组合优化的深度强化学习：覆盖推销员问题
Deep Reinforcement Learning for Combinatorial Optimization: Covering Salesman Problems
摘要：
本文介绍了一种新的深度学习方法来近似解决覆盖推销员问题（CSP）。在这种方法中，给定CSP的城市位置作为输入，深度神经网络模型被设计为直接输出解决方案。它是在没有监督的情况下使用深度强化学习训练的。具体而言，在模型中，我们应用多头注意力来捕捉结构模式，并设计了一个动态嵌入来处理问题的动态模式。一旦模型经过训练，它就可以推广到各种类型的CSP任务（不同大小和拓扑），而不需要重新训练。通过控制实验，所提出的方法显示出理想的时间复杂度：它运行速度比传统的启发式求解器的最优性的微小差距超过20倍。此外，它在训练和推理方面都明显优于当前最先进的组合优化深度学习方法。与传统的求解器相比，这种方法对于实践中大多数具有挑战性的任务都是非常可取的，这些任务通常是大规模的，需要快速决策。
英文摘要：
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.
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。
