Existing deep reinforcement learning (DRL)-based methods for solving the capacitated vehicle routing problem (CVRP) intrinsically cope with a homogeneous vehicle fleet, in which the fleet is assumed as repetitions of a single vehicle. Hence, their key to construct a solution solely lies in the selection of the next node (customer) to visit excluding the selection of vehicle. However, vehicles in real-world scenarios are likely to be heterogeneous with different characteristics that affect their capacity (or travel speed), rendering existing DRL methods less effective. In this article, we tackle heterogeneous CVRP (HCVRP), where vehicles are mainly characterized by different capacities. We consider both min–max and min–sum objectives for HCVRP, which aim to minimize the longest or total travel time of the vehicle(s) in the fleet. To solve those problems, we propose a DRL method based on the attention mechanism with a vehicle selection decoder accounting for the heterogeneous fleet constraint and a node selection decoder accounting for the route construction, which learns to construct a solution by automatically selecting both a vehicle and a node for this vehicle at each step. Experimental results based on randomly generated instances show that, with desirable generalization to various problem sizes, our method outperforms the state-of-the-art DRL method and most of the conventional heuristics, and also delivers competitive performance against the state-of-the-art heuristic method, that is, slack induction by string removal. In addition, the results of extended experiments demonstrate that our method is also able to solve CVRPLib instances with satisfactory performance.

中文翻译：

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深度强化学习解决异构容量车辆路径问题


现有的基于深度强化学习（DRL）的方法用于解决容量车辆路径问题（CVRP），本质上是应对同质车队，其中车队被假设为单个车辆的重复。因此，他们构建解决方案的关键在于选择下一个访问的节点（客户），而不包括车辆的选择。然而，现实场景中的车辆可能是异构的，具有影响其容量（或行驶速度）的不同特征，使得现有的 DRL 方法效果较差。在本文中，我们将解决异构 CVRP (HCVRP)，其中车辆的主要特征是不同的容量。我们考虑 HCVRP 的最小-最大和最小-总目标，旨在最大限度地减少车队中车辆的最长或总行驶时间。为了解决这些问题，我们提出了一种基于注意力机制的 DRL 方法，该方法具有考虑异构车队约束的车辆选择解码器和考虑路线构建的节点选择解码器，该方法通过自动选择车辆和节点来学习构建解决方案。该车辆在每个步骤的一个节点。基于随机生成实例的实验结果表明，通过对各种问题规模的理想泛化，我们的方法优于最先进的 DRL 方法和大多数传统启发式方法，并且还提供了与最先进的方法相比的竞争性能。 -艺术启发式方法，即通过去除字符串来进行松弛归纳。此外，扩展实验的结果表明，我们的方法也能够以令人满意的性能解决 CVRPLib 实例。