## 3 Problem Description and Model  
Packages in the trans-shipment depot need to be delivered to multiple areas. In the traditional logistics delivery scenario, one courier is responsible for a certain small area. Many couriers work together to complete the delivery of all packages in the trans-shipment depot. Multiple UAVs are being used to replace one courier. The above mentioned automatic delivery system for logistics UAVs is used to support the execution of the above workflow. Package tasks for one courier are scheduled by this system respectively. In order to deploy the UAV delivery system on existing resources, the following components need to be used in logistics distribution. (i) Some package loading equipment in the trans-shipment depot, they are responsible for loading packages into UAVs and replacing UAV's battery for their next flight. (ii) Each of these UAVs will complete the delivery according to the route specified by the dispatch center. These package tasks in a certain area require multiple UAVs to collaborate. Furthermore, these package tasks are usually completed through multiple flights. (iii) Some express cabinets are placed near these package destinations. The express cabinet supports UAVs to automatically place the package inside it, and it allows customers to pick up their packages at any time after delivery. (iv) The dispatch center performs resource scheduling in units of areas. It updates the status of the transit warehouse, UAVs and express cabinets in real time, and notifies the corresponding staff in time when the system fails. We consider the scheduling problem of the system in a certain area. Since one courier has to deliver a certain number of packages in a day, there is a small-scale scheduling problem in the specific area that needs to be addressed. The search ability of three algorithm frameworks proposed in this section are adequate for this problem. The customer satisfaction and the total completion time, which are critical to the problem, are selected as the two optimization objectives for this problem. The scheduling problem is modeled as a MILP. Notations are summarized in Table 1. \begin{table}
\begin{tabular}{l l} \hline \hline
**Notation** & **Description** \\ \hline \(h\) & Number of UAVs \\ \(u_{k}\) & The \(k^{th}\) UAV \\ \(U=\{u_{1},u_{2},\ldots,u_{h}\}\) & Set of UAVs \\ \(e\) & Maximum flight time of UAV \\ \(c\) & Load capacity of UAV \\ \(v\) & Average speed of UAV \\ \(t^{d}\) & Time for UAV to load packages in \(s_{0}\) \\ \(t^{e}\) & Time for UAV to unload packages into \(s_{1},\ldots,s_{m}\) \\ \(n\) & Number of packages \\ \(p_{i}\) & The \(t^{th}\) package \\ \(P=\{p_{1},p_{2},\ldots,p_{n}\}\) & Set of packages \\ \(w_{i}\) & Weight of \(p_{i}\) \\ \(l_{i}\) & Destination of \(p_{i}\) \\ \(t_{i}^{0}\) & Best delivery time of \(p_{i}\) \\ \(t_{i}\) & Actual delivery time of \(p_{i}\) \\ \(g\) & Maximum weight of packages \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Notations description. There is a small scale problem. All packages that a courier needs to deliver are represented by \(P=\{p_{1},p_{2},\ldots,p_{n}\}\). A set of stations \(S=\{s_{0}\}\cup\ \{s_{1},s_{2},\ldots,s_{m}\}\) are set up in the scenario, where \(s_{0}\) is the trans-shipment depot and the set of \(\{s_{1},s_{2},\ldots,s_{m}\}\) represents these express cabinets in the area. \(l_{k,f,b}\) represents the destination of the \(b^{th}\) package delivered by \(u_{k}\) on \(f^{th}\) flight. We determine a minimum circle that covers all these stations, and \(r\) is the radius of the circle. According to customer requirements, the optimal delivery time \(t_{i}^{0}\) is set for each package, and the actual delivery time of the package is represented as \(t_{i}\). A set of UAVs \(U=\{u_{1},u_{2},\ldots,u_{h}\}\) is used to accomplish these package tasks. \(S^{intr}\) is the solution of the task scheduling for all UAVs. It contains the scheduling results of multiple flights and is an intuitive representation of the scheduling scheme.