Abstract

Translate

To address the insufficient evaluation of scenario adaptability in the coordinated control of shared waypoints within multi-airport systems, this study proposes two optimization strategies: the Multi-Waypoint Rolling Horizon Control (MWRHC) and the Multi-Waypoint Ant Colony Optimization (MWACO) algorithms. A systematic comparison of their applicability and control performance is conducted. Using empirical data from peak-hour operations in the Yangtze River Delta multi-airport system, the applicability and optimization effectiveness of both algorithms in arrival–departure sequencing are evaluated. The metric “Average Flight Time Improvement” is introduced to quantify and compare the performance of different airports during the optimization process, thereby revealing the operational characteristics of MWRHC and MWACO under varying traffic conditions. The results demonstrate that the MWACO algorithm exhibits superior global optimization capability in high-traffic airport environments, whereas the MWRHC algorithm performs better in local optimization and real-time scheduling under moderate traffic conditions.

Full text

Turn on search term navigation

Translate

1. Introduction

1.1. Background

Over more than a century of evolution, air transportation has become a fundamental mode of global passenger and cargo movement. With its steady growth, however, the traditional single-airport traffic management paradigm has become increasingly inadequate to handle the surging flight demand and the growing complexity of air traffic environments. In recent years, the concept of the Multi-Airport System (MAS) has attracted significant attention and has emerged as a defining feature of air traffic management in major global aviation hubs.

A Multi-Airport System refers to a network of two or more airports located within the same metropolitan area or air traffic hub, jointly serving the air transportation demand of that region. Because the airports within an MAS are often situated in close proximity, flight trajectories tend to overlap, with multiple flights frequently passing through the same waypoints or air routes. Despite this operational interdependence, flight scheduling and traffic management at each airport are typically conducted independently, which can lead to congestion and capacity bottlenecks at shared waypoints. These waypoints thus become critical nodes that directly influence the efficiency and safety of arrival and departure operations across the entire system.

1.2. Literature Review

Ren et al. [1] conducted a comprehensive evaluation of four major airport groups in the United States and revealed several critical challenges in the operation of multi-airport systems. Their study emphasized that interdependence in airspace resource sharing and runway configuration among airports can lead to significant flight delays and airspace congestion. The Federal Aviation Administration (FAA) refers to such systems as Metroplexes, defining them as geographically concentrated areas containing multiple airports, typically located in high-demand metropolitan regions. These systems are characterized by dense traffic flows, closely spaced airport operations, and environmental constraints, all of which jointly reduce the overall efficiency of MAS operations.

In recent years, numerous scholars have explored multi-airport and multi-runway flight scheduling and coordination to address these challenges. Ma et al. [2] (2014) developed a coordinated sequencing model for arrival flights in multi-airport terminal areas, incorporating constraints such as air traffic control handovers, wake turbulence separation, and multi-runway operations. Wang et al. [3] introduced a dual-encoding genetic algorithm to construct an arrival and departure sequencing model for parallel runways, explicitly accounting for cargo flights. Sidiropoulos et al. [4] (2015) proposed an optimization strategy for sequencing arrival and departure flights within airport groups. Their method involved clustering flights based on spatiotemporal distributions to identify dynamic routing paths, ranking these paths by priority, and then sequencing flights dynamically at shared waypoints while maintaining minimum separation standards [5]. Zhang et al. [6] (2017) modeled the multi-airport terminal area as a unified system and introduced the concept of peripheral air traffic flow. Using an improved simulated annealing algorithm, they solved the arrival–departure sequencing problem for multiple airports. Wang et al. [7] subsequently employed a fuzzy self-adaptive multi-objective particle swarm optimization (FS-MOPSO) approach to construct a collaborative decision-making model for multi-airport flight scheduling. In 2019, Zhang et al. [8] developed a multi-objective programming model to establish a capacity-matching-based traffic flow allocation strategy for airport groups, aimed at mitigating flight delays and airspace congestion. Yin et al. [9] (2020) examined the impact of runway configurations at multiple airports within an airport group on overall traffic flow management and proposed an integrated runway assignment and sequencing method that optimizes multi-airport and multi-runway utilization. Wang et al. [10] (2021) investigated the coupled operation of shared waypoints in multi-airport systems, introducing a penalty factor and formulating an optimization model that minimizes the total delay cost. Their approach combined a sliding time-window algorithm with particle swarm optimization to dynamically sequence flights at shared waypoints.

1.3. Contribution of the Research

Although existing studies have proposed various solutions for multi-airport flight sequencing, runway assignment, and dynamic routing optimization [2,3,4,5,6,7,8,9], most of them treat shared waypoints as static constraints, lacking a systematic modeling framework for multi-waypoint dynamic coordination and control mechanisms. Moreover, few have quantitatively evaluated the scenario adaptability of different control strategies.

The Rolling Horizon Control (RHC) approach has been widely adopted for real-time scheduling due to its dynamic adjustment capability; however, its global optimization performance is inherently constrained by the rolling window length [11,12]. In contrast, the Ant Colony Optimization (ACO) algorithm demonstrates superior global convergence in path optimization and resource allocation but may struggle to meet real-time computational requirements in high-density operational environments [13,14]. These two approaches exhibit complementary strengths—RHC excels at local dynamic adjustment, while ACO is more effective in global coordination—collectively addressing the multi-dimensional demands of a MAS that range from tactical scheduling to strategic optimization.

To bridge these gaps, this study investigates coordinated regulation of shared waypoints in MAS and develops two optimization frameworks: Multi-Waypoint Rolling Horizon Control (MWRHC) and Multi-Waypoint Ant Colony Optimization (MWACO). In this research, optimization refers to minimizing flight delay by reducing the difference between scheduled and realized landing, takeoff, and waypoint-passing times. The optimization objectives are achieved under the full consideration of operational constraints including wake turbulence separation, runway capacity, airspace interactions, and waypoint occupancy. A comparative analysis between the two approaches is conducted to examine their differences in optimization behavior, and scenario adaptability, with the aim of identifying their applicability under complex conditions.

Using empirical ADS-B data from the Yangtze River Delta multi-airport system during peak traffic periods, the study evaluates how each algorithm enhances arrival–departure coordination, mitigates congestion effects, and reduces total delay. The findings not only reveal the operational value of each method but also provide theoretical support for developing differentiated traffic flow control strategies and multi-objective optimization schemes for complex multi-airport environments.

