Optimizing delivery routes for last-mile logistics service is challenging and has attracted the attention of many researchers. These problems are usually modeled and solved as variants of vehicle routing problems (VRPs) with challenging real-world constraints (e.g., time windows, precedence). However, despite many decades of solid research on solving these VRP instances, we still see significant gaps between optimized routes and the routes that are actually preferred by the practitioners. Most of these gaps are due to the difference between what's being optimized, and what the practitioners actually care about, which is hard to be defined exactly in many instances. In this paper, we propose a novel hierarchical route optimizer with learnable parameters that combines the strength of both the optimization and machine learning approaches. Our hierarchical router first solves a zone-level Traveling Salesman Problem with learnable weights on various zone-level features; with the zone visit sequence fixed, we then solve the stop-level vehicle routing problem as a Shortest Hamiltonian Path problem. The Bayesian optimization approach is then introduced to allow us to adjust the weights to be assigned to different zone features used in solving the zone-level Traveling Salesman Problem. By using a real-world delivery dataset provided by the Amazon Last Mile Routing Research Challenge, we demonstrate the importance of having both the optimization and the machine learning components. We also demonstrate how we can use route-related features to identify instances that we might have difficulty with. This paves ways to further research on how we can tackle these difficult instances.

翻译：优化最后一公里物流服务的配送路线极具挑战性，并吸引了众多研究者的关注。此类问题通常被建模为包含现实约束（如时间窗、顺序约束）的车辆路径问题（VRP）变体并加以求解。然而，尽管数十年来对VRP实例的求解研究已十分扎实，优化路线与实际从业者偏好的路线之间仍存在显著差距。这些差距主要源于优化目标与从业者实际关注点之间的不一致，而后者在多数情况下难以精确定义。本文提出一种新型分层式路径优化器，其参数可学习，融合了优化与机器学习方法的双重优势。该分层路由首先通过具有可学习权重的区域级特征求解区域级旅行商问题（TSP）；在确定区域访问顺序后，将站点级车辆路径问题转化为最短哈密顿路径问题求解。随后引入贝叶斯优化方法，允许调整求解区域级TSP时分配给不同区域特征的权重。通过亚马逊最后一公里路线规划研究挑战赛提供的真实配送数据集，我们证明了优化与机器学习组件并重的重要性。同时，展示了如何利用路线相关特征识别难以处理的实例，这为攻克此类复杂实例的后续研究奠定了基础。