# Dynamic UAV Inspection Boosted by Vehicle Collaboration Under Harsh Conditions in the IoT Realm
## 2 Related Work  
### Heuristic Algorithms and Vehicle Routing Problems (VRPs)  
In the field of operations research, the Vehicle Routing Problem (VRP) [23; 24] has long been at the core of academic research and is crucial for solving complex logistics problems. Since its emergence, the VRP has drawn the attention of scholars worldwide and has developed into a complex research area. Initially, the traditional VRP focused on planning efficient routes for vehicles to serve customers, aiming to minimize various costs. With the rapid popularity of drones in modern logistics, the VRP has undergone changes, giving rise to the Vehicle Routing Problem with Drones (VRPD) [25; 26; 27]. This not only inherits the core challenges of the traditional VRP but also brings about new complexities due to the characteristics of drones, such as battery life limitations, payload constraints, and airspace regulation issues. Numerous heuristic algorithms have been proposed to solve VRPs and their variants. For example, [PERSON] et al. [28] proposed two multi-trip VRP models for drone delivery. They derived an energy consumption model for multi-rotor drones and established a mixed-integer linear programming model. A Simulated Annealing (SA) heuristic algorithm was then applied to find sub-optimal solutions for practical scenarios. [PERSON] et al. [29] considered a scenario involving multiple trucks, multiple drone stations,and drones within each station serving customers in the VRPD. They proposed a bi-level approach that combines the Brain Storm Optimization algorithm and the Adaptive Large Neighborhood Search. Their research demonstrated the ability of this method to solve the problem and its research value. [PERSON] et al. [30] designed an improved artificial bee colony algorithm to solve a multi-objective vehicle routing problem with time window and drone transportation constraints, aiming to minimize the total energy consumption of trucks, drones, and the total number of trucks. Moreover, [PERSON] et al. [31] focused on the development of effective heuristics for solving the vehicle routing and scheduling problem with time window constraints. Both tour construction and local search tour improvement heuristics were developed, and computational results were reported for test problems from the literature as well as real-world applications. [PERSON] et al. [32,33] developed an SFT route optimization model using NSGA-II, considering travel time and cumulative strain, and applied it to the Mokpo-Jeju Island section, obtaining travel-time-saving optimal routes to facilitate decision-making. Additionally, they employed the Gaussian Mixture Model and the Vehicle Routing Problem with Time Windows model to develop a routing strategy for accessible taxis in Seoul, effectively reducing the total waiting time and travel distance of the vehicles. [PERSON] et al. [34] formulated a mathematical model for a problem similar to the flying sidekick traveling salesman problem but for the capacitated multiple-truck case with time limit constraints and minimizing cost as the objective function.