2. Algorithm

2.1. Multi-Waypoint Rolling Horizon Control (MWRHC)

The Multi-Waypoint Rolling Horizon Control (MWRHC) algorithm is designed to address the flight sequencing problem across multiple shared waypoints in a MAS [11,12], as illustrated in Figure 1. This approach extends the concept of Rolling Horizon Control (RHC) by decomposing the overall planning horizon into a sequence of overlapping time windows, each with a duration of 3T, where the window advances by one time step T at each iteration. Within each rolling window, the algorithm optimizes flight trajectories and sequencing based on real-time traffic conditions and updated constraints. By dynamically adjusting the arrival sequence of flights passing through shared waypoints, MWRHC effectively enhances the traffic flow management efficiency of multi-airport systems. This dynamic optimization framework allows the system to respond adaptively to fluctuations in traffic demand, runway configurations, and separation constraints, ensuring both operational feasibility and system-level coordination among airports within the MAS.

The model parameters and decision variables are defined in Table 1, Table 2 and Table 3.

To enhance operational efficiency while maintaining safety standards, the objective function is constructed from the perspective of air traffic flow management. It is defined as a weighted linear combination of three components, aiming to balance the overall reduction in total flight delays and the advancement of maximum departure times for outbound flights. This balance maximizes runway utilization at each airport and improves the overall operational efficiency of the terminal area within the multi-airport system.

The objective function is defined as follows:

(1) $\min [ω_{1} \cdot \sum_{i \in F^{in}} (A L T_{i} - S c h e d u l e d_{i}) + ω_{2} \cdot \sum_{j \in F^{out}} (A L T_{j} - S c h e d u l e d_{j}) + ω_{3} \cdot \max_{j \in F^{out}} (A T_{j}^{endpoint})]$

where ω1, ω2, and ω3 are the weighting coefficients assigned to the three components of the objective function.

The first term represents the cumulative deviation between the actual landing times (ALT_i) and the scheduled landing times of all arrival flights (F_in); the second term represents the cumulative deviation between the actual takeoff times (ALT_j) and the scheduled takeoff times of all departure flights (F_out); and the third term denotes the time when the last departure flight (F_out) leaves the terminal airspace of the airport group.

The goal is to minimize the weighted sum of these three components. The weighting coefficients can be adjusted according to the preferences and requirements of air traffic management.

Assume that flight i corresponds to target airport a, and flight j corresponds to target airport b. If $\forall i \in F$ , it indicates any arrival or departure flight. The corresponding constraints are presented in Table 4. Assuming that flight i corresponds to its target airport a.

As outlined in Table A1, the constraint conditions are described as follows.

Constraint (1): Unique path assignment—Each flight must be assigned a unique approach or departure path to ensure the exclusivity and safety of route and runway allocation, thereby avoiding potential conflicts [15].

Constraint (2): Runway as the terminal waypoint for arrival flights—For each arrival flight, the runway is always the final waypoint on its route, and the arrival time at this waypoint corresponds to the actual landing time. This constraint ensures the rationality and logical consistency of the flight path, guaranteeing that once an arrival flight reaches its final waypoint, the landing operation is completed, thus preventing looping or excessive delay along the route.

Constraint (3): Runway as the initial waypoint for departure flights—For each departure flight, the runway is always the first waypoint on its route, and the passage time at this waypoint corresponds to the actual takeoff time.

Constraint (4): Minimum time interval between consecutive waypoints—The time interval between two consecutive waypoints along a flight’s route must not be less than the minimum required flight time for that segment. This prevents unrealistic time assignments or excessively short traversal intervals, ensuring both safety and operational feasibility along the route.

Constraints (5) and (6): Initial waypoint time constraints—For arrival flights, the passage time at the initial waypoint is assumed to be equal to the scheduled entry time into the controlled airspace, ensuring that the flight enters within the planned time window. For departure flights, the passage time at the initial waypoint must fall within the interval defined by the scheduled and actual pushback times, ensuring feasibility of the takeoff time and preventing conflicts with other flights.

Constraints (7) and (8): Flight sequencing uniqueness—These constraints ensure a unique ordering between any two flights. If flight i precedes flight j at a specific waypoint, then flight i must not lag behind flight j at any other waypoint along their shared route. This enforces consistent sequencing and eliminates potential order conflicts across multiple waypoints.

Constraint (9): Minimum separation at shared waypoints—Within radar-controlled airspace, the time interval between any two flights passing through the same waypoint must satisfy the minimum separation required by air traffic control regulations. A binary variable is introduced to determine the sequence of flight passage, thereby reducing the risk of congestion and loss of separation in dense airspace [16,17].

Constraints (10)–(13): Runway wake turbulence separation constraints—These constraints focus on landing sequence and wake turbulence separation on runways. By introducing binary variables to distinguish runway usage scenarios and flight categories, the model ensures that the required wake turbulence separation standards between consecutive flights are maintained, thereby mitigating wake-related safety risks.

Constraints (14)–(19): Logical consistency constraints—For flights sharing the same route, their path selection and waypoint passage sequence must maintain logical consistency. This is achieved by enforcing consistency constraints between the corresponding binary variables, ensuring that flight order and route selection remain coherent.

Constraint (20): Maximum departure time constraint—The maximum departure time is defined as the latest passage time among all departure flights at their final waypoints. This auxiliary constraint enables the computation of the third component of the objective function, which represents the maximum exit time from the terminal airspace of the multi-airport system.

2.2. Multi-Waypoint Ant Colony Optimization (MWACO)

We further propose a coordinated control model for arrival and departure flights in a multi-airport system, integrating the ant colony optimization (ACO) algorithm with a dynamic congestion coefficient adjustment strategy. Through waypoint conflict detection, temporal dynamic adjustment, and runway resource allocation and optimization, the proposed model achieves cooperative flow management for arrival and departure operations across the multi-airport system.

The overall workflow of the algorithm is shown in Figure 2.

