Towards a General Recipe for Combinatorial Optimization With Multi-Filter GNNs

Frederik Wenkel, Semih Cantürk, Stefan Horoi, Michael Perlmutter, Guy Wolf
Proceedings of the Third Learning on Graphs Conference, PMLR 269:3:1-3:20, 2025.

Abstract

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 clique, minimum dominating set, and maximum cut problems in a self-supervised 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v269-wenkel25a, title = {Towards a General Recipe for Combinatorial Optimization With Multi-Filter GNNs}, author = {Wenkel, Frederik and Cant{\"u}rk, Semih and Horoi, Stefan and Perlmutter, Michael and Wolf, Guy}, booktitle = {Proceedings of the Third Learning on Graphs Conference}, pages = {3:1--3:20}, year = {2025}, editor = {Wolf, Guy and Krishnaswamy, Smita}, volume = {269}, series = {Proceedings of Machine Learning Research}, month = {26--29 Nov}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v269/main/assets/wenkel25a/wenkel25a.pdf}, url = {https://proceedings.mlr.press/v269/wenkel25a.html}, abstract = {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 clique, minimum dominating set, and maximum cut problems in a self-supervised 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.} }
Endnote
%0 Conference Paper %T Towards a General Recipe for Combinatorial Optimization With Multi-Filter GNNs %A Frederik Wenkel %A Semih Cantürk %A Stefan Horoi %A Michael Perlmutter %A Guy Wolf %B Proceedings of the Third Learning on Graphs Conference %C Proceedings of Machine Learning Research %D 2025 %E Guy Wolf %E Smita Krishnaswamy %F pmlr-v269-wenkel25a %I PMLR %P 3:1--3:20 %U https://proceedings.mlr.press/v269/wenkel25a.html %V 269 %X 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 clique, minimum dominating set, and maximum cut problems in a self-supervised 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.
APA
Wenkel, F., Cantürk, S., Horoi, S., Perlmutter, M. & Wolf, G.. (2025). Towards a General Recipe for Combinatorial Optimization With Multi-Filter GNNs. Proceedings of the Third Learning on Graphs Conference, in Proceedings of Machine Learning Research 269:3:1-3:20 Available from https://proceedings.mlr.press/v269/wenkel25a.html.

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