# Time-Dependent Vehicle Routing Problem with Drones Under Vehicle Restricted Zones and No-Fly Zones
## 2 Literature Review  
The impact of road traffic flow on delivery vehicles results in time-dependent vehicle speeds, making the time-dependent vehicle routing problem (TDVRP) a central focus in vehicle routing research in recent years. [PERSON] et al. [6] used traffic data from Chongqing to simulate vehicle speeds and proposed a mixed-integer programming model. They also performed a sensitivity analysis considering four road congestion indices. [PERSON] et al. [7] used different step functions to model the speed variations across different road networks. They considered customers with hard time windows, formulated a model aimed at minimizing total delivery costs, and developed a tabu search heuristic algorithm for solving it. With the continuous development and upgrading of new energy electric vehicles, many scholars have conducted research on the time-dependent electric vehicle routing problem (TDEVRP). [PERSON] et al. [8] investigated a TDEVRP considering stochastic traffic flow and proposed a nonlinear dynamic energy consumption model for vehicles. They formulated a mathematical model with the objective of minimizing total delivery time and developed a heuristic algorithm to solve it. [PERSON] et al. [9] optimized the vehicle's energy consumption per kilometer and battery loss rate, using a fast elitist non-dominated sorting genetic algorithm to optimize acceleration curves and establish the relationship between vehicle energy consumption, battery life, and acceleration profiles. [PERSON] et al. [10] addressed the TDEVRP by using piecewise functions to model vehicle speeds and formulated a mathematical model with the aim of minimizing both total delivery time and costs. [PERSON] et al. [11] employed piecewise functions to model the speed of electric vehicles, formulated a mathematical model to minimize total delivery costs, and proposed a variable neighborhood search algorithm for its solution. [PERSON] et al. [12] introduced a two-stage TDEVRP, developing a Bayesian machine learning probabilistic model to predict the energy consumption of vehicles on each road segment. [PERSON] et al. [4] considered the presence of steep roads and proposed an energy consumption formula that takes into account the impact of steep roads. The vehicle-drone collaborative delivery routing problem has become a research hotspot in recent years. [PERSON] et al. [13] first proposed the flying sidekick traveling salesman problem (FSTSP), aiming to minimize delivery time. [PERSON] et al. [14] proposed a two-stage iterative algorithm for the solving the FSTSP. [PERSON] et al. [15] studied the traveling salesman problem with drones (TSPD), where the drone's pickup and drop-off points were allowed to coincide. They formulated the problem with the goal of minimizing delivery time and proposed solution methods based on local search and dynamic programming. [PERSON] et al. [16] studied an improved dynamic programming algorithm for solving the TSPD problem. [PERSON] et al. [17] solved the TSPD using reinforcement learning and devised the distribute-and-follow policy gradient training algorithm. Considering that multiple vehicles are often required to carry drones in real-world delivery tasks, [PERSON] et al. [18] introduced the vehicle routing problem with drones (VRPD), aiming to minimize delivery time. They designed a branch-and-bound algorithm for the solution. [PERSON] et al. [19] considered a VRPD where the drone delivers one parcel at a time and must return to the truck after each delivery to recharge its battery. [PERSON] et al. [20] focused on VRPD with the goal of minimizing delivery costs and employed a deep reinforcement learning strategy to dynamically optimize delivery routes. [PERSON] et al. [21] effectively solved the VRPD problem based on mixed-integer linear programming, aiming to find the optimal drone allocation and scheduling plan. The complex urban environment brings more severe challenges to delivery tasks, especially with the establishment of vehicle-restricted zones and drone no-fly zones.