Deep learning has shown significant potential in solving combinatorial optimization problems such as the Euclidean traveling salesman problem (TSP). However, most training and test instances for existing TSP algorithms are generated randomly from specific distributions like uniform distribution. This has led to a lack of analysis and understanding of the performance of deep learning algorithms in out-of-distribution (OOD) generalization scenarios, which has a close relationship with the worst-case performance in the combinatorial optimization field. For data-driven algorithms, the statistical properties of randomly generated datasets are critical. This study constructs a statistical measure called nearest-neighbor density to verify the asymptotic properties of randomly generated datasets and reveal the greedy behavior of learning-based solvers, i.e., always choosing the nearest neighbor nodes to construct the solution path. Based on this statistical measure, we develop interpretable data augmentation methods that rely on distribution shifts or instance perturbations and validate that the performance of the learning-based solvers degenerates much on such augmented data. Moreover, fine-tuning learning-based solvers with augmented data further enhances their generalization abilities. In short, we decipher the limitations of learning-based TSP solvers tending to be overly greedy, which may have profound implications for AI-empowered combinatorial optimization solvers.

翻译：深度学习在解决欧几里得旅行商问题等组合优化问题上展现出巨大潜力。然而，现有旅行商问题算法的大多数训练和测试实例均从均匀分布等特定分布中随机生成。这导致对深度学习算法在分布外泛化场景下的性能缺乏分析和理解，而该场景与组合优化领域的最坏情况性能密切相关。对于数据驱动算法，随机生成数据集的统计特性至关重要。本研究构建了一种称为最近邻密度的统计度量，以验证随机生成数据集的渐近特性，并揭示基于学习的求解器的贪婪行为，即总是选择最近邻节点来构建解路径。基于此统计度量，我们开发了可解释的数据增强方法，这些方法依赖于分布偏移或实例扰动，并验证了基于学习的求解器在此类增强数据上的性能显著退化。此外，使用增强数据对基于学习的求解器进行微调，可进一步提升其泛化能力。简而言之，我们揭示了基于学习的旅行商问题求解器倾向于过度贪婪的局限性，这可能对人工智能赋能的组合优化求解器产生深远影响。