A Unified Framework for Combinatorial Optimization Based on Graph Neural Networks

TL;DR

This paper introduces a comprehensive GNN-based framework that unifies the approach to solving a broad spectrum of combinatorial optimization problems, including both graph-structured and non-graph-structured types.

Contribution

It presents a novel, generic framework that converts various COPs into graph representations and applies GNNs, overcoming limitations of previous specialized methods.

Findings

Effective graph representation of diverse COPs

Unified approach improves solution quality

Handles complex and non-graph-structured COPs

Abstract

Graph neural networks (GNNs) have emerged as a powerful tool for solving combinatorial optimization problems (COPs), exhibiting state-of-the-art performance in both graph-structured and non-graph-structured domains. However, existing approaches lack a unified framework capable of addressing a wide range of COPs. After presenting a summary of representative COPs and a brief review of recent advancements in GNNs for solving COPs, this paper proposes a unified framework for solving COPs based on GNNs, including graph representation of COPs, equivalent conversion of non-graph structured COPs to graph-structured COPs, graph decomposition, and graph simplification. The proposed framework leverages the ability of GNNs to effectively capture the relational information and extract features from the graph representation of COPs, offering a generic solution to COPs that can address the limitations of state-of-the-art in solving non-graph-structured and highly complex graph-structured COPs.