This paper introduces a new deep learning approach to approximately solve the Covering Salesman Problem (CSP). In this approach, given the city locations of a CSP as input, a deep neural network model is designed to directly output the solution. It is trained using the deep reinforcement learning without supervision. Specifically, in the model, we apply the Multi-head Attention to capture the structural patterns, and design a dynamic embedding to handle the dynamic patterns of the problem. Once the model is trained, it can generalize to various types of CSP tasks (different sizes and topologies) with no need of re-training. Through controlled experiments, the proposed approach shows desirable time complexity: it runs more than 20 times faster than the traditional heuristic solvers with a tiny gap of optimality. Moreover, it significantly outperforms the current state-of-the-art deep learning approaches for combinatorial optimization in the aspect of both training and inference. In comparison with traditional solvers, this approach is highly desirable for most of the challenging tasks in practice that are usually large-scale and require quick decisions.

翻译：本文介绍了一种新的深层次学习方法,以大致解决覆盖销售商问题(CSP)。在这种方法中,鉴于CSP的城市位置是投入,因此设计了一个深神经网络模型,直接输出解决方案。它受过培训,使用深度强化学习而无需监督。具体地说,在模型中,我们应用多头关注来捕捉结构模式,并设计一个动态嵌入器来处理问题的动态模式。一旦模型经过培训,它可以概括到各类不需要再培训的CSP任务(不同大小和地形)。通过受控实验,拟议方法显示了理想的时间复杂性:它比传统的超额解决者运行速度快20倍以上,且存在很小的优化差距。此外,它大大超出了当前在培训和推断两方面进行组合优化的先进学习方法。与传统解决者相比,这一方法对于大多数通常规模大、需要快速决定的具有挑战性的任务是非常可取的。