^{1}

Aiming at the phenomenon of a large number of flight delays in the terminal area makes a reasonable scheduling for the approach and departure flights, which will minimize flight delay losses and improve runway utilization. This paper considered factors such as operating conditions and safety interval of multi runways; the maximum throughput and minimum flight delay losses as well as robustness were taken as objective functions; the model of optimization scheduling of approach and departure flights was established. Finally, the genetic algorithm was introduced to solve the model. The results showed that, in the program whose advance is not counted as a loss, its runway throughput is improved by 18.4%, the delay losses are reduced by 85.8%, and the robustness is increased by 20% compared with the results of FCFS (first come first served) algorithm, while, compared with the program whose advance is counted as a loss, the runway throughput is improved by 15.16%, flight delay losses are decreased by 75.64%, and the robustness is also increased by 20%. The algorithm can improve the efficiency and reduce delay losses effectively and reduce the workload of controllers, thereby improving economic results.

Flight delay is one of the problems to restrict the development of the world aviation industry and also the main source for the airline passengers’ dissatisfaction with the service. At present, countries around the world have taken various measures to reduce flight delay; many airports in our country improve capacity by increasing the number of runways and other methods, thereby alleviating the flight delay. Because the airport runways are the resources of the air traffic system, within a certain time, making good use of runway resources can effectively alleviate the flight delay. In addition, the approach and departure flight scheduling of terminal area also plays an important role in reducing the flight delay, so reasonable scheduling of flights has an influence on ensuring flight safety, improving resource utilization, and reducing the loss of delay as well as improving airline credibility and so forth. In our country, FCFS (first come first served) was used for aircraft terminal controllers to make a sorting for the arrival aircraft. While the fact shows that FCFS is not the best strategy to maximize the use of existing airport capacity so is reducing the average delay losses [

Starting in early twentieth Century, domestic and foreign scholars have launched the research on scheduling flight optimization problem. Dear and Sherif proposed a methodology for sequencing and scheduling of aircraft in high density terminal areas. Termed constrained position shifting (CPS), this methodology was examined and its effectiveness was tested. Potential capacity improvements were noted over the first-come, first-served, runway (FCFS-RW) strategy, especially during peak periods [

Compared to other developed countries, the research of air traffic flow management started late in China. Ye and Tao established a dynamic model of the aircraft sequencing in terminal area and dynamic scheduling which was based on genetic algorithm and made a reasonable arrangement for the flight landing sequence, thereby improving the runway utilization, reducing flight delay losses [

Although the scholars had done a lot of research on flights sorting optimization methods, still they had disadvantages. For example, some models were established in the ideal situations and did not take into account the actual situation of the weather, air traffic control, airport surrounding environment, and so forth. Moreover most models were for single runway, rather than the multirunways, and did not meet with the trend of current development of the airport.In addition, the problem of taking off and landing of flight scheduling on multirunways is more complex with the increasement of runways, and the influence of human factors will be deepened. So it is needed to further improve the algorithm, so as to run closer to the real-time control. Considering the weather, air traffic control, route and other factors, the model was established in this paper to make optimization of approach and departure flight scheduling. The model was solved by genetic algorithm, thus improving the runway throughput and reducing flight delay losses. At last, the economic benefit of the airlines is improved.

Robust optimization solution is obtained in every possible case (but the probability is unknown in each case). It is the solution which is with small deviation from the optimal solution. For different problems, the robust optimization methods are also different. In order to solve the robust optimization problem in this paper, make use of the advantage of genetic algorithm, combine with the robustness, and find out the flight sequence with minimal changes, then make simulation. This method is proved to be correct.

In recent years, with the rapid development of China’s civil aviation, busy airport passenger throughput increased significantly, resulting in the aviation market demand for sustained growth and the increasement of flight traffic, coming with it is the problem of flight delay, and,thus, leading to the dissatisfaction of passengers, or even making a confliction. Therefore, considering a variety of factors, such as weather, traffic control, air traffic control, route, and other restrictions, make a reasonable scheduling of approach and departure flights under the premise of ensuring safety, which will minimize the flight delay and alleviate the dissatisfaction of passengers caused by flight delay.

Air traffic controllers make a reasonable allocation of the approach and departure flights waiting in the queue. Distribute taxiways and runways for the incoming flights to make them a smooth landing, reaching the apron safely; while for the departure flights, arrange appropriate taxiways and runways, making it leave the airport safely and smoothly take off. Approach and departure flights schematic is showed in Figure

Simple diagram of approach and departure flights.

