Traveling Salesman Problem (TSP), as a classic routing optimization problem originally arising in the domain of transportation and logistics, has become a critical task in broader domains, such as manufacturing and biology. Recently, Deep Reinforcement Learning (DRL) has been increasingly employed to solve TSP due to its high inference efficiency. Nevertheless, most of existing end-to-end DRL algorithms only perform well on small TSP instances and can hardly generalize to large scale because of the drastically soaring memory consumption and computation time along with the enlarging problem scale. In this paper, we propose a novel end-to-end DRL approach, referred to as Pointerformer, based on multi-pointer Transformer. Particularly, Pointerformer adopts both reversible residual network in the encoder and multi-pointer network in the decoder to effectively contain memory consumption of the encoder-decoder architecture. To further improve the performance of TSP solutions, Pointerformer employs both a feature augmentation method to explore the symmetries of TSP at both training and inference stages as well as an enhanced context embedding approach to include more comprehensive context information in the query. Extensive experiments on a randomly generated benchmark and a public benchmark have shown that, while achieving comparative results on most small-scale TSP instances as SOTA DRL approaches do, Pointerformer can also well generalize to large-scale TSPs.

本文提出了一种新的端到端深度强化学习方法Pointerformer，基于多指针变压器，可解决旅行商问题（TSP）的内存消耗和算力问题，通过特征增强方法探索TSP的对称性以及增强上下文嵌入方法以包含更多综合上下文信息，此方法在小规模和大规模问题上均表现出了竞争优势。

指针转换器：用于旅行商问题的深度强化多指针Transformer