求解旅行商问题的Transformer网络
The Transformer Network for the Traveling Salesman Problem
摘要：
旅行商问题（TSP）是最流行和研究最多的组合问题，始于1951年的冯·诺依曼。它推动了几种优化技术的发现，如切割平面，分支定界，局部搜索，拉格朗日松弛和模拟退火。在过去的五年里，出现了一些有前途的技术，其中（图）神经网络已经能够学习新的组合算法。主要的问题是，深度学习是否可以从数据中学习更好的算法，即取代人类工程算法？这很有吸引力，因为开发有效解决NP难题的算法可能需要多年的研究，而许多工业问题本质上是组合的。在这项工作中，我们建议适应最近成功的Transformer架构最初开发的自然语言处理的组合TSP。训练通过强化学习完成，因此没有TSP训练解决方案，并且解码使用束搜索。我们报告了最近学到的改进性能，TSP 50的最佳差距为0.004%，TSP 100的最佳差距为0.39%。
英文摘要：
The Traveling Salesman Problem (TSP) is the most popular and most studied combinatorial problem, starting with von Neumann in 1951. It has driven the discovery of several optimization techniques such as cutting planes, branch-and-bound, local search, Lagrangian relaxation, and simulated annealing. The last five years have seen the emergence of promising techniques where (graph) neural networks have been capable to learn new combinatorial algorithms. The main question is whether deep learning can learn better heuristics from data, i.e. replacing human-engineered heuristics? This is appealing because developing algorithms to tackle efficiently NP-hard problems may require years of research, and many industry problems are combinatorial by nature. In this work, we propose to adapt the recent successful Transformer architecture originally developed for natural language processing to the combinatorial TSP. Training is done by reinforcement learning, hence without TSP training solutions, and decoding uses beam search. We report improved performances over recent learned heuristics with an optimal gap of 0.004% for TSP50 and 0.39% for TSP100.
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。
