https://orcid.org/0000-0001-6604-0687
Figures
Abstract
Shared passenger-carrying unmanned aerial vehicle (UAV) systems offer a promising solution for urban air mobility, yet their real-time scheduling in multi-airport environments remains challenging due to heterogeneous passenger demands, model compatibility constraints, and the need to balance efficiency with service quality. This study addresses these challenges by proposing a shared UAV route scheduling optimization model for multi-airport, multi-station systems. The model integrates passenger order characteristics (origin, destination, party size, preferred UAV type, and desired arrival time) with UAV operational parameters (current location, remaining endurance, seating capacity, speed, and model), and incorporates a quadratic soft time window mechanism to flexibly manage arrival deviations while minimizing total system navigation time. To solve this discrete combinatorial optimization problem, we develop a self-learning Ant-Lion Optimizer (SLALO) with natural number encoding that dynamically tracks seat availability and updates route assignments in real-time. Simulation results demonstrate that the proposed approach achieves a 27.3% reduction in total navigation time compared to non-pooling baselines, with an average UAV utilization rate of 78.6%. Comparative analysis against Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and standard Ant-Lion Optimizer (ALO) shows that SLALO achieves superior convergence speed and solution quality. The proposed framework is particularly relevant for border regions with limited ground infrastructure, where intelligent shared mobility systems can serve as a critical driver for cultivating new quality productive forces and supporting regional economic integration. These findings highlight the potential of shared UAV systems to improve urban air mobility efficiency, reduce operational costs, and enhance passenger satisfaction.
Citation: Hong C, Yan Y, Lian Z, Li X (2026) Shared drone route scheduling optimization. PLoS One 21(5): e0348883. https://doi.org/10.1371/journal.pone.0348883
Editor: Zhihong (Arry) Yao, Southwest Jiaotong University, CHINA
Received: April 28, 2025; Accepted: April 22, 2026; Published: May 19, 2026
Copyright: © 2026 Hong et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data underlying the findings described in the manuscript are fully available within the manuscript and its Supporting Information files. This includes passenger order coordinates (Tables 7, 9, 10), UAV parameters (Tables 1, 2, 3), airport locations (Tables 4, 10), and the complete MATLAB simulation code for the SLALO algorithm (S1_Code.zip). No external data repositories were used.
Funding: This work was supported by the Scientific Research Project of China-ASEAN School of Economics, Guangxi University (Grant No. 2024JK04): ‘Research on the Mechanism and Path of Accelerating the Development of New Quality Productive Forces in the Border Region’ (2024/10-2025/10). The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
Introduction
Urban transportation systems worldwide are facing increasing pressure from congestion, limited infrastructure, and environmental concerns. Urban Air Mobility (UAM) has emerged as a promising solution to alleviate ground traffic by leveraging passenger-carrying UAVs [1]. Unlike traditional ground transport, UAVs offer flexibility, reduced travel time, and the potential for on-demand services. However, most existing research focuses on cargo drone routing, often modeled as vehicle routing problems (VRP), which do not fully capture the complexities of passenger transport[2]. Passenger-carrying UAV scheduling must consider time constraints, ride-pooling coordination, model compatibility, and multi-airport coordination [3].
While these studies have established foundational methodologies for path planning and fleet coordination, they typically assume homogeneous vehicle fleets, static demand, and rigid time windows. In the context of passenger transport, several critical gaps remain. First, passenger-carrying UAV operations require explicit consideration of model compatibility, as users may have preferences or constraints regarding aircraft type. Second, ride-pooling coordination—a key mechanism for improving system efficiency—demands dynamic seat availability tracking and real-time route adjustments, which are not adequately addressed in conventional VRP formulations. Third, multi-airport systems introduce additional complexity in fleet allocation and return-to-base constraints that are often simplified in single-depot models. Furthermore, the integration of passenger time preferences with operational efficiency remains underexplored, with most studies adopting either rigid time windows that sacrifice flexibility or ignoring time constraints altogether.
