Integrated development and operational collaboration of regional airport groups have the potential to improve capacity and safety and also reduce environmental impacts and operational costs. However, research in multiairport systems (MASs), especially in China, is still in its infancy, with the consequences of unbalanced development, inadequate coordination, unclear function partitioning, difficulty in air traffic management, and poor service quality of regional airports. Considering these characteristics influencing effective interaction and collaboration of regional airports, this paper formulates a model to optimize the flight schedules in the MAS with multiple objectives of minimizing the maximum displacement of all flights, the weighted sum of total flight adjustment of each airport, and flight delays. An improved simulated annealing algorithm (SAA) is designed to solve the proposed multiobjective optimization problem. The model is applied to a case of the Beijing-Tianjin-Hebei Airport Group. The computational results demonstrate that the model generates significant reductions in maximum displacement, average displacement, and average delay, compared to the First-Come-First-Served (FCFS) principle. The model proposed in this paper can be used by civil aviation authorities, air navigation service providers, and airlines to facilitate the integrated management of flight schedules in the MAS.
In order to improve the integrated development and operation of a group of airports in a multiairport system, the allocation of achievable flight resources should be fully optimized to significantly reduce congestion and delays. In a multiairport system, the relevant airports work together in a collaborative way towards their common goals. To date, research has focused on optimizing flight time resources at the tactical level. However, delivering real change in resolving congestion and delay requires the consideration of strategic level of operations, through optimizing the flight schedules.
Recently, the problem of flight scheduling and demand management has attracted considerable attention. Several studies focus on slot allocation based on market-based mechanisms such as congestion pricing and slot auctions [
The existing studies above are limited as they only consider adjusting the demands through flight schedules, while ignoring the interaction of several airports in a region that compete for limited airspace resources. The former is addressed by [
The optimization of flight allocation has been widely studied through various operation research approaches. Unfortunately, most of the corresponding models are formulated as a single-objective optimization which mainly focuses on minimizing flight delay [
When optimizing flight schedule, the first thing is to comply with the safety requirements and relevant operational regulations. All aircraft’s takeoff and landing times must be assigned as soon as possible to achieve optimal allocation of airspace and runway resources and minimal total delay time of TMA departures and arrivals. Besides, a scheduling scheme must be set without extra workload on air traffic controllers. In addition, the system should facilitate a flight to land at the most economic speed, minimizing the total fuel cost resulting from deviation of aircraft start-times from respective ready-times. The scheduling should be generated to facilitate the required arrival within a TMA as a flight can be delayed by waiting at holding points, speed control, and maneuver operation. In a word, the current optimization of a single airport flight schedule without the consideration of the other proximate airports in a multiairport system is suboptimal. To solve this problem, this paper develops a framework for the optimization of the operation of multiairport systems. The contributions of this paper are summarized as follows: we formulate a model to optimize the flight schedules in multiairport systems with the objectives of minimizing the maximum displacement of all flights, the weighted sum of total flight adjustment of each airport, and flight delays. An improved simulated annealing algorithm (SAA) is designed to solve the proposed multiobjective optimization problem. The model is applied to the case of the Beijing-Tianjin-Hebei Airport Group. The results demonstrate that the model generates significant reductions in maximum displacement, average displacement, and average delay, compared to the First-Come-First-Served (FCFS) principle.
The paper is structured as follows. In Section
Consider a set of flights
Notations
Notations | Explanation |
---|---|
The set of waypoints, | |
The set of flights in airport | |
The set of flights which go through the waypoint | |
The slot adjustment for flight | |
The delay of flight | |
The weight of airport | |
The total number of flights. | |
The minimum turn-around times for connecting flights | |
The maximum turn-around times for connecting flights | |
The immediate successor departure flight of arrival flight | |
The capacity of airport | |
The capacity of waypoint | |
The maximum flight adjustment in the MAS. | |
The total flight adjustments in the MAS. | |
The capacity of airport | |
The service rate of arrival and departure of airport |
The flight scheduling problem in a multiairport system involves different objectives from different perspectives that consider, for example, displacement of flight adjustment and flight delay. In this paper, we seek to balance a number of optimization objectives including the maximum displacement of all flights, weighted sum of total flight adjustment of each airport in the multiairport system, and the average flight delay in the multiairport system. The optimization model of flight scheduling in the MAS is presented as follows:
The first objective function (i.e., the first part in equation (
The constraints in equations (
To address the limitations of existing approaches discussed in Section
The SAA is a random optimization algorithm based on the Monte Carlo iterative solution strategy and is an extension of the local search algorithm. Specifically, it is a metaheuristic algorithm to approximate global optimization in a large search space for an optimization problem. The starting point is the similarity between the annealing process of solid substances and general combinatorial optimization problems. By simulating the solid annealing process, starting from a certain initial temperature, as the temperature decreases, the optimal solution is searched in the solution space in combination with the probability jump characteristic tending to a global optimal. It uses the Metropolis-Hastings acceptance criteria and controls the algorithmic process with a set of parameters called a cooling schedule.
