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Paper · 2310.10603 · 2023

Exploring the Power of Graph Neural Networks in Solving Linear Optimization Problems

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 8 functions out of this paper's own repositories and ran 8 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
chendiqian/IPM_MPNN canonical 8 of 8
FunctionStatusWhere it lives
conjugate_gradient Ran chendiqian/IPM_MPNN/solver/customized_solver.py
pointer only (licence: NONE) · get_code("7955265e3c15e7cf")
generate_cauctions Ran chendiqian/IPM_MPNN/generate_instances.py
pointer only (licence: NONE) · get_code("6c046af73ef8cd52")
generate_indset Ran chendiqian/IPM_MPNN/generate_instances.py
pointer only (licence: NONE) · get_code("7d5a765761e14c57")
generate_setcover Ran chendiqian/IPM_MPNN/generate_instances.py
pointer only (licence: NONE) · get_code("67c3ee9f8aaa3b8b")
group Ran chendiqian/IPM_MPNN/models/hetero_conv.py
pointer only (licence: NONE) · get_code("9487a12f79643518")
ipm_overleaf Ran chendiqian/IPM_MPNN/solver/customized_solver.py
pointer only (licence: NONE) · get_code("1bf4f353e2d721f2")
mu Ran chendiqian/IPM_MPNN/solver/customized_solver.py
pointer only (licence: NONE) · get_code("82b3f377465b4232")
strseq2rank Ran chendiqian/IPM_MPNN/models/hetero_gnn.py
pointer only (licence: NONE) · get_code("2e76d1aa4e238af5")

Repositories linked to this paper

Some links come from the archived Papers with Code dataset (CC BY-SA 4.0): attribution and licence.

Abstract

Recently, machine learning, particularly message-passing graph neural networks (MPNNs), has gained traction in enhancing exact optimization algorithms. For example, MPNNs speed up solving mixed-integer optimization problems by imitating computational intensive heuristics like strong branching, which entails solving multiple linear optimization problems (LPs). Despite the empirical success, the reasons behind MPNNs' effectiveness in emulating linear optimization remain largely unclear. Here, we show that MPNNs can simulate standard interior-point methods for LPs, explaining their practical success. Furthermore, we highlight how MPNNs can serve as a lightweight proxy for solving LPs, adapting to a given problem instance distribution. Empirically, we show that MPNNs solve LP relaxations of standard combinatorial optimization problems close to optimality, often surpassing conventional solvers and competing approaches in solving time.

For agents

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get_code_for_paper("2310.10603")
have("2310.10603")

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