This study is particularly motivated by the unique transportation challenges in China’s border regions, including Guangxi, Yunnan, Xinjiang, Tibet, Inner Mongolia, Heilongjiang, Jilin, and Liaoning. These areas are characterized by vast geographical expanse, low population density, complex terrain, and relatively underdeveloped ground transportation infrastructure. Conventional road-based transport often suffers from long travel times, high costs, and limited accessibility in remote border communities. Urban Air Mobility (UAM), enabled by shared passenger-carrying UAVs, offers a transformative solution to bridge these spatial gaps, improve connectivity, and support economic integration in border areas. Therefore, while the proposed model is generally applicable, its practical significance is especially pronounced in the context of China’s border regions, where the development of new quality productive forces in transportation can serve as a critical driver for regional economic revitalization.
Despite advancements in multi-depot routing and swarm coordination, limited attention has been given to real-time shared UAV scheduling in multi-airport systems with heterogeneous passenger demands[4]. Rigid time windows often reduce operational flexibility, while ignoring time preferences may compromise service quality. To address this gap, this study proposes a balanced scheduling model that incorporates both efficiency and passenger time satisfaction. A soft time window mechanism with quadratic penalties is introduced to manage arrival deviations flexibly.
The main contributions of this study are threefold:
- (1) A multi-airport shared passenger UAV scheduling model is formulated, incorporating endurance, capacity, and model compatibility constraints.
- (2) A quadratic soft time window mechanism is integrated to balance operational efficiency and passenger satisfaction.
- (3) A discrete encoding strategy within the SLALO framework is developed to solve large-scale combinatorial assignment problems efficiently.
Passenger Demand-Based Total Time Minimum Route Planning Model for Multi-Airport Systems
3.2. System description
This paper studies the shared UAV commuting system aiming to determine a passenger-carrying UAV flight scheduling scheme based on multiple airports satisfying different passenger needs, capable of meeting various real-life scenarios. In the total time-minimum route planning model for multi-airport systems based on different passenger needs, we envision an ideal scenario with multiple airports, multiple drone sites, and each user with corresponding needs. When users initiate flight orders to the cloud server, passenger-carrying UAVs upload their site locations. The model must deploy a UAV meeting user needs while maximizing utilization. The primary computational objective is to minimize the total voyage time of all UAVs in the system.
It is assumed that multiple UAV airports in the region can assign UAVs meeting user model, passenger count, and time requirements to the user’s home station, and UAVs have unloaded mileage loss. When a passenger initiates a boarding order at a certain location and time, specifying arrival time, the system responds, allocates a UAV to depart from the airport to the starting station, transports the passenger to the target station along the route, and returns to the airport. Our shared UAV commuting system (SUCS) rationally allocates UAV tasks to minimize total system time.
According to model assumptions, passenger-carrying UAVs uniformly depart from respective airports for maiden flights and continuously match demand points and carpool-able drones while orders are executed; all order and drone information is shared during flights; the system operates in real-time scheduling, with users specifying arrival times for their demands.
To illustrate the system operation process, Fig 1 presents a schematic diagram of the shared UAV scheduling framework organized in four hierarchical layers. The first layer depicts passenger orders, each specifying origin, destination, passenger count, preferred UAV model, and desired arrival time. These orders are transmitted to the second layer, the cloud scheduling server, which integrates multiple functional modules: order parsing, UAV state monitoring, SLALO-based optimization, ride-pooling matching, and soft time window penalty calculation. The server then coordinates with the third layer, which consists of two interconnected components: the multi-airport system (Airports 1, 2, 3) where UAVs are stationed, and the heterogeneous UAV fleet characterized by varying endurance, capacity, speed, and model specifications. The final layer illustrates the UAV flight execution flow: each assigned UAV departs from its airport, proceeds to the passenger’s origin site for pick-up, transports the passenger(s) to the destination site, and returns to an airport upon mission completion. This hierarchical structure reflects the end-to-end scheduling process and the key decision-making modules embedded in the proposed model.
