, F Zhu, HL Zhen, W Luo, M Lu, Y Huang… - arXiv preprint arXiv …, 2024 - arxiv.org
In an era of digital ubiquity, efficient resource management and decision-making are
paramount across numerous industries. To this end, we present a comprehensive study on …

Accelerate presolve in large-scale linear programming via reinforcement learning

Y Kuang, X Li, J Wang, F Zhu, M Lu, Z Wang… - arXiv preprint arXiv …, 2023 - arxiv.org
Large-scale LP problems from industry usually contain much redundancy that severely hurts
the efficiency and reliability of solving LPs, making presolve (ie, the problem simplification …

Learning to Cut via Hierarchical Sequence/Set Model for Efficient Mixed-Integer Programming

J Wang, Z Wang, X Li, Y Kuang, Z Shi, F Zhu… - arXiv preprint arXiv …, 2024 - arxiv.org
Cutting planes (cuts) play an important role in solving mixed-integer linear programs
(MILPs), which formulate many important real-world applications. Cut selection heavily …

Smart initial basis selection for linear programs

Z Fan, X Wang, O Yakovenko… - International …, 2023 - proceedings.mlr.press
The simplex method, introduced by Dantzig more than half a century ago, is still to date one
of the most efficient methods for solving large-scale linear programming (LP) problems …

G2MILP: Learning to Generate Mixed-Integer Linear Programming Instances for MILP Solvers

J Wang, Z Geng, X Li, J Hao, Y Zhang, F Wu - Authorea Preprints, 2023 - techrxiv.org
There have been significant efforts devoted to developing advanced mixed-integer linear
programming (MILP) solvers, which are powerful tools for solving various real-world …

HGCN2SP: Hierarchical Graph Convolutional Network for Two-Stage Stochastic Programming

Y Wu, Y Zhang, Z Liang, J Cheng - Forty-first International Conference on … - openreview.net
Two-stage Stochastic Programming (2SP) is a standard framework for modeling decision-
making problems under uncertainty. While numerous methods exist, solving such problems …