# Time-Dependent Vehicle Routing Problem with Drones Under Vehicle Restricted Zones and No-Fly Zones
## 2 Literature Review
Delivery vehicles are not only affected by road traffic flow during their tasks but are also subject to restricted zones during specific periods. The constraint of traffic restrictions for hazardous material logistics was studied by [PERSON] et al. [22], and vehicle obstacle avoidance was taken into consideration for the VRPD [23]. A truck-drone routing problem considering vehicle obstacle avoidance was studied and an algorithm based on deep reinforcement learning was developed by [PERSON] et al. [24]. [PERSON] et al. [25] considered the VRPD under restricted zones and road congestion, aiming to minimize the delivery cost. They established a model and proposed a hybrid genetic and dynamic programming algorithm for solving it. [PERSON] et al. [26] focused on the impact of restricted zones on the VRPD, with the objective of minimizing the delivery time. They developed a model and proposed a hybrid leapfrog algorithm for solving it. [PERSON] et al. [27] investigated the VRPD under the influence of restricted zones, aiming to minimize delivery time. They established a model and designed a two-stage heuristic algorithm for solving the problem. [PERSON] et al. [28] studied the vehicle-drone collaborative delivery problem under flood disaster conditions with waterlogged obstacle areas, aiming to minimize the delivery time. They developed a model and designed a two-stage algorithm for solving the problem. In practical logistics delivery, restricted no-fly zones are often established in areas such as schools, large factories, and major events. [PERSON] et al. [29] studied the FSTSP with time-varying no-fly zones, proposed a drone rerouting strategy, and developed a two-stage heuristic algorithm for solving it. [PERSON] et al. [30] presented a mixed-integer linear programming model that is formulated for the path optimization problem of VRPD, with the inclusion of no-fly zones and simultaneous pickup and delivery. [PERSON] et al. [31] focused on the VRPD with vehicle-restricted areas and drone no-fly zones, and the grid search improved support vector machine algorithm was used to solve it. [PERSON] et al. [32] addressed the vehicle-drone collaborative delivery problem considering customer locations where drones cannot land and vehicles cannot deliver. They formulated a model with the objective of minimizing the delivery time and designed a hybrid neighborhood search algorithm to solve the problem. [PERSON] et al. [33] focused on TSPD under all-period-restricted no-fly and vehicle-restricted zones, aiming to minimize the delivery cost. They established a model and proposed a hybrid tabu search algorithm to solve it. A review of the existing literature reveals that while substantial progress has been made in the vehicle routing problem with drones, there are still some limitations:(1) Setting the vehicle speed as a constant value or using a piecewise step function or piecewise continuous function to model time-varying road networks results in a significant discrepancy from the actual vehicle speeds observed in real-world delivery scenarios. (2) Regarding vehicle-restricted zones and no-fly zones, previous studies have not considered time-varying restrictions, such as allowing normal deliveries during non-restricted periods. Moreover, when it comes to detouring around restricted zones or no-fly zones, most approaches either ignore detouring or use simple detour rules. While these strategies reduce the complexity of the problem, they fail to fully exploit the advantages of vehicle-drone collaborative delivery. Therefore, TDVRPD-VRZ-NFZ, as investigated in this paper, represents a critical issue that logistics companies need to address for effective vehicle-drone collaborative delivery operations.