Key Steps of the Algorithm Construction

For the m-th ant in the g-th iteration, each flight progressively constructs a complete route from the decision point to the destination runway or waypoint based on the current time state, pheromone value, and congestion coefficient. The process is divided into several substeps as follows:

2.2.1. Path Selection

Let the current waypoint of flight f_i be w_current. If the flight type is arrival, the next waypoint w_k is selected from the candidate segment set {(w_current, w_k)}; for departure flights, a similar search is performed among feasible outbound segments. Optional segment set S:

(2) $S = \{(w_{c u r r e n t}, w_{k}) | τ (w_{c u r r e n t}, w_{k}) = τ (f_{i})\}$

where

τ (f_{i})

denotes the flight type (arrival/departure) of flight f_i,

τ (w_{c u r r e n t}, w_{k})

denotes the type of candidate segment. For each selectable segment (w_current, w_k)∈S, let Γ_i denote the pheromone value and η_i the heuristic factor.

The pheromone value Γ_i associated with a segment reflects its learned desirability accumulated through previous iterations. Its meaning is twofold:

(a). segments that historically contribute to smaller total delay retain higher pheromone values through reinforcement;

(b). segments leading to infeasible or inefficient schedules gradually lose attractiveness due to evaporation or penalty.

Thus, Γ_i represents global, experience-driven guidance, encoding how past solutions evaluated a segment.

The heuristic factor η_i provides local, real-time guidance based on operational conditions. In this study, η_i is defined to reflect instantaneous desirability of a segment, including minimum travel time, local congestion proximity, and potential efficiency gain associated with moving toward the runway or exit point.

Higher η_i indicates a segment that is operationally preferable at the current decision moment.

The probability p_i of selecting this segment is given by:

(3) $P_{i} = \frac{{[Γ_{i}]}^{α} \cdot {[η_{i}]}^{β}}{\sum_{j \in S} {[Γ_{j}]}^{α} \cdot {[η_{j}]}^{β}}$

where α is the pheromone importance factor, regulates how strongly the model exploits historical learning; β is the heuristic importance factor, governs reliance on the current operational heuristic; and index j refers to each candidate segment in set S.

A segment (w_current, w_k) is then randomly selected according to the probability p_i, and the corresponding waypoint w_k is stored in f_i.waypoints_list.

2.2.2. Congestion Coefficient Computation and Time Adjustment

Once the next segment (w_current, w_k) is determined, the arrival time at w_k is determined by adding the minimum flight time Δt_min to the previous waypoint time f_i.waypoints_time[−1], where

(4) $Δ t_{\min} = T_{\min} (ω_{current}, ω_{k})$

where T_min(⋅)is defined as the minimum flight time of the segment. Then, the congestion coefficient λ is calculated as:

(5) $λ = \frac{N (Δ t)}{Λ_{thr}}$

where N(Δt) is the number of flights passing through the waypoint during time interval Δt, and

Λ_{thr}

represents the congestion threshold parameter.

If λ > 1, it indicates that an excessive number of flights have already occupied the waypoint during the time interval Δt, and the arrival time $T_{f_{i}}^{(w_{k})}$ must be delayed accordingly:

(6) $T_{f_{i}}^{(w_{k})} \leftarrow T_{f_{i}}^{(w_{k})} + δ \cdot λ$

where δ is a fixed step size (e.g., 10 s). If the waypoint remains congested after adjustment, the delay process continues iteratively until the congestion factor satisfies λ ≤ 1. If w_k∈runway_list, the minimum runway separation time is defined as min_runway_gap = 120 s to avoid excessive density on the same runway.

(7) $T_{f_{i}}^{(w_{k})} - T_{o t h e r s}^{(w_{k})} \geq \min_runway_gap$

If the constraint is not satisfied, the time adjustment procedure is repeated. For airports with multiple runways, a runway-switching mechanism may also be triggered to reduce delays.

2.2.3. Path Penalty for Invalid Routes

If the feasible segment set becomes empty or the number of retries exceeds a predefined threshold, the corresponding pheromone value Γ_i is multiplicatively decayed to prevent other ants from repeatedly selecting the same invalid path.

If a flight successfully reaches its final waypoint—i.e., the destination runway for arrival flights or the final departure decision point for departure flights—its complete waypoints_list and waypoints_time are recorded into the schedule, and all relevant route information is updated accordingly.

2.2.4. Fitness Evaluation

After an ant completes a full scheduling scheme for all flights, the fitness of its solution is evaluated based on two indicators: the maximum delay D_max and the total delay D_total.

Maximum delay:

(8) $D_{\max} = \max_{f_{i} \in F} \{\max (T_{f_{i}}^{finish} - T_{f_{i}}^{sched}, 0)\}$

where

T_{f_{i}}^{finish}

is the actual landing (or takeoff) time, and

T_{f_{i}}^{sched}

is the scheduled time. If no delay occurs, the value is set to zero.

Total delay:

(9) $D_{total} = \sum_{f_{i} \in F} \max (T_{f_{i}}^{finish} - T_{f_{i}}^{sched}, 0)$

The algorithm records the D_max and D_total for each ant, and compares them to identify the optimal solution.

2.2.5. Pheromone Update

After all M ants complete a construction round, the pheromone matrix Γ is updated in two stages:

Pheromone Evaporation

(10) $Γ (d, a, (w_{s t a r t}, w_{e n d})) \leftarrow Γ (d, a, (w_{s t a r t}, w_{e n d})) \cdot (1 - ρ)$

where ρ is the evaporation rate.

This prevents unlimited accumulation of historical pheromone trails and encourages the search to escape local optima.

Pheromone Reinforcement

Each ant’s solution is evaluated based on its total delay D_total. For every traversed segment (w_j, w_j+1), pheromone is increased proportionally to 1/(D_total + ε):

(11) $Δ Γ = \frac{Q}{D_{total} + ε}$

where Q is a constant coefficient and ε is a small positive number to prevent division by zero. Hence, smaller delays yield larger pheromone increments.

Let P be the set of all route segments traversed by an ant starting from decision_point = d and airport = a. Then, for each segment (w_j, w_j+1)∈P:

(12) $Γ (d, a, (w_{j}, w_{j + 1})) \leftarrow Γ (d, a, (w_{j}, w_{j + 1})) + Δ Γ$

This reinforcement mechanism across all ants forms an adaptive search process that suppresses inferior solutions and strengthens superior ones, effectively balancing exploration and exploitation in the optimization.

