A traveling salesman problem (TSP) is a well-known NP-complete problem. Traditional TSP presumes that the locations of customers and the traveling time among customers are fixed and constant. In real-life cases, however, the traffic conditions and customer requests may change over time. To find the most economic route, the decisions can be made constantly upon the time-point when the salesman completes his service of each customer. This brings in a dynamic version of the traveling salesman problem (DTSP), which takes into account the information of real-time traffic and customer requests. DTSP can be extended to a dynamic pickup and delivery problem (DPDP). In this article, we ameliorate the attention model to make it possible to perceive environmental changes. A deep reinforcement learning algorithm is proposed to solve DTSP and DPDP instances with a size of up to 40 customers in 100 locations. Experiments show that our method can capture the dynamic changes and produce a highly satisfactory solution within a very short time. Compared with other baseline approaches, more than 5% improvements can be observed in many cases.

中文翻译：

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通过深度强化学习解决动态旅行商问题


旅行商问题（TSP）是一个众所周知的 NP 完全问题。传统的TSP假设客户的位置和客户之间的旅行时间是固定且恒定的。然而，在现实生活中，交通状况和客户请求可能会随着时间的推移而变化。为了找到最经济的路线，可以在推销员完成对每个客户的服务的时间点上不断地做出决策。这带来了动态版本的旅行商问题（DTSP），它考虑了实时交通和客户请求的信息。 DTSP 可以扩展到动态取货和送货问题 (DPDP)。在本文中，我们改进了注意力模型，使其能够感知环境变化。提出了一种深度强化学习算法来解决 100 个地点的 40 个客户规模的 DTSP 和 DPDP 实例。实验表明，我们的方法可以捕获动态变化并在很短的时间内产生非常令人满意的解决方案。与其他基线方法相比，在许多情况下可以观察到超过 5% 的改进。