Yuzhuo Zong*
School of physics, Ningxia University, Yinchuan, China, 750021
*Corresponding author: zyz16638992@126.com
Keywords: UAV delivery; Genetic Algorithm; path optimization; cluster analysis.
Abstract: With the rapid development of the low-altitude economy, unmanned aerial vehicles (UAVs) have been increasingly applied in last-mile urban logistics. How to achieve optimal delivery efficiency under complex environmental constraints has become a key issue that smart logistics scheduling systems must urgently address. This paper focuses on three typical optimization tasks in low-altitude UAV delivery—path planning, multi-UAV scheduling, and resource allocation with time windows—and proposes a multi-level, scalable algorithmic optimization framework. By integrating the Genetic Algorithm (GA), Analytic Hierarchy Process (AHP), and clustering strategies, the framework enables systematic modeling from single-route generation to global scheduling control. Specifically, for the single-UAV path optimization problem, we construct a delivery path combination model under battery endurance constraints and design a GA to solve for the minimum travel time. In the multi-UAV cooperative scheduling scenario, a scheduling criterion based on minimizing the maximum route length is proposed, effectively reducing the overall delivery duration. For cases with limited resources and time-sensitive orders, an AHP-based weighting system combined with spatial clustering is introduced to partition user task regions and determine the minimum feasible number of UAVs. Under a unified experimental platform, all three models achieve significant optimization results: the shortest single-route delivery time is 1.04 hours, the maximum parallel flight time is controlled within 0.13 hours, and time-window scheduling requires only five UAVs to complete all tasks, meeting the 15-minute delivery requirement. The results demonstrate that the proposed multi-algorithm fusion model exhibits strong optimization performance and practical adaptability, making it applicable to various real-world scenarios such as smart cities, warehouse delivery, and edge-computing-based scheduling.
- Introduction
Driven by the vision of “Digital China” and the advancement of smart logistics, low-altitude UAV delivery is gradually evolving into an indispensable infrastructure in urban operational systems. Small rotor UAVs, owing to their advantages in speed, wide-area coverage, and precise maneuverability, have been widely adopted in multiple fields [1]. Applying green transportation tools to the logistics sector can help mitigate environmental problems such as global warming; in this context, UAVs have the potential to become a novel mode of transportation [2]. From an environmental perspective, studies have shown that when small UAVs are powered electrically and supplied by a low-carbon power grid, they consume less energy compared to conventional diesel trucks [3]. Research further indicates that UAVs in urban areas can achieve a delivery cost per package ranging from USD 0.03$ to 0.67$, which is competitive with traditional electric vans; in high-demand urban scenarios, the cost per order can be reduced to approximately USD 0.07$ [4,5]. Although UAVs still face challenges such as energy costs, regulatory restrictions, weather conditions, and endurance limitations, they possess significant time-efficiency advantages in scenarios such as emergency supply delivery [6].
To address UAV path planning in specific environments, numerous theoretical models based on real-world problems have been proposed [7]. The Traveling Salesman Problem (TSP) is a classic problem in combinatorial optimization and operations research, with broad applications in robotics, transportation, network communications, and other practical domains [8]. Derivative algorithms based on TSP have already been widely applied in UAV delivery [9].
However, previous research in this area has primarily focused on scenarios such as truck–UAV cooperative delivery, cost-oriented optimization, and multi-trip UAV operations [10,11,12]. In contrast, studies addressing single-UAV operations with both time-window and energy constraints, multi-UAV coordinated scheduling, and multiple fixed delivery point configurations remain relatively scarce.
- Related work
Golabi et al. proposed a UAV path planning method based on a discrete three-dimensional grid model, which allows UAVs to avoid or fly over obstacles while simultaneously optimizing multiple objectives such as path length, energy consumption, and maximum risk [13]. Phung and Ha proposed the SPSO (Spherical Vector-based Particle Swarm Optimization) algorithm, which introduces a safety cost function and uses particle swarm optimization to search for paths in multi-threat trajectory planning problems under complex environments [14]. Yi Jiang et al. pointed out that in UAV path planning, evolutionary computation shows strong adaptability in complex search spaces, dynamic time control, and multi-objective optimization, making it a research hotspot in recent years [15].