3. Experimentation

3.1. Data Description

The Yangtze River Delta (YRD) Airport Metroplex, which is also called as Airport Cluster, is one of the four world-class airport clusters in China. The major airports identifier and corresponding names are listed in Table 4. The operational scale and flight volume of these airports are representative of the overall regional traffic characteristics.

The study data consist of typical high-traffic flight records within a two-hour peak period (from 17:00:00 to 19:00:00), covering all arrival and departure flights within the YRD airport cluster. A total of 328 flights are included, comprising 153 arrival flights and 175 departure flights. To meet the requirements of the collaborative control model, this research systematically organized and coded the arrival and departure routes, segments, and corresponding waypoints, providing full coverage of each airport’s approach and departure paths as well as their shared waypoints.

The input data required for the model include each flight’s origin or destination waypoint (decision point), scheduled time, flight priority, and all available route information. The detailed components are as follows:

3.1.1. Arrival Flight Data

This dataset includes the entry waypoints of flights entering the YRD area, actual passing times at these entry waypoints, scheduled arrival times, target airports, available landing runways, and flight priority levels.

3.1.2. Departure Flight Data

This dataset includes the departure airports, available takeoff runways, actual pushback times, scheduled takeoff times, exit waypoints through which flights leave the YRD area, and flight priority levels.

3.1.3. Route Segment and Time Constraints

The route segment information table defines in detail each segment’s starting and ending waypoints, minimum and maximum flight times, and segment attributes (arrival or departure). As shown in Figure 3, blue nodes represent shared waypoints for both arrival and departure flights, labeled with the prefix M. Based on differences in crossing altitude, the same waypoint may be further divided into multiple vertical levels—for example, M_io_1, M_io_2, M_io_3, and M_io_4, each with low (L) and high (H) designations. Red nodes denote arrival waypoints, labeled with the prefix A, where A_in represents the entry waypoint into the airport cluster and A_mid indicates intermediate arrival waypoints. Green nodes denote departure waypoints, labeled with the prefix D, where D_out represents the exit waypoint from the cluster and D_mid indicates intermediate departure waypoints.

3.1.4. Route Data

This dataset contains the waypoint sequences, associated airports, and route identifiers. Each route is assigned a unique numeric code to explicitly define the set of feasible route options available for each flight. The available routes information for arrival/departure flights are listed in Table A2, Table A3, Table A4 and Table A5.

3.2. Model Verification

The computational experiments were conducted using the Python 3.9 programming interface. The simulation environment was configured on a 2.4 GHz Intel i9-12900 CPU. In the rolling time-domain algorithm, the Mixed Integer Programming (MIP) model was solved using the Gurobi 10.0 optimizer. The initial time T₀ was set to 0. Based on the operational experience and preferences of air traffic control (ATC) departments, the weight coefficients of the three components in the objective function were set as ω₁ = ω₂ = 1, ω₃ = 1.5.

At shared waypoints, specific safety separation requirements were imposed to ensure flight safety [10]: Radar vectoring separation, $T_{i j}$ = 60 s; same-runway wake turbulence separation, $S_{i j}$ = 108 s; adjacent-runway wake turbulence separation, $s_{i j}$ = 48 s.

During the iterative process of the rolling time-domain algorithm, both the initial and terminal time domains lacked the support of adjacent time-domain data, which could introduce deviations between the computational results and actual operations. Therefore, to ensure fairness and accuracy in comparison, this study focused only on the results obtained within the intermediate time domains across the entire time range.

To validate the effectiveness of MWRHC and MWACO, the optimized results were compared against actual operational data and model outputs from both methods. Figure 4 and Figure 5 illustrate the optimized arrival and departure sequences for different routes under the two algorithms, respectively.

A comparative analysis of Figure 4 and Figure 5 shows that, in terms of both landing time and takeoff time optimization, the MWACO model outperforms the MWRHC model, particularly during peak traffic periods, where it demonstrates stronger global optimization capability. The optimization of landing times primarily reduces airborne holding durations, while takeoff time optimization effectively mitigates conflicts in runway resource allocation. Although the rolling time-domain algorithm (MWRHC) performs well in local optimization, it lacks sufficient global coordination capability under high-traffic conditions. In contrast, the ant colony optimization algorithm (MWACO), with its global search and multi-objective optimization abilities, achieves more efficient flight sequencing and resource allocation.

Both models significantly improved operational performance while satisfying all safety separation requirements, with particularly notable improvements during high-traffic periods. The MWRHC model is more suitable for localized optimization scenarios, whereas the MWACO model demonstrates distinct advantages in global optimization, providing an effective solution for flight scheduling and airspace management in multi-airport systems.

To evaluate and compare the effectiveness of the two algorithms, the concept of Average Flight Time Improvement was introduced as an overall indicator for improvement for the achieved optimization benefit.

For arrival flights, let LTⁱ_actual denote the actual landing time of flight i, and LTⁱ_MWRHC and LTⁱ_MWACO represent the optimized landing times obtained by the MWRHC and MWACO algorithms, respectively. The average improvement in arrival time for airport a, denoted as c_Arr_a, is defined as:

(13) $c_A r r_{a} = \sum_{i \in F_{a}^{i n}} (L T_{M W R H C}^{i} (o r L T_{M W A C O}^{i}) - L T_{a c t u a l}^{i}) / N_{a}^{i n}$

Similarly, for departure flights, let LT^j_actual denote the actual takeoff time of flight j, and LT^j_MWRHC and LT^j_MWACO represent the optimized takeoff times obtained by the two algorithms. The average improvement in departure time for airport b, denoted as c_Dep_b, is defined as:

(14) $c_D e p_{b} = \sum_{j \in F_{b}^{o u t}} (L T_{M W R H C}^{j} (o r L T_{M W A C O}^{j}) - L T_{a c t u a l}^{j}) / N_{b}^{o u t}$

As shown in Figure 6, the average flight time improvement c (in seconds) is presented for all six airports after applying the two algorithms. In terms of arrival performance, the MWACO algorithm consistently generates greater time savings than MWRHC. At high-traffic airports such as PVG, NKG, and HGH, although the improvement magnitude is lower than that of WUX (a low-traffic airport), the time improvement remains relatively stable. For departure flights, all six airports exhibit relatively similar improvements, with MWACO still showing slightly better performance.

