Combinatorial optimization with physics-inspired graph neural networks
| Autor: | Martin J. A. Schuetz, J. Kyle Brubaker, Helmut G. Katzgraber |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Machine Learning Quantum Physics Computer Science - Artificial Intelligence Computer Networks and Communications FOS: Physical sciences Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks Machine Learning (cs.LG) Human-Computer Interaction Artificial Intelligence (cs.AI) Artificial Intelligence Optimization and Control (math.OC) FOS: Mathematics Computer Vision and Pattern Recognition Quantum Physics (quant-ph) Mathematics - Optimization and Control Software |
| Popis: | Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical physics is still outstanding. Here we demonstrate how graph neural networks can be used to solve combinatorial optimization problems. Our approach is broadly applicable to canonical NP-hard problems in the form of quadratic unconstrained binary optimization problems, such as maximum cut, minimum vertex cover, maximum independent set, as well as Ising spin glasses and higher-order generalizations thereof in the form of polynomial unconstrained binary optimization problems. We apply a relaxation strategy to the problem Hamiltonian to generate a differentiable loss function with which we train the graph neural network and apply a simple projection to integer variables once the unsupervised training process has completed. We showcase our approach with numerical results for the canonical maximum cut and maximum independent set problems. We find that the graph neural network optimizer performs on par or outperforms existing solvers, with the ability to scale beyond the state of the art to problems with millions of variables. Comment: Manuscript: 13 pages, 5 figures, 1 table. Supplemental Material: 1 page, 1 table |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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