The Electric Autonomous Dial-A-Ride Problem (E-ADARP) consists in scheduling a fleet of electric autonomous vehicles to provide ride-sharing services for customers that specify their origins and destinations. The E-ADARP considers the following perspectives: (i) a weighted-sum objective that minimizes both total travel time and total excess user ride time; (ii) the employment of electric autonomous vehicles and a partial recharging policy. This paper presents the first labeling algorithm for a path-based formulation of the DARP/E-ADARP, where the main ingredient includes: (1) fragment-based representation of paths, (2) a novel approach that abstracts fragments to arcs while ensuring excess-user-ride-time optimality, (3) construction of a sparser new graph with the abstracted arcs, which is proven to preserve all feasible routes of the original graph, and (4) strong dominance rules and constant-time feasibility checks to compute the shortest paths efficiently. This labeling algorithm is then integrated into Branch-and-Price (B&P) algorithms to solve the E-ADARP. In the computational experiments, the B&P algorithm achieves optimality in 71 out of 84 instances. Remarkably, among these instances, 50 were solved optimally at the root node without branching. We identify 26 new best solutions, improve 30 previously reported lower bounds, and provide 17 new lower bounds for large-scale instances with up to 8 vehicles and 96 requests. In total 42 new best solutions are generated on previously solved and unsolved instances. In addition, we analyze the impact of incorporating the total excess user ride time within the objectives and allowing unlimited visits to recharging stations. The following managerial insights are provided: (1) solving a weighted-sum objective function can significantly enhance the service quality, while still maintaining operational costs at nearly optimal levels, (2) the relaxation on charging visits allows us to solve all instances feasibly and further reduces the average solution cost.

中文翻译：

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电动自主叫车问题的分支价格算法


电动自动驾驶拨号问题 (E-ADARP) 包括调度电动自动驾驶车队，为指定出发地和目的地的客户提供乘车共享服务。 E-ADARP 考虑以下观点： (i) 最小化总出行时间和总超额用户乘坐时间的加权总和目标； (ii) 电动自动驾驶汽车的使用和部分充电政策。本文提出了第一个基于路径的 DARP/E-ADAARP 表述的标记算法，其中主要成分包括：（1）基于片段的路径表示，（2）一种将片段抽象为弧的新颖方法，同时确保过量用户乘坐时间最优性，（3）用抽象弧构造一个稀疏的新图，这被证明可以保留原始图的所有可行路线，以及（4）强大的支配规则和恒定时间可行性检查有效地计算最短路径。然后将该标记算法集成到分支与价格 (B&P) 算法中以求解 E-ADARP。在计算实验中，B&P 算法在 84 个实例中的 71 个实例中实现了最优。值得注意的是，在这些实例中，有 50 个实例在根节点处得到了最佳解决，无需分支。我们确定了 26 个新的最佳解决方案，改进了之前报告的 30 个下限，并为最多 8 辆车和 96 个请求的大型实例提供了 17 个新的下限。在之前已解决和未解决的实例上总共生成了 42 个新的最佳解决方案。此外，我们还分析了将超额用户总骑行时间纳入目标并允许无限制访问充电站的影响。 提供了以下管理见解：（1）解决加权和目标函数可以显着提高服务质量，同时仍将运营成本保持在接近最优的水平，（2）收费访问的放宽使我们能够可行地解决所有情况，并且进一步降低了平均解决方案成本。