## 1 Introduction
### Related Work
The results affirm the superiority of SBAO over traditional heuristic approaches in optimizing both IOPID and FOPID controllers, underscoring its potential to enhance computational efficiency and control effectiveness in practical applications. Path optimization plays a crucial role in enhancing the energy efficiency of UAVs. Among the various challenges in UAV path planning, the traveling salesman problem with drone (TSP-D) stands out as a significant issue. TSP-D involves routing where a predefined set of customer locations must be visited in the shortest possible time. This objective can be accomplished either by a truck route originating and concluding at a depot or by integrating drone deployment on the truck while on route. The study referenced in [38] specifically focuses on the TSP-D model and introduces a mixed-integer programming formulation that leverages the problem's inherent structure. This formulation divides the problem into two distinct decision stages: firstly, selecting and organizing a subset of customers to be serviced by the truck, and secondly, determining optimal drone deployment from the truck to reach the remaining customer locations. To solve this complex optimization challenge, the authors developed a Benders-type decomposition algorithm. This algorithm incorporates enhanced optimality cuts derived from the structural properties of optimal solutions, alongside innovations like t-shortcut and t-reduction concepts, which are significant contributions. The effectiveness of their proposed solution approach is validated through extensive testing on a diverse set of randomly generated instances. This empirical evaluation demonstrates the method's capability to efficiently solve real-world instances of the TSP-D, showcasing its potential to advance operational efficiencies in UAV logistics and transportation systems. Ref. [39] addresses a variation of the well-known TSP, which has been expanded to accommodate the unique characteristics of a new drone-based distribution model in last-mile logistics. In the scenario, the salesperson symbolizes the driver of a home delivery vehicle. With a list of customers to visit, the vehicle has a restricted capacity, allowing only a portion of shipments to be loaded when departing from the warehouse. The remaining shipments must be replenished to the vehicle during its route by a single unmanned aerial vehicle (drone). The drone collects shipments (one at a time) from the warehouse and transports them to the vehicle. The modified TSP focuses on planning the vehicle's route through the customer list and a replenishment schedule for the drone to minimize overall delivery expenses. They devise appropriate optimization methods and implement them in both static and dynamic problem scenarios. Additionally, they compare the cost savings achieved by drone replenishment to other home delivery options, with and without drone assistance. The findings indicate that drone replenishment offers significant benefits when utilized in the appropriate delivery context. The concept of utilizing drones in last-mile delivery logistics presents a complex challenge known as the TSP-D. TSP-D involves creating an efficient route to distribute packages to customers using either a truck or a drone, with the goal of reducing operational expenses. Due to its complexity, TSP-D is classified as NP-hard, prompting the use of metaheuristics as a promising approach. A recent study [40] introduces a hybrid metaheuristic method for TSP-D that combines two advanced algorithms: the genetic algorithm and ant colony optimization algorithm. Existing heuristics in the TSP-D literature typically focus on truck routing and drone assignment separately. In contrast, the proposed metaheuristic simultaneously optimizes both truck and drone routes. Furthermore, the study introduces a novel approach based on ant colony optimization for TSP-D, along with a unique binary pheromone framework for drones and trucks.