Flight sorting is a dynamic continuous process. It is needed to make corresponding adjustments according to the change of real-time information. Assume that there are a lot of flights coming into the terminal area, waiting for the traffic controllers to make arrangements for them. It is required that meeting the restrictions of minimum safety interval among aircraft, arranging the order of flights, thus minimizing the time of the completion of approach and departure flights scheduling.

The robust optimization method of approach and departure flight scheduling is studied in this paper, which assumes the following:

there are

the estimated time and actual time of each flight are not the same and they can be determined at the time 0;

the airport studied in this paper contains multiple parallel runways, and each of them meets independent operation standards;

the information of approach and departure flight (including flight number, flight model, and the estimated arriving time of flights) is known;

the capacity of the airport meets the assumption. That is the number of flight and the time distributed within the range of airport capacity licensing;

the approach flights do not delay when they take-off at the departure airport, and arrive on time at the terminal area waiting for landing.

: is the collection of approach flights,

Suppose that the actual scheduling time of the first flight on the runway

The objective function of the maximum throughput of the runway is

Taking into account the actual situation, in most cases, either the approach or departure flights, the actual arrival time is almost impossible to be consistent with the estimated time, so we make the following provision. The following two situations are not treated as delay:

The delay time of the flight

Suppose that there are

That is,

The objective of robustness can be achieved by adjusting the minimal flight sorties, that is, it is needed to try to make the flight schedule time consistent with the estimated time, So that, the smaller adjustments, the better robustness. Meanwhile, reduce the workload of controllers.

Therefore, the objective function robustness can be measured by the number of flights which the schedule time is not the same as the estimated time; the smaller the robustness the better.

We introduce variables 0, 1:

Equation (

Equation (

Equations (

Equation (

Equation (

Equation (

Equation (

For the mixed types of aircraft, the International Civil Aviation Organization (ICAO) specifies the minimal interval standards, denoted as

The wake separation of various types of aircraft.

Types of aircraft | Tailing | ||||||
---|---|---|---|---|---|---|---|

Minimum distance interval/km | Minimum time interval/s | ||||||

S | L | H | S | L | H | ||

Leading | S | 3 | 3 | 3 | 98 | 74 | 74 |

L | 4 | 3 | 3 | 138 | 74 | 74 | |

H | 6 | 5 | 4 | 167 | 114 | 94 |

The basic idea of the genetic algorithm is to simulate the natural process of genetic mechanism and biological evolution that form a process to search for the optimal solution. The characteristic of it is that the treatment objects of it are the parameters of the code collection rather than the problem parameters themselves. Besides, its searching process is not influenced by the constraint of connection of the optimization functions, also the optimization functions do not need to be differentiable. Therefore it has better ability of searching [

According to the real characteristic of the flight scheduling problem, in this paper, real-coded schema is adopted, that is, the digital serial number encoding. Every flight queue is a chromosome, and each flight

The fitness function is also known as the evaluation function. It is a symbol to judge the individual is good or bad based on the objective functions. It is also the driving force of the evolution process. Because the fitness function is always nonnegative, so under any circumstances hoping its value the bigger the better.

Real-coded schema is used in this paper, so by using the sorting method according to performance degree to determine its fitness [

Make genetic operations of selection, crossover, and mutation of individual to produce more new individuals in the genetic algorithm. Although with the evolution of populations, it will produce more and more excellent individuals, because selection, crossover, mutation, and other operations are random, so it may also destroy the current individual with the best fitness. In order to choose the best to retain to the next generation, using the optimal preservation strategy to make elimination or survival; namely, the individual with best fitness does not involve in the operation of crossover and mutation, instead of replacing the individual with the worst fitness produced by crossover and mutation in the population.

The roulette selection operator is used in this paper; namely, the probability of the fitness in proportion decides the possibility of its descendants going or staying. If a certain individual is

For

In the process of crossover, the runway of the flight does not make chiasma but allocates runways randomly to the new fight queue after chiasma. That is allocating multirunways for

Suppose that

In Equation (

The process of the algorithm is showed in Figure

The flowchart of genetic algorithm.

