In some special rescue scenarios, the needed goods should be transported by drones because of the landform. Therefore, in this study, we investigate a multi-objective vehicle routing problem with time window and drone transportation constraints. The vehicles are used to transport the goods and drones to customer locations, while the drones are used to transport goods vertically and timely to the customer. Three types of objectives are considered simultaneously, including minimization of the total energy consumption of the trucks, total energy consumption of the drones, and the total number of trucks. An improved artificial bee colony algorithm is designed to solve the problem. In the proposed algorithm, each solution is represented by a two-dimensional vector, and the initialization method based on the Push-Forward Insertion Heuristic is embedded. To enhance the exploitation abilities, an improved employed heuristic is developed to perform detailed local search. Meanwhile, a novel scout bee strategy is presented to improve the global search abilities of the proposed algorithm. Several instances extended from the Solomon instances are used to test the performance of the proposed improved artificial bee colony algorithm. Experimental comparisons with the other efficient algorithms in the literature verify the competitive performance of the proposed algorithm.

中文翻译：

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求解带时间窗和无人机的多目标车辆路径问题的元启发式算法

在一些特殊的救援场景中，由于地形的原因，需要的物资需要通过无人机运输。因此，在本研究中，我们研究了具有时间窗口和无人机运输约束的多目标车辆路线问题。车辆用于将货物和无人机运送到客户位置，而无人机则用于垂直及时地将货物运送到客户处。同时考虑三类目标，包括卡车总能耗最小化、无人机总能耗最小化和卡车总数量最小化。设计了一种改进的人工蜂群算法来解决该问题。该算法将每个解用一个二维向量表示，并嵌入了基于Push-Forward Insertion Heuristic的初始化方法。为了增强开发能力，开发了一种改进的启发式方法来执行详细的本地搜索。同时，提出了一种新的侦察蜂策略，以提高所提出算法的全局搜索能力。使用从 Solomon 实例扩展的几个实例来测试所提出的改进人工蜂群算法的性能。与文献中其他有效算法的实验比较验证了所提出算法的竞争性能。使用从 Solomon 实例扩展的几个实例来测试所提出的改进人工蜂群算法的性能。与文献中其他有效算法的实验比较验证了所提出算法的竞争性能。使用从 Solomon 实例扩展的几个实例来测试所提出的改进人工蜂群算法的性能。与文献中其他有效算法的实验比较验证了所提出算法的竞争性能。