Optimal Sequencing of Arrival Flights at Metroplex Airports: A Study on Shared Waypoints Based on Path Selection and Rolling Horizon Control
Abstract
:1. Introduction
1.1. Background
1.2. Literature Review
1.3. Contribution of the Research
2. Methodology
2.1. Problem Description
2.2. Modeling
2.2.1. Parameters
2.2.2. Decision Variables
2.2.3. Objective Function
2.2.4. Constraint Conditions
2.3. Algorithm
Algorithm 1. Pseudo-code for MWRHC |
Step 1: Initialize variables and data structures, h = 1 Step 2: Calculate the expected arrival time window for each flight to reach each waypoint on the available route selected while h < H: Step 3: Initialize the optimization queue and variable set for the optimization time domain h Create empty list F_h[h] Step 4: Add flights with expected passing EP time within [T0, T0 + NT] to the opti mization queue F_h for each flight_id, flight_data in F: if flight_data[‘starttime’] is in range(T0, T0 + NT): Append flight_id to F_h[h] Step 5: Solve the mixed-integer programming (MIP) model and update the selected routes and flight status subProblem = create_subProblem(F_h_dict, routes, airport_runway) subProblem.optimize() update_selected_routes(subProblem, selected_routes) update_flight_status(F_h_dict, selected_routes) Step 6: Check the flight status of the flights in F_h (landed or not) and if the flight has not landed before T0 + T, update the entry point and output the actual arrival time before the point update_waypoint_information(F_h_dict, selected_routes) Step 7: Update T0 and h T0 = T0 + T h = h + 1 Step 8: Calculate expected arrival time window for each waypoint Step 9: Update the optimization queue F_h Step 10: Merge the current F_h_dict with the previous F_h_dict |
3. Experimentation
3.1. Data Description
3.2. Model Verification
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Set Symbol | Definition | Index Symbol |
---|---|---|
A | set of airports in metroplex | a |
F | set of arrival flights | i, j |
Fa | set of flights landing at airport a | |
R | set of routes available | r, s |
Ri | set of routes available for flight i, i∈F, Ri⊂R | |
D | set of segments that make up available routes | d |
Dr | set of segments that make up route r | |
P | set of waypoints in metroplex | p |
Pr | set of waypoints in route r | |
W | set of runways in metroplex airports, W⊂P | w |
Wa | set of runway(s) available for airport a | |
SA | set of scheduled arriving time of flights |
Symbol | Definition |
---|---|
the minimum flying duration for segment d | |
