发表机构
IDSIA（IDSIA研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究旅行商问题，提出将热图转换为旅行路线的算法，有理论保证将近似比与热图质量联系起来，通过实验与先前工作对比。
AI 中文摘要
旅行商问题长期以来一直是评估经典算法理论中优化技术强度的基准。在将机器学习应用于算法问题的近期努力中，它也成为基于机器学习技术发展的自然试验台。一种常见方法是训练神经网络输出热图来估计每条边成为最优路线一部分的可能性，然而将热图转换为实际路线仍然是一个不平凡且通常计算密集的步骤。在这项工作中，我们提出了将热图转换为路线的算法，并给出理论保证，将实现的近似比与所提供热图的质量联系起来。本着带预测算法的精神，我们的结果可以描述为$(1 + 2\frac{\eta}{\mathrm{OPT}})$近似算法，其中$\eta$表示预测（热图）与最优解（路线）之间的L1距离。由于先前的工作缺乏这样明确的保证，我们通过实验将我们的方法与它们进行比较。
英文摘要
The Traveling Salesperson Problem (TSP) has long served as a benchmark for evaluating the strength of optimization techniques in the classical theory of algorithms. In recent efforts to apply ML to algorithmic problems, TSP has also become a natural testbed for the development of ML-based techniques. A common approach is to train a neural network to output a heatmap estimating the likelihood of each edge to be part of the optimal tour; however, converting such a heatmap into an actual tour remains a non-trivial and often computationally intensive step. In this work, we propose algorithms for transforming heatmaps into tours with theoretical guarantees linking the achieved approximation ratio to the quality of the provided heatmap. In the spirit of algorithms with predictions, our results can be described as $(1+2\fracη{\mathrm{OPT}})$-approximation algorithms, where $η$ denotes the L1 distance between the prediction (heatmap) and an optimal solution (tour). Since the previous works lack such explicit guarantees, we compare our approach against them experimentally.
