The development of electric vehicle (EV) techniques has led to a new vehicle routing problem (VRP) called the capacitated EV routing problem (CEVRP). Because of the limited number of charging stations and the limited cruising range of EVs, not only the service order of customers but also the recharging schedules of EVs should be considered. However, solving these two aspects of the problem together is very difficult. To address the above issue, we treat CEVRP as a bilevel optimization problem and propose a novel bilevel ant colony optimization algorithm in this article, which divides CEVRP into two levels of subproblem: 1) capacitated VRP and 2) fixed route vehicle charging problem. For the upper level subproblem, the electricity constraint is ignored and an order-first split-second max-min ant system algorithm is designed to generate routes that fulfill the demands of customers. For the lower level subproblem, a new effective heuristic is designed to decide the charging schedule in the generated routes to satisfy the electricity constraint. The objective values of the resultant solutions are used to update the pheromone information for the ant system algorithm in the upper level. Through good orchestration of the two components, the proposed algorithm can significantly outperform state-of-the-art algorithms on a wide range of benchmark instances.

中文翻译：

---

容量化电动汽车路径问题的双层蚁群优化算法。

电动汽车（EV）技术的发展导致了一种新的车辆路径选择问题（VRP），称为电容式EV路径选择问题（CEVRP）。由于充电站的数量有限以及电动汽车的续航范围有限，因此不仅应考虑客户的服务顺序，还应考虑电动汽车的充电时间表。但是，很难同时解决问题的这两个方面。为了解决上述问题，我们将CEVRP视为双层优化问题，并在本文中提出了一种新颖的双层蚁群优化算法，该算法将CEVRP分为两个子问题级别：1）电容式VRP和2）固定路线车辆充电问题。对于上层子问题，忽略了电力约束，设计了顺序优先的第二秒最大最小蚂蚁系统算法来生成满足客户需求的路线。对于较低级别的子问题，设计了一种新的有效启发式方法来确定所生成路线中的充电时间表，以满足电力约束。所得解决方案的目标值用于更新上层蚂蚁系统算法的信息素信息。通过对这两个组件进行良好的编排，在广泛的基准实例上，所提出的算法可以显着优于最新算法。所得解决方案的目标值用于更新上层蚂蚁系统算法的信息素信息。通过对这两个组件进行良好的编排，在广泛的基准实例上，所提出的算法可以显着优于最新算法。所得解决方案的目标值用于更新上层蚂蚁系统算法的信息素信息。通过对这两个组件进行良好的编排，在广泛的基准实例上，所提出的算法可以显着优于最新算法。