Energy consumption has become a crucial problem in the design of vehicle routing problems, hence the need to use another delivery method powered by batteries. Unmanned aerial vehicles have become fundamental tools in tasks for which man has limited skills that prevent a superlative optimization of time. The increasing use of drones by commercial companies such as Amazon, Google, and DHL has given birth to a new variant of vehicle routing problem (VRP) called VRP with drones (VRPD) which has a positive influence on the environment. Where vehicles and drones are used to deliver packages or goods to customers. In VRPD, vehicles and drones make dependent or independent deliveries. In the case of a dependent delivery, at a given point (customer or depot) the drone takes off from a vehicle to serve a customer and then return to travel with the same vehicle, as long as the capacity and endurance constraints for a drone are satisfied. In the other case, each type of vehicle travels independently to others. A MILP model is presented to describe the problem, and then we confirm the formulation via a CPLEX software with small instances. We propose a hybrid genetic algorithm to solve the VRPD. Experiments are carried out on the instances taken from the literature in different settings. The results show the performance of the proposed algorithm to solve this variant.

能源消耗已成为设计车辆路线问题的关键问题，因此需要使用另一种由电池供电的输送方法。无人驾驶飞行器已成为人类技能有限的任务中的基本工具，这些技术阻碍了时间的最优化。诸如亚马逊，谷歌和DHL之类的商业公司对无人机的越来越多的使用催生了一种新的车辆路由问题（VRP），称为无人机VRP（VRPD），它对环境产生积极影响。使用车辆和无人机向客户运送包裹或货物的地方。在VRPD中，车辆和无人机进行依赖或独立的交付。如果是依赖交付，在给定的地点（客户或仓库），只要满足无人机的容量和耐力约束，无人机就会从车辆上起飞以服务客户，然后返回同一辆车旅行。在另一种情况下，每种类型的车辆都独立行驶。提出了一个MILP模型来描述问题，然后我们通过带有小实例的CPLEX软件来确认配方。我们提出了一种混合遗传算法来求解VRPD。实验是在不同背景下对从文献中获取的实例进行的。结果显示了所提出算法解决该变体的性能。然后我们通过带有小实例的CPLEX软件确认配方。我们提出了一种混合遗传算法来求解VRPD。实验是在不同背景下对从文献中获取的实例进行的。结果显示了所提出算法解决该变体的性能。然后我们通过带有小实例的CPLEX软件确认配方。我们提出了一种混合遗传算法来求解VRPD。实验是在不同背景下对从文献中获取的实例进行的。结果显示了所提出算法解决该变体的性能。