Sawadsitang et al. developed the MODD system, which applies a three-stage stochastic programming method to address the multi-objective UAV delivery scheduling problem and uses the ε-constraint method for solving it, reflecting the core idea of optimizing multiple objectives in uncertain environments [16,17]. In the context of alliance cooperation, the same team further proposed the BCoSDD framework, embedding uncertainty in multi-carrier joint scheduling into dynamic game modeling, thereby addressing more complex multi-criteria scheduling strategies [18].
Japanese scholars Omagari and Higashino applied a hybrid evolutionary algorithm combining Genetic Algorithm (GA) and Tabu Search to UAV path generation, which reduces non-convergence problems in multi-objective optimization and improves both solution quality and search efficiency [19]. Mahmoodi et al. proposed an environmentally friendly RPAS (Remotely Piloted Aircraft Systems) optimization model within a multi-objective location–routing optimization framework, balancing delivery timeliness, cost, risk, and carbon emissions [20].
Meanwhile, several studies have explored cooperative delivery strategies involving UAVs and ground vehicles or public transportation. For example, integrating k-means clustering with GA to optimize a human–vehicle joint delivery network effectively accounts for factors such as energy consumption, payload capacity, and terrain conditions [21]. Recent studies such as those by AlZafar Khan and AlKaraki have introduced Model Predictive Control (MPC) into UAV delivery path optimization, achieving superior performance in cost minimization and path convergence speed [22]. Paul et al. proposed a data-driven online demand optimization strategy that combines Markov Decision Processes with machine learning; by predicting network states and prioritizing links, their method guides resource allocation and path optimization, improving profitability and delivery efficiency in dynamic demand environments [23].
At present, research on UAV delivery systems mainly focuses on trajectory planning, charging strategies, safety, and hybrid delivery modes, while comprehensive studies that cover the entire delivery process—including path planning and energy management—are still relatively scarce. Some studies have noted that UAV path planning can draw upon classical problem types such as CVRP (Capacitated Vehicle Routing Problem) and VRPTW (Vehicle Routing Problem with Time Windows), but must be modeled with consideration of UAV-specific constraints such as energy capacity, time windows, and airspace restrictions [24].
GA, based on the principles of natural selection and genetic mechanisms, has strong global search capabilities and has become one of the most representative heuristic methods in path optimization problems. On the scheduling side, balancing multi-UAV task synchronization with maximum route control remains a key bottleneck affecting system responsiveness. Recent research on UAV delivery network optimization has even explored hybrid methods combining quantum computing with classical algorithms; for example, the QUADRO hybrid framework has been proposed to solve energy-constrained multi-UAV route planning and scheduling problems [25].
This study addresses three subproblems in UAV delivery—path optimization, cooperative scheduling, and resource-constrained scheduling—by developing an evolutionary search strategy, a multi-path parallel scheduling mechanism, and a multi-criteria clustering-based scheduling model, thereby achieving a multi-level algorithmic design that spans from single-UAV optimization to system-wide optimization.
- Methodology
3.1 Single-UAV Path Optimization: Evolutionary Search Based on Genetic Algorithm
In the basic path planning scenario, the UAV delivery problem is modeled as a bounded Traveling Salesman Problem (TSP) with energy consumption and path-closure constraints. To solve this problem, this study designs an adaptive Genetic Algorithm (GA) whose core steps include: Encoding Design: Represent the delivery route as a binary or integer sequence, where each gene position corresponds to a customer node. Fitness Function Construction: Incorporate the battery capacity constraint by transforming the problem so that the objective is to minimize travel time. Selection and Crossover Strategy: Apply tournament selection and single-point crossover to enhance local search intensity. Mutation Mechanism and Repair Operator: Maintain gene diversity and ensure results satisfy the task quantity constraints.
For the single-UAV delivery problem under energy constraints, we define: Suppose a UAV departs from the central airport and, before returning, completes deliveries for nnn customers. Let the Euclidean distances from customer iii to the delivery point and to the airport be denoted as and , respectively. The total travel distance for a single sortie is given by Eq. (1):
(1)
Here,represents the distance from the airport to the delivery point. If the UAV conducts sorties, the total travel distance for all deliveries can be expressed as Eq. (2):
(2)
From this, it can be observed that the total distance is independent of the sequence in which each customer is served, but depends on whether the UAV returns to the airport after a delivery. Let setcontain customers who are served last before returning to the airport, and setcontain all other customers. By calculating all customer-to-airport and customer-to-delivery-point distances, the GA is used to obtain the minimum travel distance for all possible sortie combinations. We then check whether each minimum-distance combination satisfies the UAV battery constraint. Finally, the minimum travel distance satisfying the constraint is converted into time, giving the minimum travel timefor the single-UAV delivery problem under energy and closure constraints:
(3)
whereis the UAV cruising speed.
