Combinatorial optimization and reasoning with graph neural networks

TL;DR

This paper reviews recent advances in applying graph neural networks to combinatorial optimization, highlighting their ability to encode relational data and improve solver performance.

Contribution

It provides a conceptual overview of how GNNs are being integrated into combinatorial optimization, emphasizing their inductive biases and practical applications.

Findings

GNNs encode combinatorial and relational structures effectively.

Recent methods improve solution quality and computational efficiency.

GNNs enable learning-based approaches to traditional optimization problems.

Abstract

Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring that they often stem from related data distributions in practice. However, recent years have seen a surge of interest in using machine learning, especially graph neural networks (GNNs), as a key building block for combinatorial tasks, either directly as solvers or by enhancing exact solvers. The inductive bias of GNNs effectively encodes combinatorial and relational input due to their invariance to permutations and awareness of input sparsity. This paper presents a conceptual review of recent key advancements in this emerging field, aiming at optimization and machine learning researchers.