4. Discussions

From the perspective of average flight time improvement for arrival flights, the MWACO model generally outperforms the MWRHC model, demonstrating a stronger ability to reduce operational delay. This superiority arises because the ant colony algorithm dynamically adjusts path selection and comprehensively accounts for congestion factors, allowing it to respond more flexibly to route resource competition and dynamic traffic variations.

Among the six airports, NKG exhibits the lowest improvement for arrival flights, indicating that its approach routes are relatively uncongested, resulting in lower adjustment demand. In contrast, SHA shows a notably higher improvement due to its heavy arrival traffic and intense route competition. PVG demonstrates a moderate level of improvement, with relatively small differences between the MWRHC and MWACO results. WUX achieves the highest time improvement despite having a lower overall traffic volume. This is because its approach operations are affected by overlapping airspace with nearby airports such as Shanghai and Nanjing, leading to frequent adjustments in arrival sequencing. Therefore, both algorithms perform comparably at WUX. HGH and NGB, with moderate traffic levels, show intermediate time improvements, where MWACO slightly outperforms MWRHC.

For departure flights, the results further support the superiority of MWACO. Regardless of traffic level, MWACO consistently achieves larger improvements than MWRHC. However, the inter-airport variation for departures is smaller than for arrivals. This is mainly because departure timing is constrained by pushback readiness and ground procedures, resulting in narrower adjustment windows.

These findings reflect the operational characteristics of airports within the Yangtze River Delta multi-airport system. High-traffic airports (such as SHA and PVG) exhibit higher average optimization times, reflecting their greater operational complexity and intense competition for airspace and runway resources. Medium-traffic airports (such as HGH and NGB) show moderate levels of time improvement, with relatively balanced route resources and scheduling complexity. Low-traffic airports (such as NKG and WUX) display more variability in improvement magnitudes; Wuxi shows a higher adjustment demand due to its proximity to major airports, while NKG displays limited improvement potential.

In terms of algorithmic performance, MWACO consistently achieves higher performance effectiveness than MWRHC across all airports and flight types. Its advantage is particularly evident in complex operational environments or highly competitive airspace conditions, confirming its strong potential for improving traffic coordination and control in multi-airport systems. While this study focuses on time-based outcome improvements, future work will further compare computational time performance between the two algorithms to assess real-time applicability.

5. Conclusions

This study focuses on the congestion and resource competition frequently occurring at shared waypoints within multi-airport systems. To address these challenges, two adaptive regulation strategies were proposed: the Multi-Waypoint Rolling Horizon Control (MWRHC) method and the Multi-Waypoint Ant Colony Optimization (MWACO) algorithm. Furthermore, the average flight optimization time was introduced as a quantitative performance indicator to evaluate the effectiveness of different control approaches in flight scheduling and flow regulation.

Empirical validation was conducted using peak-hour operational data from the Yangtze River Delta multi-airport system. The main conclusions are summarized as follows:

(1). Performance under different traffic conditions: The MWRHC strategy demonstrates strong capability in local optimization and real-time scheduling under medium traffic conditions, whereas the MWACO algorithm shows superior global optimization performance under high-traffic scenarios.

(2). Applicability across airport types: Both models effectively regulate high-density flight operations in regional hub and sub-hub airports, confirming their adaptability to different airport roles within the system.

(3). Comprehensive comparison: The MWACO algorithm exhibits advantages in overall coordination and airspace resource integration, while the MWRHC model provides higher implementation simplicity and better adaptability for local real-time applications.

Overall, the proposed strategies provide a feasible framework for dynamic traffic flow regulation in multi-airport systems, offering theoretical support and practical reference for the coordinated management of terminal area operations.

Author Contributions

Conceptualization, F.J. and Z.Z.; methodology, Z.Z.; data curation, F.J.; writing—original draft preparation, F.J.; writing—review and editing, F.J., T.L. and Z.Z. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1 Window processing in rolling horizon framework when sliding window is 3T and step is T.

Figure 2 MWACO algorithm control flow chart.

Figure 3 Distribution of Major Waypoints along Arrival and Departure Routes in YRD Airport Metroplex.

Figure 4 Comparison of flight landing sequence and landing time.

Figure 5 Comparison of flight takeoff sequence and landing time.

Figure 6 Comparison of the average flight time improvement across six airports.

Table 1

Definitions for sets.

Set Symbol	Definition	Index Symbol
A	Set of airports in the multi-airport system	a
F ⁱⁿ	Set of arrival flights	i
F ^out	Set of departure flights	j
R	Set of available routes	r, s
R_i	Set of optional routes for flight i, i∈F, R_i⊂R
D	Set of route segments constituting available routes	d
D_r	Set of route segments constituting route r
P	Set of waypoints in the multi-airport system	p
P_r	Set of waypoints on route r
W	Set of runways in the multi-airport system, W⊂P	w
$W_{a}^{Arr}$	Set of arrival runways at airport a
$W_{a}^{Dep}$	Set of departure runways at airport a

Table 2

Definitions for parameters.

Symbol	Definition
V _{i (or j)}	Priority of flight i (or j)
a _{i (or j)}	Arrival (or departure) airport of flight i (or j)
$S c h e d u l e d_{i}^{Arr}$	Scheduled arrival time of arrival flight i
$T_{i}^{inwaypoint}$	Actual time when arrival flight i passes through the entry waypoint
$S c h e d u l e d_{j}^{Dep}$	Scheduled departure time of departure flight j
$T_{j}^{pullout}$	Actual time when departure flight j passes through the exit waypoint
$T_{d}^{\min}$	Minimum flight time of route segment d
$p_{d}^{start}$	Maximum flight time of route segment d
$p_{d}^{end}$	Starting waypoint of route segment d
$S_{i_{1} i_{2} (or j_{1} j_{2})}$	Ending waypoint of route segment d
$s_{i_{1} i_{2} (or j_{1} j_{2})}$	Minimum separation time satisfying wake turbulence requirements when flights i₁ (or j₁) and i₂ (or j₂) use the same runway at the same airport
$S^{R}$	Minimum separation time satisfying wake turbulence requirements when flights i₁ (or j₁) and i₂ (or j₂) use different runways at the same airport
M	Minimum time interval when two flights (arrivals or departures) pass through the same waypoint under air traffic control constraints
N	A very large number

Table 3

Definitions for decision variables.