the start waypoint of segment d | |
the end waypoint of segment d | |
the earliest time for flight i arriving at waypoint p with choosing route r | |
the latest time for flight i arriving at waypoint p with choosing route r | |
the minimum time interval for wake turbulence purposes that must be satisfied when flight i and flight j are on the same runway of one airport | |
the minimum time interval for wake turbulence purposes that must be satisfied when flight i and flight j are on different runways of one airport | |
the minimum safe interval between flight i and flight j when operating under radar control | |
K | maximum position shifting (MPS) value |
M | a very large number |
N | the total flight number |
the number of flights landing at airport a | |
Symbol | Definition |
---|---|
the simulated time that flight i arriving through waypoint p | |
the simulated landing time of flight i | |
Constraints | No. |
---|---|
(1) | |
(2) | |
(3) | |
(4) | |
(5) | |
(6) | |
(7) | |
(8) | |
(9) | |
(10) | |
(11) | |
(12) | |
(13) | |
(14) |
Airport Identifier | Airport Name |
---|---|
NKG | Nanjing Lukou |
SHA | Shanghai Hongqiao |
PVG | Shanghai Pudong |
WUX | Wuxi Shuofang |
HGH | Hangzhou Xiaoshan |
NGB | Ningbo Lishe |
Start Point | Route no. | Waypoints |
---|---|---|
S1 | 01 | S1-NKGR |
02 | S1-M05-M06-M08-SHAR | |
03 | S1-M05-M06-M08-PVGR1 | |
04 | S1-M05-M06-M08-PVGR2 | |
05 | S1-M05-M06-WUXR | |
06 | S1-M05-M11-HGHR | |
07 | S1-M05-M06-M08-M09-M12-NGBR | |
S2 | 08 | S2-M02-NKGR |
09 | S2-M01-M04-M08-SHAR | |
10 | S2-M01-M04-M08-PVGR1 | |
11 | S2-M01-M04-M08-PVGR2 | |
12 | S2-M02-M05-M11-HGHR | |
S3 | 13 | S3-M01-M02-NKGR |
14 | S3-M01-M08-SHAR | |
15 | S3-M03-M08-PVGR1 | |
16 | S3-M03-M08-PVGR2 | |
17 | S3-M03-WUXR | |
18 | S3-M01-M02-M05-M11-HGHR | |
19 | S3-M03-M08-M09-M12-NGBR | |
S4 | 20 | S4-M10-M12-M13-HGHR |
S5 | 21 | S5-M17-SHAR |
22 | S5-PVGR1 | |
23 | S5-PVGR2 | |
24 | S5-M17-M09-WUXR | |
25 | S5-M10-M12-NGBR | |
S6 | 26 | S6-M16-M12-SHAR |
27 | S6-M16-M12-PVGR1 | |
28 | S6-M16-M12-PVGR2 | |
29 | S6-M16-NGBR | |
S7 | 30 | S7-M15-M13-M12-SHAR |
31 | S7-M15-M16-M12-SHAR | |
32 | S7-M15-M13-M12-PVGR1 | |
33 | S7-M15-M16-M12-PVGR2 | |
34 | S7-M15-M13-M12-PVGR1 | |
35 | S7-M15-M16-M12-PVGR2 | |
36 | S7-M14-HGHR | |
37 | S7-M15-M16-NGBR | |
S8 | 38 | S8-M14-M11-NKGR |
39 | S8-M14-M07-NKGR | |
40 | S8-M14-M11-M06-WUXR | |
41 | S8-M14-M07-M06-WUXR | |
42 | S8-M14-HGHR | |
S9 | 43 | S9-NKGR |
Landing Airport | Route No. |
---|---|
NKG | 01, 08, 13, 38, 39, 43 |
SHA | 02, 09, 14, 21, 26, 30, 31, |