By preprocessing the coordinates of customers, the airport, and the delivery point, unnecessary combinations are eliminated, significantly improving algorithm iteration speed. This results in an abstracted mathematical model suitable for GA application. To enhance exploration of the solution space for route combinations, a structural repair mechanism is incorporated during the evolutionary process to ensure solution feasibility and convergence in every iteration.
3.2 Multi-UAV Cooperative Scheduling: A Scheduling Strategy Based on Maximum Path Minimization
Under the assumption of sufficient UAV availability, we design a “minimize the maximum task” strategy to measure and optimize efficiency bottlenecks in parallel scheduling. The main logic is as follows: each UAV is assigned to execute one or more orders, and the total flight time for all UAVs is computed. The completion time of the last UAV (i.e., the maximum delivery time across all UAVs) is taken as the overall task duration indicator. By repeatedly simulating and searching for allocation schemes that yield the smallest maximum completion time, the problem of improving multi-UAV scheduling efficiency is transformed into a classical makespan minimization problem.
By controlling the system’s longest execution path, fluctuations in overall performance are significantly reduced. The minimum total delivery time is calculated as:
(4)
whereis determined by the maximum sum of distances from a customer to both the delivery point and the airport.
3.2 Resource-Constrained and Time-Window Scheduling: Regional Task Partitioning Model Based on AHP and Clustering
To classify tasks quantitatively, it is first necessary to quantify the similarity between them. A task often requires multiple variables for characterization. Ifvariables are needed to describe a set of nnn sample points to be classified, then each sample can be represented as a point inspace. In clustering analysis, the Minkowski distance is used to measure the similarity between samples, as expressed in Eq. (5):
(5)
,, When,orwe obtain:
Manhattan (absolute) distance:
(6)
Manhattan (absolute) distance:
(7)
Manhattan (absolute) distance:
(8)
Among these, the Euclidean distance is most commonly used because it is invariant under orthogonal rotation of the coordinate system. Therefore, translations or rotations of the original coordinate system do not change the distances between sample points.
In the most complex scheduling scenario, this study introduces an Analytic Hierarchy Process (AHP) combined with clustering algorithms to construct an intelligent regional scheduling model with time-window and resource constraints, aiming to complete all tasks with the minimum number of UAVs. The implementation steps are as follows: first, three key indicators are considered—order sequence (time), user distribution density (space), and distance to delivery points (infrastructure). Next, judgment matrices and consistency checks are used to quantify the importance of each indicator, and users are spatially grouped based on the weighted feature vectors. Finally, each group of users is examined to determine whether the time constraints are met, and the minimum required number of UAVs is obtained.
- Experimental Design and Result Analysis
To verify the effectiveness of the three proposed optimization methods, simulations were conducted under a unified delivery scenario with the following settings and parameters:
Within a certain city, multiple centralized delivery points are available. UAVs serve as the delivery vehicles, and the logistics distribution center is located at a central airport in the city, equipped with suitable takeoff and landing facilities as well as a battery replacement platform. After placing an order via a mobile application, the customer’s order information—including delivery address, package type, and quantity—is transmitted to the scheduling center.
4.1 Experimental Design
4.1.1 Single-UAV Path Optimization
The coordinates of Delivery Point 1 are (0.5, 0.5) in a Cartesian coordinate system (in kilometers) with the airport at the origin. A UAV departs from the airport, and using the data in Table 1, the model aims to determine the shortest delivery time from Delivery Point 1 to the users, ensuring the UAV can ultimately return to the airport.
4.1.2 Multi-UAV Cooperative Path Optimization
Assume all UAVs depart from the airport and collaborate to complete the deliveries. Using the data in Table 1, the goal is to determine the shortest time to complete deliveries from Delivery Point 1 to the users, ensuring all UAVs can return to the airport upon task completion.
