# Study on an Airport Gate Reassignment Method and Its Application

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Construct a Gate Reassignment Model

#### 3.1. Gate Reassignmet Modeling for Delayed Flights

#### 3.2. Linearize the Gate Reassignment Model

## 4. Two Stages Hybrid Algorithm

#### 4.1. GA

#### 4.2. ACO Algorithm

#### 4.3. Two Stages Hybrid Algorithm

#### 4.3.1. The Idea of Two Stages Hybrid Algorithm

#### 4.3.2. The Flow of the Proposed GAOTWSH Algorithm

#### 4.3.3. The Steps of the Proposed GAOTWSH Algorithm

**Step****1.**- Read flight information and initialize the parameters of GA.
**Step****2.**- The initial solution is randomly generated. The selection factor, crossover factor and mutation factor are obtained according to the elitist strategy and the offline ranking selection method.
**Step****3.**- Implement selection operation, crossover operation and mutation operation.
**Step****4.**- Determine whether the three successive generations are less than the evolution rate, and the number of iterations is larger than the maximum iterations. If the three successive generations are less than the evolution rate and the number of iterations is larger than the maximum iterations, then continue Step 5. Otherwise go to Step 3.
**Step****5.**- The several optimization solutions are generated by suing adaptive GA, then the optimization solutions are used to initialize the initial pheromone concentration of ACO algorithm.
**Step****6.**- The parameters of ACO algorithm are initialized. The number of gates and sub-populations and ants are set according to the number of flight delays. The unvisited nodes are filled in the Tabuk table.
**Step****7.**- The optimal solutions of ants are searched by using ACO algorithm.
**Step****8.**- The pheromone concentrations of the ACO algorithm are updated, and the Tabuk table is cleaned.
**Step****9.**- Determine whether the number of iterations reaches the maximum number of iterations. If the number of iterations reaches the maximum number of iterations, the continue Step 10. Otherwise go to Step 7.
**Step****10.**- Obtain the optimal solution and the optimal scheme of the gate reassignment.

