## 5 Review of Case Studies: Flying Vehicle Routing Optimization
Their aim was to develop an algorithm for efficient and safe UAV navigation from a hospital to the location of a medical emergency. Their proposed algorithm focused on optimizing path planning to minimize computational time and transportation costs. Various algorithms, including capacitated vehicle routing problem (CVRP), PSO, ACO, and GA, are compared for vehicle routing. The results demonstrated that the CVRP algorithm outperforms the others, particularly when the vehicle capacity is increased. This indicated that the proposed path planning method hasthe potential to effectively provide real-time medical aid with improved efficiency. [PERSON] and [PERSON] [67] addressed the issue of energy consumption in VRPs by proposing the use of UAVs as a battery-powered delivery method. The emergence of commercial companies like Amazon, Google, and DHL utilizing drones for package delivery has led to the development of a new variant of the VRP known as VRP with drones (VRPD). In VRPD, vehicles and drones are employed to deliver packages to customers either independently or in a dependent manner. An MILP model is presented to describe the problem, and a hybrid GA is proposed to solve the VRPD. Experimental results demonstrated the effectiveness of the proposed algorithm in solving this variant of the VRP. The study highlighted the potential of using UAVs for efficient and environmentally friendly deliveries, providing insights for companies looking to optimize their logistics operations. [PERSON] et al. [68] addressed the optimization of package delivery using a fleet of drones with different capabilities. The problem is formulated as an extension of the classic VRP and involves scheduling operations in a package depot center. A mixed-integer programming (MIP) model is proposed to minimize the delivery time for a set of packages. To tackle the computational complexity, two GAs, FBGA and RBGA, are developed. RBGA incorporates a rescheduling-based optimization model to adjust drone operations and minimize completion time. Extensive experiments show that the proposed algorithms outperform the MIP approach, particularly for larger problem instances. The findings highlighted the practicality and effectiveness of these methods for real-world implementation in drone-assisted package delivery systems. [PERSON] et al. [69] focused on optimizing the delivery paths of UAVs for efficient and automated delivery in the field of e-commerce and urban logistics. The problem is formulated as a multi-objective path planning problem, aiming to minimize the total cost and maximize customer satisfaction. A novel GA based on the non-dominant sorting GA II (NSGA-II) with constraints is proposed. The algorithm represented decision vectors as one-dimensional chromosomes and utilizes specialized variation operators. These design choices, along with the properties of NSGA-II, enable the discovery of a larger number of non-crowding Pareto optimal solutions with reduced computational complexity. A case study on a portion of the Solomon dataset demonstrated the algorithm's ability to find sparse and well distributed non-dominant solutions within a short time and with a relatively small population size. [PERSON] et al. [53] addressed the need for the efficient and timely delivery of medical supplies during the COVID-19 pandemic. The use of drones for medical supply delivery offers advantages such as overcoming traffic restrictions and reducing the risk of contact with COVID-19 patients. However, existing optimization models for drone delivery are not suitable for the specific requirements of medical supply delivery during public health emergencies. To address this, the authors proposed a new bi-objective mixed integer programming model for the multi-trip drone location routing problem. This model allows for simultaneous pick-up and delivery, enabling the efficient and timely delivery of medical supplies to the right locations. To solve the model, a modified version of the NSGA-II algorithm is developed.