Table 1.Distance from User to Delivery Point and Airport
| User | User Location | Distance to Delivery Point 1 | Distance to Airport |
| User 1 | (1.2,0.7) | 0.728 | 1.389 |
| User 2 | (0.3,-1.7) | 2.209 | 1.726 |
| User 3 | (0.4,1.4) | 0.906 | 1.456 |
| User 4 | (-1.6,0.5) | 2.100 | 1.676 |
| User 5 | (-1.3,-1.3) | 2.546 | 1.838 |
| User 6 | (0.7,1.9) | 1.414 | 2.025 |
| User 7 | (-0.4,1.6) | 1.421 | 1.649 |
| User 8 | (1.1,-1.1) | 1.709 | 1.556 |
| User 9 | (1.5,-0.7) | 1.562 | 1.655 |
| User 10 | (-0.3,-1.5) | 2.154 | 1.530 |
| User 11 | (1.8,0.6) | 1.304 | 1.897 |
| User 12 | (-0.3,-1.8) | 2.435 | 1.825 |
4.1.3 Minimum-UAV Path Optimization
Assume the airport has a limited fleet (only 10 UAVs available). Both Delivery Point 1 and Delivery Point 2 can serve the users. Considering the order placement sequence and a 15-minute maximum delivery time requirement after an order is placed, the model uses the data in Table 2 to determine the minimum number of UAVs required to complete all tasks while ensuring that UAVs can return to the airport after delivery. The coordinates are: Delivery Point 1 at (0.5, 0.5) and Delivery Point 2 at (0, –1.7).
For all scenarios, the following assumptions are made: UAV preparation time for takeoff and landing is negligible; acceleration is ignored during flight; order preparation time is ignored; UAV flight speed is constant at 40 km/h; initially, all UAVs are stationed at the central airport; UAVs are unaffected by weather during flight; each UAV can carry only one order per trip; energy consumption is 1 unit/km, with a battery capacity of 10 units; UAVs must return to the airport without a payload and with non-negative remaining battery capacity; battery replacement time at the airport is negligible.
Table 2.User Location and Order Time
| User | User Location | User Order Time |
| User 1 | (1.2,0.7) | 9:00 |
| User 2 | (0.3,-1.7) | 9:01 |
| User 3 | (0.4,1.4) | 9:02 |
| User 4 | (-1.6,0.5) | 9:03 |
| User 5 | (-1.3,-1.3) | 9:04 |
| User 6 | (0.7,1.9) | 9:05 |
| User 7 | (-0.4,1.6) | 9:06 |
| User 8 | (1.1,-1.1) | 9:07 |
| User 9 | (1.5,-0.7) | 9:08 |
| User 10 | (-0.3,-1.5) | 9:09 |
| User 11 | (1.8,0.6) | 9:10 |
| User 12 | (-0.3,-1.8) | 9:11 |
| User 13 | (-1.5,-0.8) | 9:12 |
| User 14 | (1.1,-1.5) | 9:13 |
| User 15 | (1.8,2.3) | 9:14 |
| User 16 | (-0.7,-0.2) | 9:15 |
| User 17 | (-1.2,-1.4) | 9:16 |
| User 18 | (1.9,-0.5) | 9:17 |
| User 19 | (0.0,2.1) | 9:18 |
| User 20 | (-2.0,0.3) | 9:19 |
4.2 Experimental Design
4.2.1 Problem 1
A simple calculation was first used to verify the delivery combinations of the farthest and nearest customers, leading to the conclusion that a UAV can deliver to a maximum of four customers per sortie without recharging. After enumerating the feasible reduced search space of possible sortie combinations, the optimal combination was identified: when the UAV consecutively delivers to three customers twice before recharging, and then delivers to two customers three times before recharging, the minimum delivery time is achieved.
After 200 generations of evolution, the GA converged to an optimal route combination. The output for setwas [2, 4, 5, 10, 12], and for setwas [1, 3, 6, 7, 8, 9, 11]. Since the combination pattern is independent of the delivery order (as long as constraints are met), the optimal solution can be obtained. The shortest route combination is shown in Table 3.
Table 3. Shortest Route Combination
| Flight Order | Customer ID | Flight Distance (km) | ||
| 1 | 9 | 1 | 2 | 9.22 |
| 2 | 11 | 3 | 4 | 8.90 |
| 3 | 8 | 10 | 7.93 | |
| 4 | 7 | 5 | 7.80 | |
| 5 | 6 | 12 | 7.79 | |
From the calculation, the minimum delivery time is:
(9)
That is, the UAV departs from the airport, loads goods at the delivery point, and serves customers 9, 1, and 2 in sequence before returning to the airport for a battery swap, and so forth. The final optimal route is shown in Figure 1.