Symbol	Definition
$A T_{i (or j)}^{p}$	Actual passing time of flight i (or j) at waypoint p
$A L T_{i (or j)}$	Actual landing time for flight i (or takeoff time for flight j)
$x_{i (or j)}^{r}$	Binary variable: 1 if flight i (or j) selects route r; otherwise 0
$α_{i_{1} i_{2} (or j_{1} j_{2})}^{p}$	Binary variable: 1 if flight i₁ (or j₁) passes waypoint p earlier than flight i₂ (or j₂) on route r; otherwise 0
$z_{i_{1} i_{2} (or j_{1} j_{2})}$	Binary variable: 1 if flight i₁ lands before flight i₂ (or flight j₁ takes off before flight j₂); otherwise 0
$γ_{i}^{w}$	Binary variable: 1 if flight i lands on runway r; otherwise 0

Table 4

Major airports name of Yangtze River Delta Airport Metroplex.

Airport Identifier	Airport Name
NKG	Nanjing Lukou
SHA	Shanghai Hongqiao
PVG	Shanghai Pudong
WUX	Wuxi Shuofang
HGH	Hangzhou Xiaoshan
NGB	Ningbo Lishe

Appendix A

The constraint conditions of MWRHC are shown in Table A1.

Table A1

Constraint Conditions of MWRHC.

Constraints	No.
$\sum_{r \in R_{i}} x_{i}^{r} = 1, \forall i \in F$	(1)
$A T_{i}^{w} - M (1 - x_{i}^{r}) \leq A L T_{i} \leq A T_{i}^{w} + M (1 - x_{i}^{r}), \forall i \in F^{in}; r \in P_{r} \cap W_{a}^{Arr}$	(2)
$A T_{j}^{w} - M (1 - x_{j}^{r}) \leq A L T_{j} \leq A T_{j}^{w} + M (1 - x_{j}^{r}), \forall j \in F^{out}; r \in P_{r} \cap W_{b}^{Dep}$	(3)
$A T_{i}^{p_{d}^{end}} - A T_{i}^{p_{d}^{start}} \geq T_{d}^{\min}, \forall i \in F, r \in R_{i}, d \in D_{r}$	(4)
$A T_{i}^{p} = T_{i}^{inwaypoint}, \forall i \in F^{in}; p = R_{i} [0] (first point in R_{i})$	(5)
$A T_{j}^{p} \geq T_{j}^{pullout}, \forall j \in F^{out}; p = R_{i} [0] (first point in R_{j})$	(6)
$z_{i_{1} i_{2}} + z_{i_{2} i_{1}} = 1, \forall i_{1} \neq i_{2} \in F^{in}$	(7)
$z_{j_{1} j_{2}} + z_{j_{2} j_{1}} = 1, \forall j_{1} \neq j_{2} \in F^{out}$	(8)
$A T_{i_{2}}^{p} - A T_{i_{1}}^{p} \geq S^{R} - M \cdot (1 - α_{i_{1} i_{2}}^{p}), \forall i_{1}, i_{2} \in F; p \in P$	(9)
$A L T_{i_{2}} - A L T_{i_{1}} \geq S_{i_{1} i_{2}} \cdot γ_{i_{1}}^{w} γ_{i_{2}}^{w} - M \cdot (1 - z_{i_{1} i_{2}}), \forall i_{1} \neq i_{2} \in F^{in}; w \in W_{a}^{Arr}$	(10)
$A L T_{i_{2}} - A L T_{i_{1}} \geq s_{i_{1} i_{2}} \cdot (1 - γ_{i_{1}}^{w} γ_{i_{2}}^{w}) - M \cdot (1 - z_{i_{1} i_{2}}), \forall i_{1} \neq i_{2} \in F^{in}; w \in W_{a}^{Arr}$	(11)
$A L T_{j_{2}} - A L T_{j_{1}} \geq S_{j_{1} j_{2}} \cdot γ_{j_{1}}^{w} γ_{j_{2}}^{w} - M \cdot (1 - z_{j_{1} j_{2}}), \forall j_{1} \neq j_{2} \in F^{out}; w \in W_{b}^{Dep}$	(12)
$A L T_{j_{2}} - A L T_{j_{1}} \geq s_{j_{1} j_{2}} \cdot (1 - γ_{j_{1}}^{w} γ_{j_{2}}^{w}) - M \cdot (1 - z_{j_{1} j_{2}}), \forall j_{1} \neq j_{2} \in F^{out}; w \in W_{b}^{Dep}$	(13)
$α_{i_{1} i_{2}}^{p} + α_{i_{2} i_{1}}^{p} \leq 2 - x_{i_{1}}^{r} - x_{i_{2}}^{s}, \forall i_{1} \neq i_{2} \in F^{in}; \forall r \in R_{i_{1}}; \forall s \in R_{i_{2}}; \forall p \in P - P_{r} \cap P_{s}$	(14)
$α_{j_{1} j_{2}}^{p} + α_{j_{2} j_{1}}^{p} \leq 2 - x_{j_{1}}^{r} - x_{j_{2}}^{s}, \forall j_{1} \neq j_{2} \in F^{o u t}; \forall r \in R_{j_{1}}; \forall s \in R_{j_{2}}; \forall p \in P - P_{r} \cap P_{s}$	(15)
$x_{i_{1}}^{r} + x_{i_{2}}^{s} - 1 \leq α_{i_{1} i_{2}}^{p} + α_{i_{2} i_{1}}^{p} \leq, \forall i_{1} \neq i_{2} \in F^{in}; \forall r \in R_{i_{1}}; \forall s \in R_{i_{2}}; \forall p \in P_{r} \cap P_{s}$	(16)
$x_{j_{1}}^{r} + x_{j_{2}}^{s} - 1 \leq α_{j_{1} j_{2}}^{p} + α_{j_{2} j_{1}}^{p} \leq, \forall j_{1} \neq j_{2} \in F^{out}; \forall r \in R_{j_{1}}; \forall s \in R_{j_{2}}; \forall p \in P_{r} \cap P_{s}$	(17)
$\sum_{w \in W_{a}} α_{i_{1} i_{2}}^{w} \leq z_{i_{1} i_{2}}, \forall i_{1} \neq i_{2} \in F^{in}$	(18)
$\sum_{w \in W_{b}} α_{j_{1} j_{2}}^{w} \leq z_{j_{1} j_{2}}, \forall j_{1} \neq j_{2} \in F^{out}$	(19)
$\max_dep_time \geq A T_{j}^{p}, \forall j \in F^{out}; p = R_{i} [- 1] (last point in R_{i})$	(20)

Appendix B

The available routes information for arrival/departure flights in YRD Airport Metroplex are presented in Table A2, Table A3, Table A4 and Table A5.

