Towards a General Recipe for Combinatorial Optimization with Multi-Filter GNNs
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929603074850816 |
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| author | Wenkel, Frederik Cantürk, Semih Horoi, Stefan Perlmutter, Michael Wolf, Guy |
| author_facet | Wenkel, Frederik Cantürk, Semih Horoi, Stefan Perlmutter, Michael Wolf, Guy |
| contents | Graph neural networks (GNNs) have achieved great success for a variety of tasks such as node classification, graph classification, and link prediction. However, the use of GNNs (and machine learning more generally) to solve combinatorial optimization (CO) problems is much less explored. Here, we introduce GCON, a novel GNN architecture that leverages a complex filter bank and localized attention mechanisms to solve CO problems on graphs. We show how our method differentiates itself from prior GNN-based CO solvers and how it can be effectively applied to the maximum cut, minimum dominating set, and maximum clique problems in a unsupervised learning setting. GCON is competitive across all tasks and consistently outperforms other specialized GNN-based approaches, and is on par with the powerful Gurobi solver on the max-cut problem. We provide an open-source implementation of our work at https://github.com/WenkelF/copt. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_20543 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards a General Recipe for Combinatorial Optimization with Multi-Filter GNNs Wenkel, Frederik Cantürk, Semih Horoi, Stefan Perlmutter, Michael Wolf, Guy Machine Learning Artificial Intelligence Discrete Mathematics 68T07 (Primary) 68T20, 90C35, 05C62 (Secondary) F.2.2; I.2.6 Graph neural networks (GNNs) have achieved great success for a variety of tasks such as node classification, graph classification, and link prediction. However, the use of GNNs (and machine learning more generally) to solve combinatorial optimization (CO) problems is much less explored. Here, we introduce GCON, a novel GNN architecture that leverages a complex filter bank and localized attention mechanisms to solve CO problems on graphs. We show how our method differentiates itself from prior GNN-based CO solvers and how it can be effectively applied to the maximum cut, minimum dominating set, and maximum clique problems in a unsupervised learning setting. GCON is competitive across all tasks and consistently outperforms other specialized GNN-based approaches, and is on par with the powerful Gurobi solver on the max-cut problem. We provide an open-source implementation of our work at https://github.com/WenkelF/copt. |
| title | Towards a General Recipe for Combinatorial Optimization with Multi-Filter GNNs |
| topic | Machine Learning Artificial Intelligence Discrete Mathematics 68T07 (Primary) 68T20, 90C35, 05C62 (Secondary) F.2.2; I.2.6 |
| url | https://arxiv.org/abs/2405.20543 |