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

TL;DR

This paper introduces GCON, a novel GNN architecture with a complex filter bank and localized attention, effectively solving various combinatorial optimization problems on graphs and outperforming existing GNN-based methods.

Contribution

The paper presents GCON, a new GNN model that advances combinatorial optimization solutions by integrating complex filters and attention mechanisms, demonstrating superior performance.

Findings

GCON outperforms other GNN-based approaches on multiple CO tasks.

GCON matches Gurobi's performance on max-cut problem.

The method is effective in an unsupervised learning setting.

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 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.