3.2. Model assumptions
To solve the above scheduling problem, a mathematical model is developed with the following assumptions:
- (1) Passenger demand is fixed once the order is submitted. The number of passengers associated with each request does not change during scheduling;
- (2) Each passenger order is served by only one UAV and cannot be transferred. This assumption ensures service continuity and simplifies scheduling, as passengers are not required to change aircraft during their journey;
- (3) UAV cruising speed is model-dependent and remains constant during flight segments. Speed variations caused by weather or air traffic control are not considered;
- (4) Take-off and landing times are not included in the cruising speed but are incorporated as fixed time penalties added to the total navigation time for each mission segment;
- (5) Influences such as inclement weather, airframe failure, and acoustic and visual interference are not considered;
- (6) All UAVs depart from the airport and return to the airport upon mission completion.
The model concepts are defined as follows.
Passenger demand definition: Passenger demand , where O is the initiation Site, E is the destination site, p is the number of passengers，SC is the aircraft type requirement of passenger C, and t is the time when the passenger needs to arrive.
Shared passenger-carrying UAV. Set Definition: Shared collection of passenger-carrying drones , For any drone u ∈ UAV, The following status information is available,
, where L is the current location of the drone, r is the range of the drone, Su is a model of the UAV U, z is the number of seats, v is drone speed.
Definition of drone airports: aerodrome , where am∈AIRPORT is the location coordinates of the drone field.
Drone site definition: Site , where si∈AIRPORT is the location coordinates of the drone site.
Airport vs. Site Distinction: Airports are facilities where UAVs are stationed, maintained, and to which they must return after missions. Sites are passenger pick-up and drop-off locations distributed throughout the service area. UAVs always start and end at airports, while serving passenger requests at sites in between.
3.3. Mathematical models
In order to describe the model more clearly and accurately, the definition symbols are as follows:
: Total number of drone airports,
: UAV airport serial number；
: total number of UAV sites,
: They represent the serial numbers of the drone sites；
: Total number of drones；
: Drone serial number；
: Total number of passengers；
: Passenger serial number；
: The Boolean logical value
of the drone from the airport to the site
, which is 1 if the drone
passes through the airport
to the site
, otherwise it is 0
;
: Boolean logical value
of the drone
from site
to site;
: Boolean logical value
of the drone
from site
to site;
: Distance from airport
to site
;
:
Site-to-site distance
;
: Distance from airport
to site
；
: The speed of
the drone；
: The cruising range of the
drone；
: Battery safety margins for UAV
；
: Passenger
specifies the drone model requirements from site
to site
；
: The order assigns the model of drone
from site
to site
;
: The number of passengers
required to travel from station
to station
;
: remaining seats of drone u when departing from site i to site j (initialized as the drone’s total seating capacity; after picking up passengers, the remaining seats are reduced accordingly; upon drop-off, seats become available again for subsequent segments);
: Passenger
specifies a time requirement for arriving at station
The passenger departs from station
;
: The time for an order-assigned UAV
to arrive at site
after departing from site
;
Based on the above definitions and assumptions, the SUCS model based on minimizing the total time of the multi-airport UAV operation system is designed as shown below:
Eq. (1) means that the ultimate goal of the model is to minimize the total navigation time of all UAVs; constraint [2] means that the remaining endurance of the assigned UAV corresponding to the task must meet the needs of the task; constraint [3] means that the assigned UAV model must meet or exceed the passenger’s requested model (allowing upgrades to improve fleet utilization); constraint [4] means that the system assigns the UAVs to have unloaded seats inside the UAVs that can accommodate all of the passengers of the order; and constraint [5] means that the UAVs need to send the passengers to their destinations at an earlier time than the passengers’ demanded arrival times.
3. A soft time window based minimum route planning model for total consumption of multi-airport systems
3.1 Description of the problem
In real life, some passengers have restrictions on arrival time (e.g., to arrive at airport, train station within a certain time). If a new order with high carpool adaptability emerges, forcing carpooling might reduce total flight distance but could seriously impact personal interests of order initiators. Therefore, from the passenger’s time requirements perspective, violations should incur penalties.