Figure 1. Optimal Route Map for Single UAV
4.2.2 Problem 2
Each customer’s path consists of three parts: from the customer to the airport, from the airport to the starting point, and from the customer to the starting point. After calculating all route distances, the maximum value is selected as the reference for the last UAV. Dividing this maximum distance by the flight speed yields the minimum time required for the last UAV to return to the airport. The final minimum time, rounded to two decimal places, is:
(10)
Similarly, the flight paths of the twelve UAVs are shown in Figure 2.
Figure 2. Delivery Route Map for Multiple UAVs
4.2.2 Problem 3
Considering the actual situation, it is assumed that UAVs begin delivery only after the customer places an order. The Analytic Hierarchy Process is first used to determine the weights of the indicators to be considered, followed by clustering analysis. The twenty customers are first numbered from 0 to 19 according to the order in which they placed their orders. For this problem, the indicators are defined as: the difference in sequence numbers within each category is 5; the individuals within each category are as close as possible; and the two delivery points are taken as clustering centers. Since the time constraint must be satisfied, the importance of Indicator 1 is considered the highest, followed by Indicator 2, and then Indicator 3. Three judgment matrices are constructed in turn, all of which pass the consistency test, and the corresponding weights are shown in Table 4.
Matrice 1:
(11)
Matrice 2:
(12)
Matrice 3:
(13)
Table 4.Weights of Each Indicator
| Matrice 1 Matrice 1 Matrice 1 | |||
| Indicator 1 | 0.7089 | 0.6833 | 0.6483 |
| Indicator 2 | 0.1786 | 0.1998 | 0.1168 |
| Indicator 3 | 0.1125 | 0.1168 | 0.1220 |
According to the weights of the three indicators, clustering analysis is carried out, and the clustering diagrams obtained under three different weighting schemes are shown in Figure 3. The results are identical for all three sets of weights. Observing Table 5, it can be seen that in the clustering results, there are some points that are close to each other, such as points 3 and 4 in Category 1, points 15 and 16 in Category 2, and points 1 and 2 in Category 3. These points may lead to situations where the task cannot be completed on time, but after calculation for each group, it is found that all tasks can be completed on time and successfully returned.
Figure 3. User Clustering Diagram
Table 5.User Clustering Results
| Category 1 | Category 2 | Category 3 | Category 4 | Category 5 |
| 3 | 6 | 1 | 0 | 8 |
| 4 | 11 | 2 | 5 | 10 |
| 12 | 15 | 9 | 7 | 14 |
| 19 | 16 | 18 | 13 | 17 |
Future research in UAV delivery could incorporate dynamic order modeling to support real-time decision-making and task insertion, integrate deep reinforcement learning (DRL) into scheduling strategies for adaptive autonomous control, and develop more sophisticated environmental perception models to adapt to urban obstacles, weather conditions, and multi-hub takeoff–landing networks.
- Conclusions
This study focuses on an urban-scale low-altitude UAV delivery scenario and proposes a multi-level, generalizable optimization framework that systematically addresses three major challenges in UAV delivery: path optimality, scheduling efficiency, and resource–time constraints. Specifically, a Genetic Algorithm (GA) is employed to efficiently search for the shortest single-UAV path combinations under limited energy conditions; a makespan minimization approach is applied to achieve load balancing in multi-UAV parallel operations; and a combination of Analytic Hierarchy Process (AHP) and clustering algorithms is used to effectively partition delivery regions, ensuring 15-minute delivery while minimizing the number of UAVs required.
These three models form a progressive design that builds an intelligent delivery optimization system for scenarios with complex constraints, demonstrating both algorithmic stability and practical feasibility. Through the coordinated integration of multi-level algorithmic strategies, this study achieves full-process modeling of UAV logistics scheduling—from path generation, to task allocation, to resource compression—offering both theoretical value and engineering applicability. The framework is suitable for complex systems such as intelligent transportation scheduling, edge collaborative computing, and smart logistics.
Future research in UAV delivery could incorporate dynamic order modeling to support real-time decision-making and task insertion, integrate deep reinforcement learning (DRL) into scheduling strategies for adaptive autonomous control, and develop more sophisticated environmental perception models to adapt to urban obstacles, weather conditions, and multi-hub takeoff–landing networks.
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