面向神经组合优化的几何自监督预训练

中文摘要 AI 辅助

神经组合优化（Neural Combinatorial Optimization，NCO）技术已成为求解旅行商问题（Traveling Salesman Problem，TSP）等路由问题的传统精确算法的高效替代方案。然而，这些基于强化学习的模型在扩展到高维实例时，泛化能力受到严重阻碍。在计算机视觉和自然语言处理等其他领域，自监督预训练策略已缓解了这类问题，但该策略应用于仅包含二维空间坐标、缺乏复杂拓扑属性的路由图时仍是挑战。本文提出一种专门用于捕捉空间不变性和全局相对距离分布的几何自监督预训练框架，通过应用旋转、轴向反射等等距变换，使模型在策略优化阶段前学习到鲁棒的结构表示。实验结果表明，该策略始终优于从头训练的基线模型，在大规模零样本外推场景（TSP1000）中，路径长度提升7.23%；此外，所提模型具备出色的计算效率，在大规模场景下比精确求解器Concorde提速最高达两个数量级。源代码和预训练模型可在该httpsURL获取。

英文摘要

Neural Combinatorial Optimization (NCO) techniques have emerged as a highly efficient alternative to traditional exact algorithms for solving routing problems such as the Traveling Salesman Problem (TSP). However, the generalization capabilities of these Reinforcement Learning-based models are severely hindered when scaling to high-dimensional instances. This issue has been mitigated in other domains, like computer vision and natural language processing, by adopting a self-supervised pre-training strategy. Nevertheless, its application to routing graphs, which lack complex topological attributes beyond 2D spatial coordinates, remains a challenge. In this paper, we propose a geometric self-supervised pre-training framework specifically designed to capture spatial invariance and global relative distance distributions. By applying isometric transformations, such as rotations and axial reflections, the model learns robust structural representations prior to the policy optimization phase. Empirical results demonstrate that this strategy consistently outperforms models trained from scratch (baselines), achieving a 7.23\% improvement in tour length for massive zero-shot extrapolation scenarios (TSP1,000). Furthermore, the proposed model exhibits remarkable computational efficiency, delivering speedups of up to two orders of magnitude over the exact solver Concorde at massive scales. The source code and pre-trained models are publicly available at https://github.com/davidaguadocosano/TSP-GeoPretrain.git.

发表机构

• Universidad Politécnica de Madrid（马德里理工大学）
• Information Processing and Telecomunications Center（信息处理与通信中心）
• ETSI Telecomunicación（电信高等技术工程学院）
• Grupo de Tratamiento de Imágenes（图像处理组）

机构由 AI 辅助整理，请以论文原文为准。