## 5. Case Analysis

#### 5.1. Experimental Data and Environment

#### 5.2. Experimental Results

#### 5.3. Result Comparison and Analysis

## 6. Conclusions and Future Work

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Merve, S.; Nilay, N. Stochastic optimization models for the airport gate assignment problem. Transp. Res. Part E Logist. Transp. Rev.
**2012**, 48, 438–459. [Google Scholar] - Prem Kumar, V.; Bierlaire, M. Multi-objective airport gate assignment problem in planning and operations. J. Adv. Transp.
**2014**, 48, 902–926. [Google Scholar] [CrossRef] - Lai, G.M.; Yuan, D.H.; Yang, S.Y. A new hybrid combinatorial genetic algorithm for multidimensional knapsack problems. J. Supercomput.
**2014**, 70, 930–945. [Google Scholar] [CrossRef] - Colorni, A.; Dorigo, M.; Maniezzo, V. Distributed optimization by ant colonies. In Proceedings of the First European Conference of Artificial Life, Paris, France, 11–13 December 1991; pp. 134–142. [Google Scholar]
- Pan, T.H.; Wey, C.L. GRASS: An efficient gate re-assignment algorithm for inverter minimization in post technology mapping. IEE Proc. Comput. Digit. Tech.
**1997**, 144, 348–352. [Google Scholar] [CrossRef] - Gu, Y.; Chung, C.A. Genetic algorithm approach to aircraft gate reassignment problem. J. Transp. Eng.
**1999**, 125, 384–389. [Google Scholar] [CrossRef] - Wong, J.T.; Li, S.L.; Gillingwater, D. An optimization model for assessing flight technical delay. Transp. Plan. Technol.
**2002**, 25, 121–153. [Google Scholar] [CrossRef] - Lo, K.W.; Ferguson, B.G.; Gao, Y.J.; Maguer, A. Aircraft flight parameter estimation using acoustic multipath delays. IEEE Trans. Aerosp. Electron. Syst.
**2003**, 39, 259–268. [Google Scholar] [CrossRef] - Yan, S.Y.; Tang, C.H. A heuristic approach for airport gate assignments for stochastic flight delays. Eur. J. Oper. Res.
**2007**, 180, 547–567. [Google Scholar] [CrossRef] - Yan, S.; Tang, C.H.; Chen, C.H. Reassignments of common-use check-in counters following airport incidents. J. Oper. Res. Soc.
**2008**, 59, 1100–1108. [Google Scholar] [CrossRef] - Yan, S.Y.; Chen, C.Y.; Tang, C.H. Airport gate reassignment following temporary airport closures. Transportmetrica
**2009**, 5, 25–41. [Google Scholar] [CrossRef] - Churchill, A.M.; Lovell, D.J.; Ball, M.O. Flight delay propagation impact on strategic air traffic flow management. Transp. Res. Rec.
**2010**, 2177, 105–113. [Google Scholar] [CrossRef] - Eun, Y.; Bang, H.C. Optimal arrival flight sequencing and scheduling using discrete airborne delays. IEEE Trans. Intell. Transp. Syst.
**2010**, 11, 359–373. [Google Scholar] - Tang, C.H.; Yan, S.Y.; Hou, Y.Z. A gate reassignment framework for real time flight delays. 4OR-A Q. J. Oper. Res.
**2010**, 8, 299–318. [Google Scholar] [CrossRef] - Maharjan, B.; Matis, T.I. An optimization model for gate reassignment in response to flight delays. J. Air Transp. Manag.
**2011**, 17, 256–261. [Google Scholar] [CrossRef] - Tang, C.H. A gate reassignment model for the Taiwan Taoyuan airport under temporary gate shortages and stochastic flight delays. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum.
**2011**, 41, 637–650. [Google Scholar] [CrossRef] - Yan, S.Y.; Tang, C.H.; Hou, Y.Z. Airport gate reassignments considering deterministic and stochastic flight departure/arrival times. J. Adv. Transp.
**2011**, 45, 304–320. [Google Scholar] [CrossRef] - Deshpande, V.; Arikan, M. The impact of airline flight schedules on flight delays. Manuf. Serv. Oper. Manag.
**2012**, 14, 423–440. [Google Scholar] [CrossRef] - Li, J.H.; Chen, X.; Zhu, J.F. Multi-objective programming for airport gate reassignment. Trans. Nanjing Univ. Aeronaut. Astronaut.
**2013**, 30, 209–215. [Google Scholar] - Wang, H.W.; Luo, Y.X.; Shi, Z.J. Real-time gate reassignment based on flight delay feature in hub airport. Math. Probl. Eng.
**2013**, 2013, 646241. [Google Scholar] [CrossRef] - Farley, S.; Brodsky, A.; Sherry, L. Flight rescheduling decisions for minimizing passenger trip delays. Intell. Decis. Technol.
**2014**, 8, 35–44. [Google Scholar] [CrossRef] - Wu, Y.P.; Wang, X.M.; Wu, Y. Robust stability and stabilization of uncertain networked flight control system with random time delays. Int. J. Model. Identif. Control
**2014**, 21, 411–417. [Google Scholar] [CrossRef] - Radivojevic, S.; Milbredt, O. A decision support tool for evaluating decision options for out-bound flight delays considering high-valuable passengers. Eur. Transp. Res. Rev.
**2016**, 8, 1–13. [Google Scholar] [CrossRef] - Montlaur, A.; Delgado, L. Flight and passenger delay assignment optimization strategies. Transp. Res. Part C Emerg. Technol.
**2017**, 81, 99–117. [Google Scholar] [CrossRef] - Zhang, D.; Klabjan, D. Optimization for gate re-assignment. Transp. Res. Part B Methodol.
**2017**, 95, 260–284. [Google Scholar] [CrossRef] - Yu, C.H.; Zhang, D.; Lau, H.H. A heuristic approach for solving an integrated gate reassignment and taxi scheduling problem. J. Air Transp. Manag.
**2017**, 62, 189–196. [Google Scholar] [CrossRef] - Takeich, N. Nominal flight time optimization for arrival time scheduling through estimation/resolution of delay accumulation. Transp. Res. Part C Emerg. Technol.
