A Hierarchical Destroy and Repair Approach for Solving Very Large-Scale Travelling Salesman Problem

TL;DR

This paper introduces a hierarchical destroy-and-repair approach for solving extremely large-scale TSPs, achieving state-of-the-art results and breaking world records on instances with up to 10 million cities.

Contribution

The paper presents a novel hierarchical search framework that recursively simplifies large TSPs, enabling efficient and high-quality solutions for problems with up to 10 million cities.

Findings

HDR breaks world records on two large instances with over 3 million and 10 million cities.

HDR outperforms existing state-of-the-art algorithms in efficiency and solution quality.

Ablation studies confirm the effectiveness of the hierarchical search framework.

Abstract

For prohibitively large-scale Travelling Salesman Problems (TSPs), existing algorithms face big challenges in terms of both computational efficiency and solution quality. To address this issue, we propose a hierarchical destroy-and-repair (HDR) approach, which attempts to improve an initial solution by applying a series of carefully designed destroy-and-repair operations. A key innovative concept is the hierarchical search framework, which recursively fixes partial edges and compresses the input instance into a small-scale TSP under some equivalence guarantee. This neat search framework is able to deliver highly competitive solutions within a reasonable time. Fair comparisons based on nineteen famous large-scale instances (with 10,000 to 10,000,000 cities) show that HDR is highly competitive against existing state-of-the-art TSP algorithms, in terms of both efficiency and solution quality. Notably, on two large instances with 3,162,278 and 10,000,000 cities, HDR breaks the world records (i.e., best-known results regardless of computation time), which were previously achieved by LKH and its variants, while HDR is completely independent of LKH. Finally, ablation studies are performed to certify the importance and validity of the hierarchical search framework.