An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem

TL;DR

This paper presents a deep learning-based graph convolutional network method for efficiently approximating solutions to the Travelling Salesman Problem, achieving higher solution quality and faster inference than previous neural approaches.

Contribution

Introduces a novel non-autoregressive deep GCN approach with parallelized beam search for TSP, significantly improving solution quality and inference speed over prior neural methods.

Findings

Reduces average optimality gap to 0.01% for 50 nodes

Achieves faster inference than autoregressive models

Outperforms recent neural approaches in solution quality

Abstract

This paper introduces a new learning-based approach for approximately solving the Travelling Salesman Problem on 2D Euclidean graphs. We use deep Graph Convolutional Networks to build efficient TSP graph representations and output tours in a non-autoregressive manner via highly parallelized beam search. Our approach outperforms all recently proposed autoregressive deep learning techniques in terms of solution quality, inference speed and sample efficiency for problem instances of fixed graph sizes. In particular, we reduce the average optimality gap from 0.52% to 0.01% for 50 nodes, and from 2.26% to 1.39% for 100 nodes. Finally, despite improving upon other learning-based approaches for TSP, our approach falls short of standard Operations Research solvers.