**2017**, 77, 433–443. [Google Scholar] [CrossRef] - Marla, L.; Vaaben, B.; Barnhart, C. Integrated disruption management and flight planning to trade off delays and fuel burn. Transp. Sci.
**2017**, 51, 88–111. [Google Scholar] [CrossRef] - Xu, Y.; Prats, X. Effects of linear holding for reducing additional flight delays without extra fuel consumption. Transp. Res. Part D Transp. Environ.
**2017**, 53, 388–397. [Google Scholar] [CrossRef] - Genç, H.M.; Erol, O.K.; Eksin, B.; Berber, M.F.; Güleryüz, B.O. A stochastic neighbourhood search approach for airport gate assignment problem. Expert Syst. Appl.
**2012**, 39, 316–327. [Google Scholar] [CrossRef] - Gu, B.; Sheng, V.S. A robust regularization path algorithm for ν-support vector classification. IEEE Trans. Neural Netw. Learn. Syst.
**2016**, 28, 1241–1248. [Google Scholar] [CrossRef] [PubMed] - Fu, Z.J.; Wu, X.L.; Guan, C.W.; Sun, X.M.; Ren, K. Toward efficient multi-keyword fuzzy search over encrypted outsourced data with accuracy improvement. IEEE Trans. Inf. Forensics Secur.
**2016**, 11, 2706–2716. [Google Scholar] [CrossRef] - Xue, Y.; Jiang, J.M.; Zhao, B.P.; Ma, T.H. A self-adaptive artificial bee colony algorithm based on global best for global optimization. Soft Comput.
**2017**. [Google Scholar] [CrossRef] - Gu, B.; Sheng, V.S.; Tay, K.Y.; Romano, W.; Li, S. Incremental support vector learning for ordinal regression. IEEE Trans. Neural Netw. Learn. Syst.
**2015**, 26, 1403–1416. [Google Scholar] [CrossRef] [PubMed] - Zhang, J.; Tang, J.; Wang, T.B.; Chen, F. Energy-efficient data-gathering rendezvous algorithms with mobile sinks for wireless sensor networks. Int. J. Sens. Netw.
**2017**, 23, 248–257. [Google Scholar] [CrossRef] - Wang, B.W.; Gu, X.D.; Ma, L.; Yan, S.S. Temperature error correction based on BP neural network in meteorological WSN. Int. J. Sens. Netw.
**2017**, 23, 265–278. [Google Scholar] [CrossRef] - Liu, Q.; Cai, W.D.; Shen, J.; Fu, Z.J.; Liu, X.D.; Linge, N. A speculative approach to spatial-temporal efficiency with multi-objective optimization in a heterogeneous cloud environment. Secur. Commun. Netw.
**2016**, 9, 4002–4012. [Google Scholar] [CrossRef] - Pan, Z.Q.; Zhang, Y.; Kwong, S. Efficient motion and disparity estimation optimization for low complexity multiview video coding. IEEE Trans. Broadcast.
**2015**, 61, 166–176. [Google Scholar] - Xiong, L.Z.; Xu, Z.Q.; Shi, Y.Q. An integer wavelet transform based scheme for reversible data hiding in encrypted images. Multidimens. Syst. Signal Process.
**2017**. [Google Scholar] [CrossRef] - Kong, Y.; Zhang, M.J.; Ye, D.Y. A belief propagation-based method for task allocation in open and dynamic cloud environments. Knowl. Based Syst.
**2016**, 115, 123–132. [Google Scholar] [CrossRef] - Chen, B.J.; Yang, J.H.; Jeon, B.; Zhang, X.P. Kernel quaternion principal component analysis and its application in RGB-D object recognition. Neurocomputing
**2017**, 266, 293–303. [Google Scholar] [CrossRef] - Gu, B.; Sun, X.M.; Sheng, V.S. Structural minimax probability machine. IEEE Trans. Neural Netw. Learn. Syst.
**2016**, 28, 1646–1656. [Google Scholar] [CrossRef] [PubMed] - Wang, J.W.; Lian, S.G.; Shi, Y.Q. Hybrid multiplicative multi-watermarking in DWT domain. Multidimens. Syst. Signal Process.
**2017**, 28, 617–636. [Google Scholar] [CrossRef] - Zhang, Y.H.; Sun, X.M.; Wang, B.W. Efficient algorithm for K-barrier coverage based on integer linear programming. China Comm.
**2016**, 13, 16–23. [Google Scholar] [CrossRef] - Rong, H.; Ma, T.H.; Tang, M.L.; Cao, J. A novel subgraph K
^{+}-isomorphism method in social network based on graph similarity detection. Soft Comput.**2017**. [Google Scholar] [CrossRef] - Ma, T.H.; Wang, Y.; Tang, M.L.; Cao, J.; Tian, Y.; Al-Dhelaan, A.; Al-Rodhaan, M. LED: A fast overlapping communities detection algorithm based on structural clustering. Neurocomputing
**2016**, 207, 488–500. [Google Scholar] [CrossRef] - Deng, W.; Zhao, H.M.; Zou, L.; Li, G.Y.; Yang, X.H.; Wu, D.Q. A novel collaborative optimization algorithm in solving complex optimization problems. Soft Comput.
**2017**, 21, 4387–4398. [Google Scholar] [CrossRef] - Deng, W.; Zhao, H.M.; Yang, X.H.; Xiong, J.X.; Sun, M.; Li, B. Study on an improved adaptive PSO algorithm for solving multi-objective gate assignment. Appl. Soft Comput.
**2017**, 59, 288–302. [Google Scholar] [CrossRef] - Liu, W.D.; Zhu, H.; Wang, Y.P.; Zhou, S.Q.; Bai, Y.L.; Zhao, C.S. Topology optimization of support structure of telescope skin based on bit-matrix representation NSGA-II. Chin. J. Aeronaut.
**2013**, 26, 1422–1429. [Google Scholar] [CrossRef] - Deng, W.; Zhao, H.M.; Liu, J.J.; Yan, X.L.; Li, Y.Y.; Yin, L.F.; Ding, C.H. An improved CACO algorithm based on adaptive method and multi-variant strategies. Soft Comput.
**2015**, 19, 701–713. [Google Scholar] [CrossRef] - Aickelin, U.; Burke, E.K.; Li, J.P. An evolutionary squeaky wheel optimization approach to personnel scheduling. IEEE Trans. Evolut. Comput.
**2009**, 13, 433–443. [Google Scholar] [CrossRef] - Cheng, C.H.; Ho, S.C.; Kwan, C.L. The use of meta-heuristics for airport gate assignment. Expert Syst. Appl.
**2012**, 39, 12430–12437. [Google Scholar] [CrossRef]