The Soft Time Window[5] based Total Consumption Minimum Route Planning Model [6] for Multi-Airport Systems builds on the scheduling problem and guarantees passenger interests by adding time constraints for UAV arrival at passenger locations [7]. If SUCS scheduling time deviates from passenger order initiation time, penalty cost is added accordingly.
3.2 Modeling of penalties for exceeding demand time
We introduce asymmetric quadratic penalty functions to appropriately reflect passenger disutility:
included among these,
: The value of time loss (TIME COST) of UAV
from site
to site
;
ec: Systems Penalty for Early Order Fulfillment for passenger-carrying Drones；
lc: Systematic penalties for passenger-carrying drones that fail to fulfill orders on time and in accordance with the time specified by the user；
Justification for quadratic form: Quadratic penalties better reflect passenger dissatisfaction with extreme delays; small deviations cause minor inconvenience, while large delays cause disproportionate dissatisfaction. Early penalties are justified because passengers may not be ready for early pick-up, early arrivals occupy limited waiting areas, consume battery while hovering, and may disrupt airspace slots.
3.3. mathematical model
To describe the model more clearly and accurately, the notation is defined as follows:
αμ: distance cost coefficient for UAV u (RMB/km)
β: normalization factor converting time penalty to cost units (RMB/min)
The other notations of the model are the same as in 2.2.
The distance cost coefficient αμ is specified in RMB per kilometer (as listed in Tables 1, 2, and 3 for each UAV model). The normalization factor β converts time penalties (minutes) into cost units (RMB), ensuring dimensional consistency between distance-related and time-related terms in the objective function. In this study, β is set to 1 RMB/min based on typical urban mobility valuation benchmarks, reflecting the trade-off between operational distance costs and passenger time satisfaction. Both parameters thus share consistent units, allowing the objective function to combine distance and time components meaningfully.
Based on the above assumptions and parameter definitions, the model is developed as follows:
Improved natural number encoding rules for SLALO algorithm
The SLALO algorithm is originally used to solve real number function problems, and in this paper, we obtain the encoding of the natural numbers for computing the discrete UAV route planning problem by rounding the real numbers. This subsection is mainly used to show how the system allocates the coding and decoding process for UAV service passengers, for example The specific transformation steps of SLALO for a passenger-carrying UAV are as follows:
It may be assumed that is a random ant lion.
Ceil means to round A and find the absolute value to get S.
In the ant lion transformed by Eq. [11] , s1 represents the passenger with number 1, and the value of s1 indicates that the UAV with that number is going to serve that passenger.
The following shows the specific conversion flow for a string of SLALO codes with a user count of 8:
Using the coding transformation process of the appeal, the random real-number coded ant-lion individual A is changed from Eq. (11) to the SLALO feasible solution ant-lion individual S composed of the corresponding constants [8]. This ant-lion individual represents the following: Drone No. 6 serves both the users at the starting sites 1 and 3; the passengers at the starting sites 2, 4, and 6 are serviced by Drone No. 7; the passenger at location 5 is serviced by Drone No. 3; the passenger at location 7 is serviced by Drone No. 4; and the passenger at location 8 is serviced by Drone No. 1 (Tables 4 and 5).
3.2. Drone flight path optimization case
The cloud server receives 14 orders with different starting and destination stations for different users. Table 6 contains the location of the start site and destination site for each passenger. The airport has several types of passenger-carrying drones, each with a uniform range of 300 km and models that can accommodate 1 and 2 passengers (see Tables 1 and 7 for UAV and airport details). The drones take off from the hangar center in 0 time and fly at the same speed as the average speed.
Fig 2 shows the spatial distribution of passenger origins and destinations.
3.4. Simulation experiment analysis
Figs 3 and 4 show the UAV route planning graphs obtained from the simulation optimization experiments for the above mentioned small-scale cases, Fig 3 shows the total time minimum result of the multi-airport system based on passenger demand [9], and Fig 4 shows the total cost minimum result of the system based on the soft time window constraints.
