# Towards a General Recipe for Combinatorial Optimization with Multi-Filter GNNs

arXiv: https://arxiv.org/abs/2405.20543 · HTML: https://mlsanity.com/paper/2405.20543/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2024.

## Built on by (most cited first, 9 of 9)

- [Primal-Dual Neural Algorithmic Reasoning](https://mlsanity.com/paper/2505.24067/) (2025)
- [VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks](https://mlsanity.com/paper/2510.01022/) (2025)
- [A General Neural Backbone for Mixed-Integer Linear Optimization via Dual Attention](https://mlsanity.com/paper/2601.04509/) (2026)
- [Preference-Based Gradient Estimation for ML-Guided Approximate Combinatorial Optimization](https://mlsanity.com/paper/2502.19377/) (2025)
- [InfoGain Wavelets: Furthering the Design of Graph Diffusion Wavelets](https://mlsanity.com/paper/2504.08802/) (2025)
- [ARM-Explainer -- Explaining and improving graph neural network predictions for the maximum clique problem using node features and association rule mining](https://mlsanity.com/paper/2511.22866/) (2025)
- [GraIP: A Benchmarking Framework For Neural Graph Inverse Problems](https://mlsanity.com/paper/2601.18917/) (2026)
- [Can Computational Reducibility Lead to Transferable Models for Graph Combinatorial Optimization?](https://mlsanity.com/paper/2603.02462/) (2026)
- [Graph Neural Networks for Influence Maximization in Social Networks: An Unsupervised Minimum Dominating Set Approach](https://mlsanity.com/paper/2609.13836/) (2026)

## Abstract (arXiv)

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.