Empowering Targeted Neighborhood Search via Hyper Tour for Large-Scale TSP

TL;DR

This paper introduces Hyper Tour Guided Neighborhood Search (HyperNS), a novel method for large-scale TSP that improves efficiency and solution quality by clustering and hyper tour guidance, outperforming existing neural-based approaches.

Contribution

The paper presents a hyper tour guided neighborhood search method that effectively scales neural-based TSP solutions to larger instances by clustering and hyper tour guidance.

Findings

Outperforms existing neural-based methods on large-scale TSP datasets.

Reduces the solution gap significantly compared to prior approaches.

Efficiently handles larger instances with improved solution quality.

Abstract

Traveling Salesman Problem (TSP) is a classic NP-hard problem that has garnered significant attention from both academia and industry. While neural-based methods have shown promise for solving TSPs, they still face challenges in scaling to larger instances, particularly in memory constraints associated with global heatmaps, edge weights, or access matrices, as well as in generating high-quality initial solutions and insufficient global guidance for efficiently navigating vast search spaces. To address these challenges, we propose a Hyper Tour Guided Neighborhood Search (HyperNS) method for large-scale TSP instances. Inspired by the ``clustering first, route second" strategy, our approach initially divides the TSP instance into clusters using a sparse heatmap graph and abstracts them as supernodes, followed by the generation of a hyper tour to guide both the initialization and optimization processes. This method reduces the search space by focusing on edges relevant to the hyper tour, leading to more efficient and effective optimization. Experimental results on both synthetic and real-world datasets demonstrate that our approach outperforms existing neural-based methods, particularly in handling larger-scale instances, offering a significant reduction in the gap to the optimal solution.