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

2025-10-22

AI Summary

Large-scale Traveling Salesman Problems (TSP) pose three key challenges for neural solvers: excessive memory consumption, poor initial solution quality, and insufficient global search guidance. To address these, this paper proposes a hypercycle-guided neighborhood search framework. Its core innovation is a “cluster-then-route” strategy: spatial clustering is performed on a sparse heatmap; clusters are abstracted as hypernodes, which are then connected into a hypercycle serving as a structural prior to guide both solution initialization and local optimization. The method integrates cluster analysis, sparse graph modeling, and efficient neighborhood search, substantially reducing the search space and eliminating redundant computation. Evaluated on both synthetic and real-world large-scale TSP instances, our approach significantly narrows the optimality gap and outperforms state-of-the-art neural TSP solvers in solution quality and scalability.

Technology Category

• Search and Optimization: Heuristic Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Scaling neural methods to large TSP instances
• Addressing memory constraints in global heatmaps
• Improving initial solutions and global search guidance

Innovation

• Hyper Tour Guided Neighborhood Search for TSP
• Clustering first, route second strategy with supernodes
• Sparse heatmap graph reduces search space efficiently