Table A2

Available routes for arrival flights in YRD Airport Metroplex.

Landing Airport	Route No.
NKG	A-03, A-09, A-13, A-21, A-30, A-35
SHA	A-06, A-14, A-28, A-33
PVG	A-04, A-05, A-10, A-11, A-18, A-19, A-22, A-23, A-26, A-27, A-31, A-32
WUX	A-07, A-15, A-24, A-34
HGH	A-01, A-08, A-16, A-20, A-29
NGB	A-02, A-12, A-17, A-25

Table A3

Available routes for departure flights in YRD Airport Metroplex.

Departure Airport	Route No.
NKG	D-01, D-03, D-08, D-26, D-27, D-33
SHA	D-04, D-10, D-18, D-29
PVG	D-05, D-07, D-11, D-12, D-13, D-16, D-19, D-22, D-23, D-24, D-30, D-31
WUX	D-02, D-09, D-17, D-28
HGH	D-06, D-14, D-20, D-32
NGB	D-15, D-21, D-25

Table A4

Available routes for arrival flights corresponds to the route number and waypoint.

Start Point	Route No.	Waypoints
A _ IN _ 1	A-01	A _in_ 1, M_io_1_H, NKG_arr
	A-02	A _in_ 1, M_io_1_H, M_io_4_H, SHA_arr
	A-03	A _in_ 1, M_io_1_H, M_io_4_H, PVG_arr1
	A-04	A _in_ 1, M_io_1_H, M_io_4_H, PVG_arr2
	A-05	A _in_ 1, M_io_1_H, M_io_4_L, WUX_arr
	A-06	A _in_ 1, M_io_1_H, M_io_8, HGH_arr
	A-07	A _in_ 1, M_io_1_H, M_io_8, NGB_arr
A _ IN _ 2	A-08	A _in_ 2, M_io_2_H, NKG_arr
	A-09	A _in_ 2, M_io_3_H, M_io_4_H, PVG_arr1
	A-10	A _in_ 2, M_io_3_H, M_io_4_H, PVG_arr2
	A-11	A _in_ 2, M_io_2_H, M_io_8, M_io_7, HGH_arr
A _ IN _ 3	A-12	A _in_ 3, M_io_2_L, NKG_arr
	A-13	A _in_ 3, M_io_3_H, M_io_4_H, SHA_arr
	A-14	A _in_ 3, M_io_3_H, M_io_4_L, WUX_arr
	A-15	A _in_ 3, M_io_3_H, M_io_4_H, M_io_6_L, NGB_arr
A _ IN _ 4	A-16	A _in_ 4, A_mid_1, PVG_arr1
	A-17	A _in_ 4, A_mid_1, PVG_arr2
	A-18	A _in_ 4, M_io_5, M_io_6_L, HGH_arr
	A-19	A _in_ 4, A_mid_1, A_mid_2, M_io_6_L, NGB_arr
A _ IN _ 5	A-20	A _in_ 5, M_io_10, M_io_4_H, NKG_arr
	A-21	A _in_ 5, PVG_arr1
	A-22	A _in_ 5, PVG_arr2
	A-23	A _in_ 5, M_io_10, WUX_arr
	A-24	A _in_ 5, A_mid_2, M_io_6_L, HGH_arr
A _ IN _ 6	A-25	A _in_ 6, M_io_6_L, SHA_arr
	A-26	A _in_ 6, A_mid_2, PVG_arr1
	A-27	A _in_ 6, A_mid_2, PVG_arr2
	A-28	A _in_ 6, NGB_arr
A _ IN _ 7	A-29	A _in_ 7, M_io_8, NKG_arr
	A-30	A _in_ 7, M_io_6_L, SHA_arr
	A-31	A _in_ 7, A_mid_2, PVG_arr1
	A-32	A _in_ 7, A_mid_2, PVG_arr2
	A-33	A _in_ 7, M_io_8, WUX_arr
	A-34	A _in_ 7, HGH_arr
A _ IN _ 8	A-35	A _in_ 8, NKG_arr

Table A5

Available routes for departure flights corresponds to the route number and waypoint.

End Point	Route No.	Waypoints
D _ OUT _ 1	D-01	NKG_dep, M_io_1_L, D _out_ 1
	D-02	WUX_dep, M_io_4_L, M_io_1_L, D _out_ 1
D _ OUT _ 2	D-03	NKG_dep, M_io_1_L, D _out_ 2
	D-04	SHA_dep, D_mid_1, M_io_3_L, M_io_2_H, D _out_ 2
	D-05	PVG_dep1, D_mid_1, M_io_3_L, M_io_2_H, D _out_ 2
	D-06	PVG_dep2, D_mid_1, M_io_3_L, M_io_2_H, D _out_ 2
	D-07	HGH_dep, M_io_7, M_io_2_H, D _out_ 2
D _ OUT _ 3	D-08	NKG_dep, M_io_2_L, D _out_ 3
	D-09	WUX_dep, M_io_4_L, M_io_3_L, D _out_ 3
D _ OUT _ 4	D-10	SHA_dep, D_mid_1, D _out_ 4
	D-11	PVG_dep1, D_mid_1, D _out_ 4
	D-12	PVG_dep2, D_mid_1, D _out_ 4
D _ OUT _ 5	D-13	PVG_dep1, D _out_ 5
	D-14	PVG_dep2, D _out_ 5
	D-15	HGH_dep, M_io_6_L, M_io_5, D _out_ 5
	D-16	NGB_dep, M_io_6_L, D _out_ 5
D _ OUT _ 6	D-17	SHA_dep, D _out_ 6
	D-18	PVG_dep1, D_mid_2, D _out_ 6
	D-19	PVG_dep2, D_mid_2, D _out_ 6
	D-20	WUX_dep, M_io_10, D_mid_2, D _out_ 6
	D-21	HGH_dep, M_io_6_L, D_mid_2, D _out_ 6
	D-22	NGB_dep, D _out_ 6
D _ OUT _ 7	D-23	PVG_dep1, D_mid_2, D _out_ 7
	D-24	PVG_dep2, D_mid_2, D _out_ 7
D _ OUT _ 8	D-25	NGB_dep, D _out_ 8
D _ OUT _ 9	D-26	NKG_dep, M_io_8, D _out_ 9
	D-27	NKG_dep, M_io_8, M_io_7, D _out_ 9
	D-28	SHA_dep, M_io_7, D _out_ 9
	D-29	PVG_dep1, M_io_7, D _out_ 9
	D-30	PVG_dep2, M_io_7, D _out_ 9
	D-31	WUX_dep, M_io_8, D _out_ 9
D _ OUT _ 10	D-32	HGH_dep, D _out_ 10
D _ OUT _ 11	D-33	NKG_dep, M_io_1_L, D _out_ 11

