With energy and environmental issues becoming increasingly prominent, electric vehicles (EVs) have become the important transportation means in the logistics distribution. In the real-world urban road network, there often exist multiple paths between any two locations (depot, customer, and charging station) since the time-dependent travel times. That is, the travel speed of an EV on each path may be different during different time periods, and thus, this paper explicitly considers path selection between two locations in the time-dependent electric vehicle routing problem with time windows, denoted as path flexibility. Therefore, the integrated decision-making should include not only the routing plan but also the path selection, and the interested problem of this paper is a time-dependent electric vehicle routing problem with time windows and path flexibility (TDEVRP-PF). In order to determine the optimal path between any two locations, an optimization model is established with the goal of minimizing the distance and the battery energy consumption associated with travel speed and cargo load. On the basis of the optimal path model, a 0-1 mixed-integer programming model is then formulated to minimize the total travel distance. Hereinafter, an improved version of the variable neighborhood search (VNS) algorithm is utilized to solve the proposed models, in which multithreading technique is adopted to improve the solution efficiency significantly. Ultimately, several numerical experiments are carried out to test the performance of VNS with a view to the conclusion that the improved VNS is effective in finding high-quality distribution schemes consisted of the distribution routes, traveling paths, and charging plans, which are of practical significance to select and arrange EVs for logistics enterprises.

中文翻译：

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具有时间窗和路径灵活性的时变电动汽车路径问题

随着能源和环境问题日益突出，电动汽车（EV）已成为物流配送中的重要运输手段。在现实世界中的城市道路网络中，自从与时间相关的旅行时间以来，在任意两个位置（仓库，客户和充电站）之间通常存在多条路径。也就是说，电动汽车在每个路径上的行驶速度在不同时间段可能会有所不同，因此，本文明确考虑具有时间窗的时变电动汽车路径问题中两个位置之间的路径选择，称为路径灵活性。因此，综合决策不仅应包括路由计划，还应包括路径选择，本文感兴趣的问题是具有时间窗和路径灵活性的时变电动汽车选路问题（TDEVRP-PF）。为了确定任何两个位置之间的最佳路径，建立了一个优化模型，其目标是最小化与行进速度和货物负载相关的距离和电池能耗。然后，在最佳路径模型的基础上，制定0-1混合整数规划模型以最小化总行驶距离。在下文中，将使用改进版本的可变邻域搜索（VNS）算法来解决所提出的模型，其中采用多线程技术来显着提高求解效率。最终，