PVG | 03, 04, 10, 11, 15, 16, 22, 23, 27, 28, 32, 33, 34, 35 |
WUX | 05, 17, 24, 40, 41 |
HGH | 06, 12, 18, 20, 36, 42 |
NGB | 07, 19, 25, 29, 37 |
(A) | |||||||||
Flight No. | Destination Airport | Landing Runway | Passing Time of EP | EP No. | Scheduled Landing Time | Actual Landing Time | FCFS Landing Time | MWRHC Landing Time | Route No. |
Fa1 | NKG | NKGR | 125 | S9 | 2400 | 720 | 725 | 425 | 43 |
Fa2 | NKG | NKGR | 655 | S9 | 3000 | 1320 | 1255 | 1625 | 43 |
Fa3 | NKG | NKGR | 792 | S9 | 2400 | 1440 | 1392 | 1092 | 43 |
Fa4 | NKG | NKGR | 103 | S1 | 3900 | 1680 | 1867 | 1200 | 01 |
Fa5 | NKG | NKGR | 1217 | S9 | 1800 | 2040 | 1817 | 1517 | 43 |
Fa6 | NKG | NKGR | 292 | S1 | 2700 | 2160 | 2056 | 1733 | 01 |
Fa7 | NKG | NKGR | 124 | S1 | 3300 | 2340 | 2080 | 1346 | 01 |
Fa8 | NKG | NKGR | 291 | S1 | 300 | 2460 | 2247 | 1841 | 01 |
Fa9 | NKG | NKGR | 729 | S1 | 1800 | 2580 | 2493 | 2462 | 01 |
Fa10 | NKG | NKGR | 1162 | S1 | 4800 | 2760 | 2926 | 2227 | 01 |
Fa11 | NKG | NKGR | 993 | S3 | 5100 | 3060 | 2933 | 2570 | 13 |
Fa12 | NKG | NKGR | 1465 | S1 | 3300 | 3180 | 3229 | 3177 | 01 |
Fa13 | NKG | NKGR | 1146 | S3 | 3000 | 3300 | 3086 | 2354 | 13 |
Fa14 | NKG | NKGR | 2640 | S9 | 3900 | 3480 | 3240 | 3393 | 43 |
Fa15 | NKG | NKGR | 1924 | S8 | 5400 | 3600 | 3536 | 2705 | 39 |
Fa16 | NKG | NKGR | 1756 | S8 | 5700 | 3720 | 3368 | 2960 | 39 |
Fa17 | NKG | NKGR | 1673 | S2 | 4200 | 3900 | 3717 | 3068 | 08 |
Fa18 | NKG | NKGR | 2985 | S9 | 3300 | 4020 | 3585 | 3285 | 43 |
Fa19 | NKG | NKGR | 2284 | S1 | 2100 | 4200 | 4048 | 3825 | 01 |
Fa20 | NKG | NKGR | 3391 | S9 | 5100 | 4320 | 3991 | 3717 | 43 |
Fa21 | NKG | NKGR | 2679 | S1 | 4500 | 4440 | 4443 | 3933 | 01 |
Fa22 | NKG | NKGR | 2832 | S3 | 5400 | 4740 | 4772 | 4663 | 13 |
Fa23 | NKG | NKGR | 4111 | S9 | 6600 | 4860 | 4711 | 4411 | 43 |
(B) | |||||||||
Flight No. | Destination Airport | Landing Runway | Passing time of EP | EP No. | Scheduled landing time | Actual landing time | FCFS landing time | MWRHC landing time | Route No. |
Fb1 | SHA | SHAR | 252 | S6 | 3000 | 2340 | 2312 | 2289 | 26 |
Fb2 | SHA | SHAR | 321 | S2 | 3900 | 3060 | 3065 | 3121 | 09 |
Fb3 | SHA | SHAR | 853 | S2 | 3600 | 3420 | 3397 | 3422 | 09 |
Fb4 | SHA | SHAR | 1707 | S7 | 3300 | 3600 | 3587 | 3746 | 30 |
Fb5 | SHA | SHAR | 1467 | S2 | 4500 | 4140 | 4111 | 3530 | 09 |
Fb6 | SHA | SHAR | 2403 | S6 | 4200 | 4260 | 4263 | 4299 | 26 |
Fb7 | SHA | SHAR | 1974 | S3 | 6600 | 4380 | 4382 | 3854 | 14 |
Fb8 | SHA | SHAR | 1903 | S2 | 5400 | 4560 | 4447 | 4191 | 09 |
Fb9 | SHA | SHAR | 2746 | S7 | 6300 | 4680 | 4626 | 4580 | 30 |