Determine the genetic strategy, including population size

Define fitness function

Generate initialization population

Calculate the objective functions of the chromosome which is corresponding with flight queue;

Calculate the fitness value of the individuals in the population, as shown in (

Find the best individual in the population under the current conditions;

Making a judgment of whether the evolution algebra meets the condition of smaller than the maximal algebra. If it is, algebra plus 1, then keep it in order. If it is not, turn to the Step

Make crossover operation of the chromosome by Single-point crossover mapping method; make mutation operation of the chromosome by uniform mutation method, as shown in (

Execute Step

Assess the effects of the genetic algorithm;

Output the optimal function value then get the optimized flight sequence.

The constraints involved in the model are more and complicated, so they need to be processed. For the constraints such as

As for

According to the standard of the International Civil Aviation Organization (ICAO), the aircraft is divided into 3 categories in accordance with the wake intensity. The study showed that the unit time delay losses of the approach flight are larger than those of the departure flight. The operating costs are showed in Table

Operating costs of various types of aircraft.

Types of aircraft | Types of wake | Maximum take-off weight/ |
Approach delay cost/(yuan*s^{−1}) |
Departure delay cost/(yuan*s^{−1}) |
---|---|---|---|---|

H | Heavy | >136 | 60 | 4 |

M | Medium | 7~136 | 40 | 2 |

L | Light | <7 | 20 | 1 |

30 flight data of a continuous period base on Chengdu Shuangliu International Airport. There are 15 approach flights and 15 departure flights, 2 mutually independent parallel runway.

The initial data of departure flights.

Airline | Sequence number | Flight number | Type | Unit time delay loss | Estimated departure time | Actual departure time | Runway | Delay Losses |
---|---|---|---|---|---|---|---|---|

CCA | 1 | CA4441 | H | 4 | 0:00:00 | 0:00:00 | 1 | 0 |

CSC | 2 | 3U8701 | M | 2.1 | 0:00:00 | 0:02:00 | 0 | 0 |

CSC | 3 | 3U8773 | M | 2.1 | 0:00:00 | 0:03:54 | 0 | 239.4 |

CCA | 4 | CA4253 | L | 1.1 | 0:00:00 | 0:10:00 | 0 | 528 |

CES | 5 | MU5437 | M | 2.2 | 0:00:00 | 0:08:00 | 1 | 1056 |

CSZ | 6 | ZH4391 | M | 2.3 | 0:05:00 | 0:09:41 | 1 | 370.3 |

CSC | 7 | 3U8961 | H | 4.2 | 0:05:00 | 0:12:37 | 1 | 1415.4 |

CCA | 8 | CA4401 | H | 4 | 0:05:00 | 0:13:55 | 0 | 1660 |

CES | 9 | MU2531 | L | 1.2 | 0:05:00 | 0:18:22 | 0 | 818.4 |

CSC | 10 | 3U8671 | M | 2.1 | 0:05:00 | 0:16:01 | 1 | 1136.1 |

CCA | 11 | CA4391 | M | 2.2 | 0:10:00 | 0:20:56 | 0 | 1179.2 |

CCA | 12 | CA3315 | M | 2.1 | 0:10:00 | 0:19:12 | 1 | 907.2 |

CCA | 13 | CA4445 | H | 4 | 0:10:00 | 0:23:04 | 1 | 2656 |

CCA | 14 | CA4519 | L | 1.1 | 0:10:00 | 0:26:17 | 0 | 942.7 |

CSC | 15 | 3U8937 | M | 2.1 | 0:10:00 | 0:25:13 | 1 | 1665.3 |

CCA: Air China; CSC: Sichuan Airlines; CSZ: Shenzhen Airlines; CES: China Eastern; and CHH: Hainan Airlines.

The initial data of approach flights.

Airline | Sequence number | Flight number | Type | Unit time delay loss | Estimated approach time | Actual approach time | Runway | Delay Losses |
---|---|---|---|---|---|---|---|---|

