Unsupervised Graph Neural Networks for Solving Combinatorial Optimization Problems by Iterative Solution Refinement

ICLR 2026 Conference Submission15883 Authors

Keywords: graph neural networks, combinatorial optimization, binary optimization

TL;DR: We propose an unsupervised GNN with novel iterative refinement design, achieving state-of-the-art results on three classic combinatorial optimization problems.

Abstract: Combinatorial optimization (CO) problems are crucial in various scientific and industrial applications. Recently, Graph Neural Networks (GNNs) have been proposed as a framework for addressing NP-hard CO problems, demonstrating high performance and nearly linear scalability. Current approaches utilize GNNs to directly predict solutions based on standard node features. However, such methods are prone to overfitting and tend to converge to suboptimal local minima of the energy landscape, resulting in low quality solutions. We introduce a novel optimization method leveraging the power of GNNs to efficiently process CO problems with Quadratic Unconstrained Binary Optimization (QUBO) formulation. Instead of predicting a solution from a fixed static set of node features, the method implies iterative improvement of the current solution with GNNs, using the predictions obtained at each step as new properties of graph vertices. We also propose certain modifications to the GNN architecture and a set of additional static properties that can further improve quality. The performance of the proposed algorithm has been evaluated on the canonical CO benchmark datasets. Results of experiments show that our method drastically surpasses existing learning-based approaches and is comparable to the state-of-the-art conventional heuristics, improving their scalability on large instances.

Primary Area: optimization

Submission Number: 15883