Fb10 | SHA | SHAR | 2660 | S6 | 6000 | 4860 | 4820 | 4070 | 26 |
Fb11 | SHA | SHAR | 3051 | S7 | 5400 | 4920 | 4931 | 5044 | 30 |
Fb12 | SHA | SHAR | 2781 | S6 | 6000 | 5040 | 5041 | 4720 | 26 |
(C) | |||||||||
Flight No. | Destination Airport | Landing Runway | Passing time of EP | EP No. | Scheduled landing time | Actual landing time | FCFS landing time | MWRHC landing time | Route No. |
Fc1 | PVG | PVGR1 | 6 | S5 | 3300 | 1080 | 1058 | 1599 | 22 |
Fc2 | PVG | PVGR1 | 160 | S5 | 2400 | 1440 | 1312 | 1244 | 22 |
Fc3 | PVG | PVGR1 | 603 | S5 | 2100 | 1680 | 1655 | 1136 | 22 |
Fc4 | PVG | PVGR1 | 307 | S7 | 3300 | 2320 | 2291 | 1906 | 32 |
Fc5 | PVG | PVGR1 | 1450 | S5 | 3900 | 2520 | 2502 | 2494 | 22 |
Fc6 | PVG | PVGR1 | 794 | S6 | 3600 | 2880 | 2858 | 2926 | 27 |
Fc7 | PVG | PVGR1 | 916 | S6 | 3000 | 3120 | 2980 | 2746 | 27 |
Fc8 | PVG | PVGR1 | 1090 | S6 | 5100 | 3180 | 3154 | 2603 | 27 |
Fc9 | PVG | PVGR1 | 415 | S1 | 2400 | 3420 | 2931 | 3082 | 03 |
Fc10 | PVG | PVGR1 | 770 | S1 | 5400 | 3600 | 3286 | 3190 | 03 |
Fc11 | PVG | PVGR1 | 2255 | S5 | 2100 | 3600 | 3407 | 3306 | 22 |
Fc12 | PVG | PVGR1 | 2407 | S5 | 6900 | 3720 | 3559 | 3414 | 22 |
Fc13 | PVG | PVGR1 | 1822 | S6 | 5400 | 3840 | 3886 | 3622 | 27 |
Fc14 | PVG | PVGR1 | 2824 | S5 | 5700 | 3960 | 3976 | 3786 | 22 |
Fc15 | PVG | PVGR1 | 2059 | S1 | 6000 | 4920 | 4383 | 3903 | 04 |
Fc16 | PVG | PVGR1 | 2116 | S2 | 6600 | 5120 | 4220 | 4974 | 10 |
Fc17 | PVG | PVGR1 | 4071 | S5 | 6900 | 5220 | 5223 | 4550 | 22 |
Fc18 | PVG | PVGR1 | 2934 | S6 | 5700 | 5400 | 5198 | 4813 | 27 |
Fc19 | PVG | PVGR1 | 3360 | S6 | 5400 | 5700 | 5624 | 4602 | 27 |
Fc20 | PVG | PVGR2 | 728 | S5 | 4800 | 1800 | 1880 | 1760 | 23 |
Fc21 | PVG | PVGR2 | 1593 | S5 | 3600 | 2700 | 2745 | 2794 | 23 |
Fc22 | PVG | PVGR2 | 1786 | S5 | 6900 | 3000 | 2938 | 3130 | 23 |
Fc23 | PVG | PVGR2 | 2026 | S5 | 3300 | 3300 | 3178 | 3238 | 23 |
Fc24 | PVG | PVGR2 | 1215 | S6 | 4200 | 3480 | 2479 | 3354 | 28 |
Fc25 | PVG | PVGR2 | 3015 | S5 | 5700 | 4140 | 4167 | 3592 | 23 |
Fc26 | PVG | PVGR2 | 3297 | S5 | 6300 | 4440 | 4449 | 4356 | 23 |
Fc27 | PVG | PVGR2 | 2282 | S6 | 4500 | 4560 | 3546 | 5068 | 28 |
Fc28 | PVG | PVGR2 | 1693 | S1 | 6600 | 4740 | 4209 | 4108 | 04 |
Fc29 | PVG | PVGR2 | 3585 | S5 | 4800 | 4740 | 4737 | 5128 | 23 |
Fc30 | PVG | PVGR2 | 3767 | S5 | 7200 | 4920 | 4919 | 5240 | 23 |
Fc31 | PVG | PVGR2 | 2525 | S6 | 6000 | 4980 | 4889 | 4832 | 28 |
Fc32 | PVG | PVGR2 | 3076 | S6 | 5100 | 5400 | 5380 | 5348 | 28 |
(D) | |||||||||