**Figure 3.**The flow of the new two-stage hybrid algorithm based on the GA and ACO (GAOTWSH) algorithm.

Code | Price | Passengers | Type | Planed Arrival Time | Planed Departure Time | Actual Arrival Time | Actual Departure Time | Delayed Time (m) | Pre-Assigned Gate |
---|---|---|---|---|---|---|---|---|---|

1 | 3565 | 256 | Medium | 2015-7-26 6:00:00 | 2015-7-26 8:20:00 | 2015-7-26 6:00:00 | 2015-7-26 8:20:00 | - | 19 |

2 | 3058 | 606 | Large | 2015-7-26 6:00:00 | 2015-7-26 14:30:00 | 2015-7-26 6:00:00 | 2015-7-26 14:30:00 | - | 54 |

3 | 2483 | 298 | Medium | 2015-7-26 6:20:00 | 2015-7-26 8:00:00 | 2015-7-26 6:20:00 | 2015-7-26 8:00:00 | - | 17 |

4 | 1173 | 378 | Large | 2015-7-26 6:55:00 | 2015-7-26 9:10:00 | 2015-7-26 6:55:00 | 2015-7-26 9:10:00 | - | 21 |

5 | 1248 | 298 | Medium | 2015-7-26 7:50:00 | 2015-7-27 2:50:00 | 2015-7-26 7:50:00 | 2015-7-27 2:50:00 | - | 1 |

6 | 3022 | 606 | Large | 2015-7-26 7:55:00 | 2015-7-26 9:50:00 | 2015-7-26 7:55:00 | 2015-7-26 9:50:00 | - | 34 |

