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

Frederik Wenkel, Semih Cantürk, Stefan Horoi, Michael Perlmutter, Guy Wolf

Keywords: graph neural networks, graph representation learning, combinatorial optimization

TL;DR: We design a novel GNN-based encoder-decoder framework to solve combinatorial optimization problems on graphs, and demonstrate leading performance on the max-cut problem

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.

Submission Type: Full paper proceedings track submission (max 9 main pages).

Software: https://github.com/WenkelF/copt

Submission Number: 64