References

1. Ren, L.B.; Clarke, J.P.; Schleicher, D.; Timar, S.; Saraf, A.; Crisp, D.; Gutterud, R.; Lewis, T.; Thompson, T. Contrast and Comparison of Metroplex Operations: An Air Traffic Management Study of Atlanta, Los Angeles, New York, and Miami. Proceedings of the 9th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference; Hilton Head, SC, USA, 21–23 September 2009.

2. Ma, Y.; Hu, M.; Zhang, H.; Yin, J.; Wu, F. Optimized Method for Collaborative Arrival Sequencing and Scheduling in Metroplex Terminal Area. Acta Aeronaut. Astronaut. Sin.; 2015; 36, pp. 2279-2290.

3. Wang, L.; Gu, Q. Arrival and Departing Aircraft-Sequencing Optimization under the Special Circumstances. J. Transp. Syst. Eng. Inf. Technol.; 2014; 14, pp. 102-107.

4. Sidiropoulos, S.; Majumdar, A.; Han, K.; Schuster, W.; Ochieng, W.Y. A Framework for the Classification and Prioritization of Arrival and Departure Routes in Multi-Airport Systems Terminal Manoeuvring Areas. Proceedings of the 15th AIAA Aviation Technology, Integration, and Operations Conference; Dallas, TX, USA, 22–26 June 2015.

5.ICAO Doc 4444 International Civil Aviation Organization Procedures for Air Navigation Services–Air Traffic Management (PANS-ATM); ICAO: Montreal, QC, Canada, 2023.

6. Zhang, J.; Ge, T.; Zheng, Z. Collaborative Arrival and Departure Sequencing for Multi-Airport Terminal Area. J. Transp. Syst. Eng. Inf. Technol.; 2017; 17, pp. 197-204.

7. Wang, Z.; Wu, Y. Collaborative Aircraft Scheduling Strategy in Metroplex Terminal Area Based on FS-MOPSO. J. Southwest Jiaotong Univ.; 2017; 52, pp. 179-185.

8. Zhang, Z.; Wang, D. Research on Flow Allocation Strategy Based on Capacity Matching for Airport Group. Mod. Electron. Tech.; 2019; 42, pp. 113-116+120.

9. Yin, J.; Ma, Y.; Tian, W.; Chen, D.; Hu, Y.; Ochieng, W. Impact Analysis of Demand Management on Runway Configuration in Metroplex Airports. IEEE Access; 2020; 8, pp. 66189-66212. [DOI: https://dx.doi.org/10.1109/ACCESS.2020.2985288]

10. Wang, L.; Lin, Y. Aircraft Sequencing Modeling and Algorithm for Shared Waypoints in Airport Group. J. Transp. Inf. Saf.; 2021; 39, pp. 93-99+136.

11. Jiang, F.; Zhang, Z. Optimal Sequencing of Arrival Flights at Metroplex Airports: A Study on Shared Waypoints Based on Path Selection and Rolling Horizon Control. Aerospace; 2023; 10, 881. [DOI: https://dx.doi.org/10.3390/aerospace10100881]

12. Le, M.; Wu, X.; Hu, Y. Arrival Flights Optimal Sequencing Based on Path Selection and Rolling Horizon Control. J. Beijing Univ. Aeronaut. Astronaut.; 2022; 49, pp. 3222-3322. [DOI: https://dx.doi.org/10.13700/j.bh.1001-5965.2022.0120]

13. Ji, Y.; Yu, F.; Shen, D.; Peng, Y. Research on Congestion Situation Relief in Terminal Area Based on Flight Path Adjustment. Aerospace; 2025; 12, 856. [DOI: https://dx.doi.org/10.3390/aerospace12100856]

14. Zeng, X.; Chu, X.; Yao, R.; Liu, J.; Yang, Y.; Zeng, W. An Emergency Rescue Reconnaissance UAV Nest Site Selection Method Considering Regional Differentiated Coverage and Rescue Satisfaction. Aerospace; 2025; 12, 798. [DOI: https://dx.doi.org/10.3390/aerospace12090798]

15. Faye, A. Solving the Aircraft Landing Problem with time discretization approach. Eur. J. Oper. Res.; 2015; 242, pp. 1028-1038. [DOI: https://dx.doi.org/10.1016/j.ejor.2014.10.064]

16. Pawełek, A.; Lichota, P.; Dalmau, R.; Prats, X. Fuel-Efficient Trajectories Traffic Synchronization. J. Aircr.; 2019; 56, pp. 481-492. [DOI: https://dx.doi.org/10.2514/1.C034730]

17. Pawełek, A.; Lichota, P. Arrival air traffic separations assessment using Maximum Likelihood Estimation and Fisher Information Matrix. Proceedings of the 2019 20th International Carpathian Control Conference (ICCC); Krakow, Poland, 26–29 May 2019; pp. 1-6.

© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.

Comparative Analysis of Scenario-Adaptive Control Algorithms for Arrival and Departure Operations in Multi-Airport Systems

Content area