7 | 2249 | 378 | Large | 2015-7-26 8:15:00 | 2015-7-27 3:00:00 | 2015-7-26 8:45:00 | 2015-7-27 3:00:00 | 30 | 53 |

8 | 974 | 312 | Large | 2015-7-26 8:20:00 | 2015-7-26 9:20:00 | 2015-7-26 8:20:00 | 2015-7-26 9:20:00 | - | 37 |

9 | 3079 | 362 | Large | 2015-7-26 8:25:00 | 2015-7-26 10:05:00 | 2015-7-26 9:00:00 | 2015-7-26 10:05:00 | 35 | 93 |

10 | 1248 | 98 | Small | 2015-7-26 9:10:00 | 2015-7-26 10:10:00 | 2015-7-26 9:10:00 | 2015-7-26 10:10:00 | - | 55 |

… | … | … | … | … | … | … | … | … | … |

500 | 1421 | 378 | Large | 2015-7-26 23:55:00 | 2015-7-27 9:10:00 | 2015-7-26 23:55:00 | 2015-7-27 9:10:00 | - | 27 |

Code | Type | Attribute | Started Time | Closed Time |
---|---|---|---|---|

1 | Large | Boarding | 2015-7-26 6:00 | 2015-7-26 23:59 |

2 | Medium | Boarding | 2015-7-26 6:00 | 2015-7-26 23:59 |

3 | Large | Boarding | 2015-7-26 6:00 | 2015-7-26 23:59 |

4 | Large | Boarding | 2015-7-26 6:00 | 2015-7-26 23:59 |

5 | Large | Boarding | 2015-7-26 6:00 | 2015-7-26 23:59 |

6 | Large | Boarding | 2015-7-26 6:00: | 2015-7-26 23:59 |

7 | Large | Boarding | 2015-7-26 6:00 | 2015-7-26 23:59 |

8 | Medium | Boarding | 2015-7-26 6:00 | 2015-7-26 23:59 |

9 | Medium | Boarding | 2015-7-26 6:00 | 2015-7-26 23:59 |

10 | Large | Boarding | 2015-7-26 6:00 | 2015-7-26 23:59 |

… | … | … | … | … |

60 | Medium | Boarding | 2015-7-26 6:00 | 015-7-26 23:59 |

61 | Large | Remote | 2015-7-26 6:00 | 015-7-26 23:59 |

… | … | … | … | … |

100 | Large | Remote | 2015-7-26 6:00 | 015-7-26 23:59 |

Parameters | GA | ACO | NGASAH |
---|---|---|---|

Population size (${m}_{1}$) | 100 | - | 100 |

Ants (${m}_{2}$) | - | 100 | 100 |

Iteration time (${T}_{\mathrm{max}}$) | 100 | 100 | 100 |

Initial crossover probability (${p}_{c}$) | 0.90 | - | 0.90 |

Initial mutation probability (${p}_{m}$) | 0.05 | - | 0.05 |

Pheromone factor ($\alpha $) | - | 2.0 | 2.0 |

Heuristic factor ($\beta $) | - | 4.0 | 4.0 |

Initial concentration ${\tau}_{ij}$ | - | 1.5 | 1.5 |

Evaporation coefficient ($\rho $) | - | 0.80 | 0.80 |

Pheromone amount ($Q$) | - | 100 | 120 |

Gate | Total Number | Gate | Total Number | Gate | Total Number | Gate | Total Number | |||
---|---|---|---|---|---|---|---|---|---|---|