CES | 16 | MU7197 | L | 20.4 | 0:00:00 | 0:06:17 | 0 | 5242.8 |

CCA | 17 | CA4442 | H | 62.7 | 0:01:12 | 0:01:23 | 1 | 0 |

CHH | 18 | HU7141 | M | 42.5 | 0:01:59 | 0:07:59 | 0 | 10200 |

CHH | 19 | HU7147 | L | 23.1 | 0:03:28 | 0:03:59 | 1 | 0 |

CES | 20 | MU5989 | M | 43 | 0:03:21 | 0:11:10 | 0 | 15007 |

CSZ | 21 | ZH1405 | M | 41.3 | 0:04:37 | 0:12:31 | 0 | 14620.2 |

CCA | 22 | CA1405 | H | 62.7 | 0:05:33 | 0:05:54 | 1 | 0 |

CSZ | 23 | ZH1405 | H | 63.1 | 0:07:14 | 0:11:00 | 1 | 6688.6 |

CCA | 24 | CA1405 | L | 21.6 | 0:07:00 | 0:16:36 | 0 | 9849.6 |

CCA | 25 | 3U8896 | M | 43.6 | 0:06:54 | 0:14:26 | 1 | 14475.2 |

CES | 26 | MU5435 | M | 43 | 0:08:08 | 0:19:33 | 0 | 24295 |

CSC | 27 | 3U8886 | M | 42.8 | 0:09:09 | 0:17:43 | 1 | 16863.2 |

CCA | 28 | CA4488 | L | 22.1 | 0:09:55 | 0:21:25 | 1 | 12597 |

CCA | 29 | CA3393 | M | 43.6 | 0:09:24 | 0:22:20 | 0 | 28601.6 |

CSZ | 30 | ZH4402 | H | 63.1 | 0:09:58 | 0:23:48 | 0 | 44801 |

CCA: Air China; CSC: Sichuan Airlines; CSZ: Shenzhen Airlines; CES: China Eastern; and CHH: Hainan Airlines.

Running the above multiobjective genetic algorithm, the crossover probability is 0.9, the mutation probability is 0.1, the generation gap is 0.9, the elimination rate is 0.2, penalty factor

Select 7 schemes after optimization, the sequence results of the flights are as shown in Table

The sequence results of 7 optimized schemes.

Scheme 1 | Scheme 2 | Scheme 3 | Scheme 4 | Scheme 5 | Scheme 6 | Scheme 7 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Runway 0 | Runway 1 | Runway 0 | Runway 1 | Runway 0 | Runway 1 | Runway 0 | Runway 1 | Runway 0 | Runway 1 | Runway 0 | Runway 1 | Runway 0 | Runway 1 |

16 | 20 | 16 | 25 | 16 | 19 | 21 | 16 | 26 | 21 | 16 | 26 | 16 | 29 |

17 | 30 | 27 | 17 | 7 | 20 | 11 | 6 | 5 | 17 | 27 | 20 | 18 | 17 |

1 | 18 | 18 | 22 | 17 | 18 | 27 | 17 | 16 | 3 | 13 | 6 | 30 | 1 |

23 | 25 | 26 | 13 | 27 | 22 | 29 | 25 | 20 | 25 | 18 | 1 | 20 | 26 |

13 | 29 | 20 | 7 | 24 | 21 | 20 | 19 | 27 | 18 | 21 | 17 | 21 | 25 |

24 | 27 | 21 | 30 | 23 | 8 | 26 | 8 | 8 | 22 | 23 | 3 | 2 | 23 |

21 | 2 | 29 | 23 | 28 | 11 | 22 | 23 | 23 | 6 | 7 | 22 | 19 | 22 |

3 | 28 | 15 | 12 | 26 | 25 | 28 | 13 | 29 | 13 | 29 | 8 | 28 | 7 |

19 | 11 | 24 | 3 | 10 | 29 | 3 | 30 | 30 | 28 | 4 | 25 | 13 | 24 |

11 | 26 | 19 | 11 | 4 | 3 | 18 | 7 | 2 | 11 | 19 | 5 | 27 | 12 |

8 | 5 | 2 | 28 | 9 | 30 | 5 | 1 | 15 | 10 | 2 | 30 | 6 | 3 |

22 | 6 | 5 | 14 | 6 | 5 | 14 | 4 | 1 | 12 | 11 | 9 | 8 | 11 |

7 | 4 | 10 | 6 | 2 | 15 | 15 | 2 | 19 | 4 | 14 | 28 | 15 | 5 |

14 | 13 | 8 | 9 | 13 | 12 | 9 | 7 | 24 | 12 | 24 | 14 | 10 | |

15 | 9 | 1 | 1 | 10 | 24 | 14 | 9 | 10 | 15 | 4 | 9 | ||

4 | 14 |

Calculate objective function value of each program, and the results are compared with the FCFS algorithm, as shown in Table

The comparative results of multiobjectives optimization and FCFS.

