GELD: A Unified Neural Model for Efficiently Solving Traveling Salesman Problems Across Different Scales

2025-06-07

AI Summary

Existing neural TSP solvers struggle to efficiently handle multi-scale instances using a single pre-trained model, limiting practical deployment. This paper proposes GELD, the first unified neural solver capable of end-to-end solving TSP instances ranging from dozens to 744,000 nodes with one model. GELD features a lightweight global encoder coupled with a heavy local decoder, incorporates a low-complexity attention mechanism, and employs a two-stage multi-scale training strategy. Unlike divide-and-conquer approaches, GELD solves ultra-large-scale TSP instances directly and end-to-end. It consistently outperforms seven state-of-the-art methods on both synthetic and real-world benchmarks, achieving superior solution quality and inference efficiency. Moreover, GELD serves as a plug-and-play post-processor to enhance existing solvers’ performance. By bridging the gap between scalability, accuracy, and speed, GELD significantly extends the practical applicability of neural combinatorial optimization.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

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
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

The Traveling Salesman Problem (TSP) is a well-known combinatorial optimization problem with broad real-world applications. Recent advancements in neural network-based TSP solvers have shown promising results. Nonetheless, these models often struggle to efficiently solve both small- and large-scale TSPs using the same set of pre-trained model parameters, limiting their practical utility. To address this issue, we introduce a novel neural TSP solver named GELD, built upon our proposed broad global assessment and refined local selection framework. Specifically, GELD integrates a lightweight Global-view Encoder (GE) with a heavyweight Local-view Decoder (LD) to enrich embedding representation while accelerating the decision-making process. Moreover, GE incorporates a novel low-complexity attention mechanism, allowing GELD to achieve low inference latency and scalability to larger-scale TSPs. Additionally, we propose a two-stage training strategy that utilizes training instances of different sizes to bolster GELD's generalization ability. Extensive experiments conducted on both synthetic and real-world datasets demonstrate that GELD outperforms seven state-of-the-art models considering both solution quality and inference speed. Furthermore, GELD can be employed as a post-processing method to significantly elevate the quality of the solutions derived by existing neural TSP solvers via spending affordable additional computing time. Notably, GELD is shown as capable of solving TSPs with up to 744,710 nodes, first-of-its-kind to solve this large size TSP without relying on divide-and-conquer strategies to the best of our knowledge.

Problem

• Efficiently solving TSPs across different scales with one model
• Improving neural TSP solvers' generalization and scalability
• Achieving high solution quality and fast inference speed

Innovation

• Combines lightweight global encoder with local decoder
• Uses low-complexity attention for fast inference
• Two-stage training enhances generalization across scales