## 2 Materials and Methods
### Creating Sub-Routes and Examining How Vehicles Are Assigned on the Existing Route  
There are two different methods for performing deliveries in the proposed method. The first is to assign the truck for delivery. Another method is to assign the drones for delivery. The assigned drone carries the package to the delivery point, delivers it, and makes an appointment to meet the truck again at the truck's next delivery point. The proposed algorithm places emphasis on employing drones as long as the conditions under which delivery can be achieved by the drone remain favorable in order to take advantage of the drones. In Figure 3, a flowchart of how vehicles are assigned so that deliveries can be made to delivery points with the proposed algorithm is given. If the working principle of the algorithm and the calculation of individual transportation costs are examined through a scenario:  
1. According to the scenario shown in Figure 4, there is one truck and one drone at point 1 that have made their deliveries. At this stage, it is necessary to decide how to deliver to the next delivery points. In the decision-making process, the total number of drones and drone range values are used. The algorithm first sets the truck's movement from point 1 to point 2, and the distance that the truck will travel is set at \(\ell 12\). 2. The drone is then checked to see if it can deliver to the next delivery point. When the drone's movement is from point 1 to point 3, which is the next delivery point, the point where it will make an appointment with the truck will be point 2. Accordingly, the expected distance to be covered by the drone will be \(\ell 13+\ell 32\). 3. After calculating the distance that the drone will travel, there are two conditions for determining whether the drone can make this delivery. If the total number of drones is greater than the number of drones currently on duty, that is, if there are drones available for the mission and the drone range is greater than or equal to \(\ell 13+\ell 32\) distance, the drone is suitable for delivery. 4. Assuming that these conditions are met in the current scenario, the drone will go from point 1 to point 3, and then from point 3 to point 2. It will also meet the truck at point 2. Figure 3: Flow chart of the decision-making process of the vehicle for delivery. Afterward, the algorithm checks whether the next delivery point, point 4, is suitable for the drone to deliver. There is only one drone in the scenario, and since one of the conditions, the number of drones, cannot be met, the drone will not be assigned to delivery point number 4. 6. If a drone could be sent to point 4, this drone would also meet with the truck at point 2. After it is understood that no drone will be sent to point 4, the truck starts to move toward point 2, and the drone starts to move toward point 3, as seen in Figure 4b. They come together again at point 2, as seen in Figure 4c. In the given scenario, the total transportation cost is calculated for each individual, and the suitability score is obtained according to this calculated value. Afterward, since it is still in the initial population, the most suitable individual in the current population, that is, the individual with the highest compatibility score, is found and adjusted as the \"global best fit\". While the updated weight matrix is used to calculate the cost of the truck's movement, the standard weight matrix is used for the drone's movement. By dividing the relevant distance value by the speed of the vehicle, the cost value is calculated in terms of how long it will take the vehicle to cover that distance. When these movements are taken into consideration, two different situations can occur. The first of these is that the truck arrives at point 2 before the drone and waits for it to arrive. The other is the scenario where the drone arrives at point 2 before the truck and waits for the truck to arrive.