# Drone Arc Routing Problems and Metaheuristic Solution Approach
## 3 Problem Definition  
There are various types of drones based on their usage areas. This study focuses on surveillance drones. Surveillance drones travel from a central point (depot) to the areas and the borders in these areas are monitored. Monitoring processes are performed by the sensors or monitoring devices on drones. With their limited energy capacity, drones should be able to travel to the areas that need to be serviced, capture images of these service areas (areas to be monitored) using sensors or monitoring devices, transfer the images simultaneously with a communication mechanism if necessary, and then return to the central point. The characteristics of the DARP-DD investigated due to the unique structure observed in surveillance drones is presented below:  
* Drones have limited energy capacity. * Drones consume energy both when servicing the edges and when deadheading the edges (passing without servicing). * Drones consume more energy while servicing. * The demand value of the deadheading edges is equal to the amount of energy consumed by the drone during deadheading. * The demand value of the (required) edges that need to be serviced on the graph is equal to the amount of energy consumed by the drone while servicing. * After the drone has completed servicing a required edge, it can directly travel to the node of any other required edge on the graph [14]. This distance value is equal to the Euclidean distance between the two nodes. * The required edges on the graph can be linear or curved. Considering all these features, the DARP-DD is defined as an arc routing problem in which \(k\) drones start and finish their tours at the depot node to minimize the total tour distance (cost) and ensure that the energy capacity of the drones is not exceeded. Therefore, the objective function of the DARP-DD is to minimize the total distance traveled by the drones. Figure 1 shows the graph of an example generated for the DARP-DD. Through this graph, how the problem is addressed is explained. In the graph shown in Figure 1, there are 5 components, a depot where drones are available to service the required edges, 17 required edges that need to be serviced, and 19 nodes including the depot node. \(E_{R}=\{(1-2),(1-3),(3-2),(11-12),(6-4),(6-5),(5-4),\\ (7-8),(8-10),(10-9),(9-7),(13-14),(14-15),(15-16),(16-17),(17-18),(18-13)\}\) is the set of the required edges on the graph. The coordinates of the nodes on the graph are presented in Table 1.  
On the graph presented in Figure 1, the distance values of the required edges can be calculated using the Euclidean distances of the nodes belonging to the edges. For this reason, the distance values of the edges are calculated using the coordinate values of the nodes presented in Table 1. For example, the distance value of the \((1-2)\) edge is equal to \(40\) units, which is the Euclidean distance between the points \((0,\,0)\) and \((0,\,-40)\). This unit provides a more flexible framework for distance measurement, and it can be interpreted in meters, kilometers, or miles. To determine the energy consumption of drones, the energy per meter (epm) metric proposed by [PERSON] et al. (2018) for drones was considered. The epm was defined as a value that measures energy consumption per unit distance and used as energy per unit distance in this study. This way, the metric is made applicable to various scenarios. It is assumed that drones consume 1 Joule per unit distance (I Joule/distance) during deadheading. On the other hand, drones consume 2 Joules per unit distance (2 Joules/distance) during servicing. This can also work with different values and the energy per unit distance can be adjusted based on drone type, usage purpose, or environmental conditions. On the other hand, the amount of energy consumed by drones when servicing the edges is not necessarily proportional to the distance traveled. Some edges need more detailed monitoring, and more energy is consumed, while others need less detailed monitoring, and less energy is consumed when servicing them. In this problem,