arXivDaily arXiv每日学术速递 周一至周五更新
北美退伍军人节（Veterans Day），12 日无更新
arXiv 2510.03065cs.LGcs.AI
收藏

一种求解近邻旅行商问题的统一深度强化学习方法

A Unified Deep Reinforcement Learning Approach for Close Enough Traveling Salesman Problem

Department of Mechanical Engineering, National University of Singapore（新加坡国立大学机械工程系）；School of Traffic and Transportation Engineering, Central South University（中南大学交通与运输工程学院）；Department of Industrial Engineering and Innovation Sciences, Eindhoven University of Technology（埃因霍温理工大学工业工程与创新科学系）；School of Vehicle and Mobility, Tsinghua University（清华大学车辆与移动性学院）；School of Automation, Central South University（中南大学自动化学院）

Mingfeng Fan, Jiaqi Cheng, Yaoxin Wu, Yifeng Zhang, Yibin Yang, Guohua Wu, Guillaume Sartoretti

阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

针对 CETSP 的邻域访问难点，本文提出双解码器 UD3RL 框架，联合完成节点选择与路径点确定，并通过定制 REINFORCE 实现跨规模和半径类型的强泛化。

摘要：

近年来，深度强化学习（DRL）在求解 NP 难的旅行商问题（TSP）方面受到关注。然而，近邻旅行商问题（CETSP）得到的关注有限，主要原因是其基于邻域的访问准则带来挑战：只要智能体进入某个节点周围的紧凑邻域，该节点即被视为已访问。本文利用离散化方案为 CETSP 构建了马尔可夫决策过程（MDP），并提出一种新颖的统一双解码器 DRL（UD3RL）框架，将决策分为节点选择和路径点确定两部分。具体而言，该框架采用经过适配的编码器进行有效特征提取，随后分别由 node-decoder 和 loc-decoder 处理两个子任务；还引入 k 近邻子图交互策略，以增强位置解码过程中的空间推理能力。此外，我们定制了 REINFORCE 算法来训练 UD3RL，使其成为能够跨不同问题规模以及不同邻域半径类型（即恒定半径和随机半径）泛化的统一模型。实验结果表明，UD3RL 在解质量和运行时间上均优于传统方法，并在问题规模、空间分布和半径范围上表现出较强的泛化能力，同时对动态环境具有鲁棒性。

英文摘要：

In recent years, deep reinforcement learning (DRL) has gained traction for solving the NP-hard traveling salesman problem (TSP). However, limited attention has been given to the close-enough TSP (CETSP), primarily due to the challenge introduced by its neighborhood-based visitation criterion, wherein a node is considered visited if the agent enters a compact neighborhood around it. In this work, we formulate a Markov decision process (MDP) for CETSP using a discretization scheme and propose a novel unified dual-decoder DRL (UD3RL) framework that separates decision-making into node selection and waypoint determination. Specifically, an adapted encoder is employed for effective feature extraction, followed by a node-decoder and a loc-decoder to handle the two sub-tasks, respectively. A k-nearest neighbors subgraph interaction strategy is further introduced to enhance spatial reasoning during location decoding. Furthermore, we customize the REINFORCE algorithm to train UD3RL as a unified model capable of generalizing across different problem sizes and varying neighborhood radius types (i.e., constant and random radii). Experimental results show that UD3RL outperforms conventional methods in both solution quality and runtime, while exhibiting strong generalization across problem scales, spatial distributions, and radius ranges, as well as robustness to dynamic environments.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