Scheme | Delay Losses | Runway capacity | Robustness | |||
---|---|---|---|---|---|---|

Losses/yuan | Comparison % | Time of scheduling/s | Comparison % | Percentage of shift % | Comparison % | |

1 | 64391.8 | −70.4 | 1255 | −20.4 | 83.33 | 0 |

2 | 30921.6 | −85.8 | 1287 | −18.4 | 66.67 | −20 |

3 | 31868.5 | −85.3 | 1409 | −10.7 | 63.33 | −24 |

4 | 55697.1 | −74.4 | 1341 | −15.0 | 70 | −16 |

5 | 47914.8 | −78.0 | 1252 | −20.6 | 66.67 | −20 |

6 | 60326.1 | −72.3 | 1214 | −23.0 | 86.67 | 4 |

7 | 29554.9 | −86.4 | 1294 | −17.9 | 70 | −16 |

FCFS | 217815.2 | 1577 | 83.33 |

Here, “−” represents improvement and “+” represents decline.

According to Table

The comparison of FCFS and multiobjectives.

According to the data in the Table

There are three objectives in this paper, namely, minimum delay losses, maximal runway capacity as well as best robustness. Using multiobjectives genetic algorithm to solve the problem, then one can get a group of Pareto- optimal solutions. In this way, the decision makers can choose one of the schemes as the final scheduling program according to their own preferences.

In order to get a better program, design an evaluation function

The flight sorting results of three schemes.

FCFS | Optimization program 1 | Optimization program 2 | |||
---|---|---|---|---|---|

Runway 0 | Runway 1 | Runway 0 | Runway 1 | Runway 0 | Runway 1 |

2 | 1 | 16 | 25 | 16 | 14 |

3 | 17 | 27 | 17 | 21 | 25 |

16 | 19 | 18 | 22 | 30 | 18 |

18 | 22 | 26 | 13 | 6 | 17 |

4 | 5 | 20 | 7 | 20 | 7 |

20 | 6 | 21 | 30 | 1 | 22 |

21 | 23 | 29 | 23 | 29 | 23 |

8 | 7 | 15 | 12 | 26 | 9 |

24 | 25 | 24 | 3 | 12 | 28 |

9 | 10 | 19 | 11 | 27 | 19 |

26 | 27 | 2 | 28 | 24 | 5 |

11 | 12 | 5 | 14 | 13 | 15 |

29 | 28 | 10 | 6 | 11 | 8 |

30 | 13 | 8 | 9 | 10 | 3 |

14 | 15 | 1 | 2 | ||

4 | 4 |

Moreover, making a comparison of the three target values of these three schemes, get the data showed in Table

The target values of three schemes.

Target value | Scheme | ||
---|---|---|---|

FCFS | Optimization program 1 | Optimization program 2 | |

Runway Capacity/s | 1577 | 1287 | 1338 |

Delay losses/yuan | 217815.2 | 30921.6 | 53056.85 |

Robustness/% | 83.33 | 66.67 | 66.67 |

The comparison of target values of three schemes.

As can be seen from the Table

Runway capacity is improved by 18.4%

The robustness is improved by 24%

In the flight queue after optimization, there are 4 flights arriving in advance, thus saving the fuel consumption for air waiting and reducing operating costs. It is a great advantage compared with the FCFS algorithm.

The delay losses of 30 flights of three programs.

In summary, the results got by using multiobjective genetic algorithm in this paper have improved a lot compared with the FCFS algorithm. Decision makers can select the appropriate scheduling solution according to their needs based on the method of this paper, in order to obtain the satisfactory results.

In this paper the optimization problem of multirunway approach and departure flight sorting based on genetic algorithm is discussed, the targets of runway capacity, delay losses, and robustness are made; then it presents a multiobjective simulation model to solve it by using genetic algorithms. The simulation results show that the model and algorithm established in this paper on the flight scheduling problem have been greatly improved, not only runway capacity is improved, the delay losses is reduced, but it also reduces the workload of controllers and enhances the robustness of flight, which has high optimization efficiency. The method is effective and feasible in solving scheduling problems of flight at terminal area in reality; it can meet the requirements of operation controllers in real-time. The multiobjective algorithm is used in this paper, thus the decision makers can choose the final solution in the Pareto solutions. In addition, the optimization algorithm does not consider the impact on the airlines caused by flight scheduling, namely, lacking of the research on the fairness of the airlines. Therefore, the next job is to study the fairness of the airlines, consider the influence of airlines on flight sorting queue, make the improvement to the algorithm, and put forward a more perfect optimization program.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors thank the reviewers for helping them to improve this paper. This work is supported by National Natural Science Foundation of China, no. 61262002 and the Fundamental Research Funds for the Central Universities, no. NS2014064.