Combinatorial Optimization with Graph Convolutional Networks and Guided Tree Search

TL;DR

This paper introduces a novel learning-based method combining graph convolutional networks and guided tree search to efficiently approximate solutions for NP-hard problems, outperforming recent deep learning approaches and matching state-of-the-art heuristics.

Contribution

It presents a new approach that integrates deep learning with classic heuristics, enabling scalable and generalizable solutions for complex NP-hard problems.

Findings

Outperforms recent deep learning methods on NP-hard problems.

Performs comparably to optimized heuristic solvers.

Scales effectively to large graphs with up to 100,000 nodes.

Abstract

We present a learning-based approach to computing solutions for certain NP-hard problems. Our approach combines deep learning techniques with useful algorithmic elements from classic heuristics. The central component is a graph convolutional network that is trained to estimate the likelihood, for each vertex in a graph, of whether this vertex is part of the optimal solution. The network is designed and trained to synthesize a diverse set of solutions, which enables rapid exploration of the solution space via tree search. The presented approach is evaluated on four canonical NP-hard problems and five datasets, which include benchmark satisfiability problems and real social network graphs with up to a hundred thousand nodes. Experimental results demonstrate that the presented approach substantially outperforms recent deep learning work, and performs on par with highly optimized state-of-the-art heuristic solvers for some NP-hard problems. Experiments indicate that our approach generalizes across datasets, and scales to graphs that are orders of magnitude larger than those used during training.