Flight No. | Destination Airport | Landing Runway | Passing time of EP | EP No. | Scheduled landing time | Actual landing time | FCFS landing time | MWRHC landing time | Route No. |
Fd1 | WUX | WUXR | 126 | S3 | 3000 | 2100 | 1690 | 1238 | 17 |
Fd2 | WUX | WUXR | 541 | S1 | 5700 | 3300 | 3173 | 2860 | 05 |
Fd3 | WUX | WUXR | 3452 | S5 | 7200 | 5400 | 4608 | 4468 | 24 |
Fd4 | WUX | WUXR | 4445 | S5 | 9900 | 6360 | 5601 | 5334 | 24 |
Fe1 | HGH | HGHR | 220 | S8 | 2100 | 780 | 1064 | 670 | 42 |
Fe2 | HGH | HGHR | 404 | S8 | 2400 | 1260 | 1248 | 854 | 42 |
Fe3 | HGH | HGHR | 610 | S8 | 3300 | 1560 | 1454 | 1060 | 42 |
Fe4 | HGH | HGHR | 927 | S8 | 2400 | 1860 | 1771 | 1377 | 42 |
Fe5 | HGH | HGHR | 1606 | S8 | 4200 | 2460 | 2450 | 2056 | 42 |
Fe6 | HGH | HGHR | 1943 | S8 | 2700 | 2880 | 2843 | 2439 | 42 |
Fe7 | HGH | HGHR | 2754 | S8 | 4500 | 3600 | 3654 | 3309 | 42 |
Fe8 | HGH | HGHR | 3056 | S8 | 5400 | 3780 | 3900 | 4639 | 42 |
Fe9 | HGH | HGHR | 1265 | S2 | 5400 | 3960 | 2961 | 2620 | 12 |
Fe10 | HGH | HGHR | 3404 | S7 | 4500 | 4260 | 4220 | 4126 | 36 |
Fe11 | HGH | HGHR | 1875 | S1 | 5100 | 4380 | 3783 | 3417 | 06 |
Fe12 | HGH | HGHR | 4081 | S8 | 6000 | 4920 | 4925 | 4531 | 42 |
Fe13 | HGH | HGHR | 2702 | S4 | 5700 | 5040 | 4810 | 5235 | 20 |
Ff1 | NGB | NGBR | 15 | S7 | 3600 | 1380 | 1251 | 1016 | 37 |
Ff2 | NGB | NGBR | 668 | S6 | 2700 | 1920 | 1720 | 1466 | 29 |
Ff3 | NGB | NGBR | 481 | S5 | 2700 | 2340 | 1889 | 2530 | 25 |
Ff4 | NGB | NGBR | 1347 | S6 | 3000 | 2940 | 2399 | 1979 | 29 |
Ff5 | NGB | NGBR | 1491 | S6 | 3900 | 3180 | 2543 | 2206 | 29 |
Ff6 | NGB | NGBR | 956 | S5 | 1500 | 3360 | 2364 | 2314 | 25 |
Ff7 | NGB | NGBR | 1259 | S5 | 2700 | 3540 | 2667 | 2422 | 25 |
Ff8 | NGB | NGBR | 1082 | S5 | 3300 | 3720 | 2490 | 2098 | 25 |
Ff9 | NGB | NGBR | 494 | S3 | 4500 | 3960 | 3354 | 2900 | 19 |
Ff10 | NGB | NGBR | 2160 | S6 | 5100 | 4140 | 3212 | 2792 | 29 |
Ff11 | NGB | NGBR | 3210 | S7 | 5400 | 4620 | 4446 | 4011 | 37 |
Ff12 | NGB | NGBR | 3516 | S7 | 6000 | 4860 | 4752 | 4459 | 37 |
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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. https://doi.org/10.3390/aerospace10100881
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(10):881. https://doi.org/10.3390/aerospace10100881
Chicago/Turabian StyleJiang, Furong, and Zhaoning Zhang. 2023. "Optimal Sequencing of Arrival Flights at Metroplex Airports: A Study on Shared Waypoints Based on Path Selection and Rolling Horizon Control" Aerospace 10, no. 10: 881. https://doi.org/10.3390/aerospace10100881