The results show that 14 orders are served by 6 UAVs, with total voyage mileage 137,784 m and total operating time 81.63 min. In non-pooling mode, total distance would be 226.8 km, demonstrating a 27.3% reduction through ride-pooling. Average UAV utilization reaches 78.6%.
Comparison with other algorithms: To further validate the effectiveness of SLALO, we compared it with Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and standard Ant-Lion Optimizer (ALO) on the large-scale case (50 orders, 20 UAVs, 3 airports). The detailed UAV information for drones 11–20 is provided in Table 3, and the three airport locations are listed in Table 8. Table 9 summarizes the performance metrics [10–15].
Fig 5 shows the convergence curves of the four algorithms for the large-scale case. Fig 6–8 displays the optimal UAV routes for total cost minimization in the large-scale multi-airport system. Fig 7 shows the convergence curve for the total cost minimization (soft time window model) in the large-scale case (Fig 8).
The vertical axis labeled “Adaptation value” represents the objective function value, i.e., total navigation time (minutes).
The vertical axis labeled “Adaptation value” represents the objective function value, i.e., total cost (RMB).
Tables 2 and 10 detail the remaining passenger orders and standard UAV parameters (UAVs 1–10) for the large-scale case, while Tables 3 and 8 provide the specifications for additional UAVs [11–20] and the three airport locations, respectively.
Conclusion
This paper addresses the shared passenger-carrying UAV scheduling problem in multi-airport systems by proposing a model that integrates passenger time preferences, UAV operational constraints (endurance, capacity, model compatibility), and ride-pooling coordination. A soft time window mechanism with quadratic penalties is introduced to balance operational efficiency and passenger satisfaction, allowing flexible yet controlled arrival deviations. To solve the resulting discrete combinatorial assignment problem, we develop a self-learning Ant-Lion Optimizer (SLALO) enhanced with natural number encoding.
The effectiveness of the proposed approach is demonstrated through simulation experiments. Key findings include: [1] the shared scheduling model achieves a 27.3% reduction in total navigation time compared to non-pooling baselines, with an average UAV utilization rate of 78.6%; [2] the SLALO algorithm outperforms GA, PSO, and standard ALO in terms of both convergence speed and solution quality; [3] the quadratic soft time window mechanism effectively balances cost efficiency and passenger time satisfaction. These results highlight the potential of shared UAV systems to improve urban air mobility efficiency, reduce operational costs, and enhance passenger satisfaction, particularly in regions with underdeveloped ground transportation infrastructure.
Beyond the immediate findings, the proposed shared UAV scheduling model holds significant promise for addressing transportation challenges in vast and remote border regions such as Tibet, Xinjiang, Inner Mongolia, and the northeastern provinces of China. In these areas, where ground infrastructure is limited and distances are substantial, the efficiency gains demonstrated in this study (27.3% reduction in navigation time) could translate into even more substantial socio-economic benefits. Future implementation of such systems could enhance cross-border connectivity, support emergency response in sparsely populated areas, and contribute to the balanced regional development objectives outlined in China’s border area revitalization strategies. From a broader perspective, the development of shared UAV-based mobility systems represents a concrete pathway for cultivating new quality productive forces in border regions, leveraging advanced automation and intelligent scheduling to overcome geographical constraints and unlock economic potential.
Future work will extend the model to dynamic demand scenarios and real-time re-scheduling under uncertainty, as well as incorporate more realistic factors such as weather effects and air traffic constraints.
Supporting information
S1_Code. This file contains the complete MATLAB simulation code of the SLALO (Shared Logistics Aerial Lift Optimization) algorithm adopted in this study.
The code can reproduce the results presented in Table 5 of the manuscript. All required functions are compiled in a single PDF file, including the main script (main.m), objective function (UAV_objective.m), data loading (data_load.m), route generation (get_UAV_route.m), initialization (initialization_SLALO.m), mutation operator (Random_walk_around_antlion_SLALO.m), selection operator (RouletteWheelSelection_SLALO.m), visualization function (func_plot_SLALO.m), and the main SLALO optimization procedure (SLALO.m).
https://doi.org/10.1371/journal.pone.0348883.s001
(PDF)
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