The parameters of this model are set as follows: Initial optimization sequence Optimal objective function value at each temperature: total delay = optimization ( Initial global optimal objective function value total delay = optimization_value. Initial optimized scheduling time: Initial temperature: temperature ( Optimization times at the same temperature: iter = 10 + round ((1 – ((0.95)^ Initial value of repeat number: Initialize weight Execute expression ( Start time = now.
Based on the description above, the SAA implementation framework is presented in Figure
SAA iterative procedure.
WHILE temperature ( FOR Calculate Δ IF Δ Optimization ( Δ IF Δ opt_ optimization_value = optimization_value ( END ELSEIF exp(−ΔF/temperature ( optim_ END END FOR endtime1 = now; epstime1 = (endtime1 − starttime) IF epstime1 > 160 break; END temperature(l) = temperature ( IF temperature(l)<(temperature(1) temperature(l) = temperature(l) END END WHILE
FCFS is a type of service rules used in the Chinese air traffic management center, and it provides an efficient, simple, and error-free process scheduling algorithm that saves valuable computational resources [
In this paper, we conduct a case study of flight scheduling in the multiairport system of the Beijing-Tianjin-Hebei Airport Group, which includes three major airports: Beijing Capital International Airport (PEK), Tianjin Binhai International Airport (TSN), and Shijiazhuang Zhengding International Airport (SJW).
The airspace resource in the region when used individually by airports does not meet the traffic demand, causing severe congestion. One-day flight plan data in this airport group are selected for analysis in the case study. In the above regional airspace, capacity is limited with a few way points. These waypoints result in severe levels of airspace congestion in this multiairport system. Table
Basic information of the Beijing-Tianjin-Hebei Airport Group.
Airport | Runway quantity | Hour capacity | Terminal area (kilo square meters) | Number of aircraft movements in 2018 | 2018 handing capacity | |
---|---|---|---|---|---|---|
Passenger throughput (kilo person-time) | Cargo handling capacity (kilo ton) | |||||
PEK | 3 | 88 | 1414 | 614022 | 100,983 | 2074 |
TSN | 2 | 34 | 364 | 179414 | 23,591 | 258 |
SJW | 1 | 20 | 5.5 | 89717 | 11,333 | 46 |
This section presents and discusses the computational results from the FCFS and SAA methods. First, we illustrate the result of FCFS, and then the result of the SAA is produced with the same weight settings,
The computational results of max. displacement, average displacement, and average delay with the FCFS and SAA methods are illustrated in Tables
Computational results with the FCFS method.
Max. displacement (min) | Average displacement (min) | Average delay (min) |
---|---|---|
19.42 | 11.06 | 24.06 |
Computational results with the SAA method.
Max. displacement (min) | Average displacement (min) | Average delay (min) |
---|---|---|
17.40 | 10.06 | 20.06 |
From the results of the FCFS and SAA methods with equal weights in Tables
When simulated annealing is applied to solve the multiobjective optimization of takeoff and landing problem, the weights of each objective will have a strong influence on the optimization results, which are shown in Table
Computational results with different weight settings.
Instance no. | Weight setting | Max. displacement (min) | Average displacement (min) | Average delay (min) |
---|---|---|---|---|
1 | 17.40 | 10.06 | 20.06 | |
2 | 12.46 | 28.15 | ||
3 | 19.22 | 27.36 | ||
4 | 21.30 | 19.78 |
We can see from Table
Due to the characteristics of the heuristic algorithm, the simulated annealing algorithm has a challenging task to get the optimal solution by merely running once, even with appropriate parameter settings. Therefore, it is recommended to conduct multiple experiments and get the results with different weights. The evaluation method proposed in this paper can be employed to select the result which best satisfies the interests of multiple stakeholders in air transportation industry.
The limitation of our method is the sensitivity to the weights in making trade-offs among different parts of the objective function, while ignoring the flexible trade-off among different optimization objectives. We will address this limitation in future research.
This paper proposes a framework for flight schedule optimization in multiairport systems at the strategic level, while enforcing a set of constraints and an objective function with three different parts. We design an improved SAA to seek for the Pareto-optimal solutions of this computationally challenging problem, which can make trade-offs amongst three parts of the optimization objectives of the model, including the maximum displacement of all flights, weighted sum of total flight adjustment of each airport in the multiairport system, and the average flight delay in the multiairport system.
The method is applied to the Beijing-Tianjin-Hebei multiairport system, with the results showing that, compared with the classical FCFS as the baseline strategy, our optimized SAA strategy can improve the operation performance in the MAS. Improvements have been achieved in the efficiency of flight schedule, which leads to the realization of the full functionality of the international airport hub of PEK. In summary, the multiairport system schedule optimization model and algorithm can be applied to optimize flight schedule, which can significantly alleviate the congestion and delay problems in the multiple airport systems.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
This work was supported by the National Natural Science Foundation of China (grant nos. 71731001 and 61671237).