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 a novel GNN architecture which leverages a complex filter bank and localized attention mechanisms designed 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. In addition to demonstrating competitive overall performance across all tasks, we establish state-of-the-art results for the max cut problem.

翻译：图神经网络（GNNs）在节点分类、图分类和链接预测等多种任务中取得了显著成功。然而，利用GNN（以及更广泛的机器学习方法）解决组合优化（CO）问题的研究仍较为有限。本文提出一种新颖的图神经网络架构，该架构采用复合滤波器组与局部注意力机制，专门设计用于解决图上的组合优化问题。我们阐述了该方法与现有基于GNN的组合优化求解器的区别，并展示了如何通过自监督学习方式将其有效应用于最大团、最小支配集及最大割问题。实验结果表明，我们的方法在所有任务中均展现出具有竞争力的综合性能，并在最大割问题上取得了当前最优的结果。