1 | 4 | 16 | 8 | 31 | 4 | 46 | 7 | |||

2 | 2 | 17 | 8 | 32 | 5 | 47 | 8 | |||

3 | 11 | 18 | 9 | 33 | 3 | 48 | 6 | |||

4 | 13 | 19 | 11 | 34 | 6 | 49 | 5 | |||

5 | 9 | 20 | 5 | 35 | 3 | 50 | 8 | |||

6 | 9 | 21 | 12 | 36 | 8 | 51 | 6 | |||

7 | 15 | 22 | 12 | 37 | 7 | 52 | 2 | |||

8 | 3 | 23 | 3 | 38 | 4 | 53 | 7 | |||

9 | 3 | 24 | 9 | 39 | 7 | 54 | 11 | |||

10 | 9 | 25 | 11 | 40 | 6 | 55 | 3 | |||

11 | 17 | 26 | 3 | 41 | 4 | 56 | 7 | |||

12 | 10 | 27 | 9 | 42 | 4 | 57 | 4 | |||

13 | 12 | 28 | 3 | 43 | 5 | 58 | 2 | |||

14 | 9 | 29 | 4 | 44 | 9 | 59 | 10 | |||

15 | 6 | 30 | 6 | 45 | 4 | 60 | 9 |

Methods | Index | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | AVG |
---|---|---|---|---|---|---|---|---|---|---|---|---|

GA | Iteration | 71 | 71 | 60 | 49 | 61 | 72 | 70 | 66 | 72 | 71 | 66.3 |

Optimal value | 1.885 | 1.904 | 1.881 | 1.907 | 1.925 | 1.901 | 1.895 | 1.873 | 1.873 | 1.923 | 1.896 | |

ACO | Iteration | 128 | 187 | 180 | 156 | 98 | 175 | 120 | 117 | 137 | 182 | 148 |

Optimal value | 1.431 | 1.459 | 1.476 | 1.467 | 1.444 | 1.434 | 1.477 | 1.485 | 1.489 | 1.467 | 1.431 | |

GAOTWSH | Iteration | 155 | 137 | 182 | 89 | 183 | 110 | 98 | 163 | 163 | 153 | 143.3 |

Optimal value | 1.164 | 1.191 | 1.175 | 1.199 | 1.179 | 1.185 | 1.192 | 1.187 | 1.207 | 1.201 | 1.188 |

Methods | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | AVG |
---|---|---|---|---|---|---|---|---|---|---|---|

GA | 134.3 | 129.2 | 127.6 | 126.8 | 127.2 | 127.2 | 128.7 | 128.1 | 127.2 | 126.3 | 128.3 |

ACO | 164.6 | 166.3 | 164.2 | 174.1 | 162.4 | 162.2 | 163.3 | 169.2 | 162.8 | 164.8 | 165.4 |

GAOTWSH | 183.6 | 175.1 | 175.6 | 171.1 | 176.1 | 172.4 | 168.9 | 172.3 | 169.1 | 169.8 | 173.4 |

Methods | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | AVG |
---|---|---|---|---|---|---|---|---|---|---|---|

GA | 460 | 460 | 462 | 462 | 474 | 465 | 473 | 462 | 461 | 465 | 464.4 |

ACO | 344 | 345 | 344 | 355 | 349 | 344 | 351 | 346 | 345 | 347 | 347 |

GAOTWSH | 204 | 213 | 215 | 219 | 219 | 207 | 214 | 220 | 216 | 219 | 214.6 |

Time | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Average |
---|---|---|---|---|---|---|---|---|---|---|---|

GA | 3.849 | 3.848 | 3.839 | 3.785 | 3.891 | 3.881 | 3.796 | 3.859 | 3.833 | 3.715 | 3.829 |

ACO | 3.046 | 3.046 | 3.046 | 3.046 | 3.046 | 3.046 | 3.046 | 3.046 | 3.046 | 3.046 | 3.046 |

GAOTWSH | 3.072 | 3.017 | 3.072 | 3.018 | 3.072 | 3.072 | 3.016 | 3.015 | 3.072 | 3.072 | 3.050 |

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**MDPI and ACS Style**

Deng, W.; Li, B.; Zhao, H.
Study on an Airport Gate Reassignment Method and Its Application. *Symmetry* **2017**, *9*, 258.
https://doi.org/10.3390/sym9110258

**AMA Style**

Deng W, Li B, Zhao H.
Study on an Airport Gate Reassignment Method and Its Application. *Symmetry*. 2017; 9(11):258.
https://doi.org/10.3390/sym9110258

**Chicago/Turabian Style**

Deng, Wu, Bo Li, and Huimin Zhao.
2017. "Study on an Airport Gate Reassignment Method and Its Application" *Symmetry* 9, no. 11: 258.
https://doi.org/10.3390/sym9110258