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研究生:段畯茗
研究生(外文):DUAN, JYUN-MING
論文名稱:最佳化方法用於求解帶有懲罰函數的 飛機著陸問題
論文名稱(外文):An Optimization Method for Aircraft Landing Problem with Generalized Penalty Functions
指導教授:黃曜輝黃曜輝引用關係
指導教授(外文):Huang, Yao-Huei
口試委員:葉承達盧浩鈞
口試委員(外文):Yeh, Cheng-TaLu, Hao-Chun
口試日期:2022-07-28
學位類別:碩士
校院名稱:輔仁大學
系所名稱:資訊管理學系碩士班
學門:電算機學門
學類:電算機一般學類
論文種類:學術論文
論文出版年:2022
畢業學年度:110
語文別:英文
論文頁數:53
中文關鍵詞:飛機著陸問題調度問題非線性懲罰目標函數線性化技術
外文關鍵詞:Aircraft landing problemscheduling problemnonlinear penalty functionslinearization technique
相關次數:
  • 被引用被引用:0
  • 點閱點閱:127
  • 評分評分:
  • 下載下載:12
  • 收藏至我的研究室書目清單書目收藏:0
本論文主要在研究飛機著陸問題(ALP),這是一個考慮每架飛機的著陸時間窗
以及每架飛機之間被要求間隔一定時間的條件下,求出每架飛機在可用跑道上最
佳著陸時間的調度問題。本研究以非線性懲罰目標函數做為衡量飛機著陸時間偏
差,進一步計算最小化的著陸時間偏差下,從而獲得飛機著陸的最佳時間表。本論
文所提出之方法在減少決策變量的使用和增加等式約束的數量,這也是一項新的
ALP 分段線性化技術,並且通過數據實驗以比較所提出模型和文獻模型之間的效
率差異。實驗結果還表明了對於飛機數量較多的案例而言,所提出的模型遠優於過
去的文獻方法模型。
This thesis studies the aircraft landing problem (ALP), which is a scheduling problem considering the landing time of aircraft onto an available runway with time window and separated time of each aircraft. The problem is to minimize the nonlinear penalty functions caused by the aircrafts’ landing time deviation such that the best schedule for aircraft landing is obtained. In this study, a new piecewise linearization technique for ALP by reducing the number of variables and increasing the number of equality constraints is proposed. Numerical experiments are conducted to compare the efficiency between the proposed models and reference models. The experimental results also show that the proposed models are superior to state-of-the-art reference models, especially for large scale cases.
Contents
List of Tables vi
List of Figures vii
1. Introduction 1
2. Reference Methods 5
3. Proposed Method and Models 17
3.1 Proposed Model 1 17
3.2 Proposed Model 2 21
3.3 Complexity Analysis 26
4. Numerical Experiments 28
5. Extension of Multi-Runways 30
6. Conclusion 35
References 36
Appendix 38
References
[1]Bazaraa, M.S., Sherali, H.D., Shetty, C.M. (1993). Nonlinear Programming Theory and Algorithms, 2nd ed., New York: Wiley.
[2]Beasley, J.E., Krishnamoorthy, M., Sharaiha, Y.M., Abramson, D. (2000). Scheduling aircraft landings—the static case. Transportation Science 34(2), 180-197. doi: 10.1287/trsc.34.2.180.12302
[3]Bencheikh, G., Boukachour, J., Alaoui, A.E.H. (2011). Improved ant colony algorithm to solve the aircraft landing problem. International Journal of Computer Theory and Engineering 3(2), 224-233.
[4]Dantzig, G.B. (1960). On the significance of solving linear-programming problems with some integer variables. Econometrica 28(1), 30–44. doi: 10.2307/1905292
[5]Farah, I., Kansou, A., Yassine, A., Galinho, T. (2011). Ant colony optimization for aircraft landings. 2011 4th International Conference on Logistics, 235-240. doi: 10.1109/LOGISTIQUA.2011.5939296
[6]Faye, A. (2015). Solving the aircraft landing problem with time discretization approach. European Journal of Operational Research 242(3), 1028-1038. doi: 10.1016/j.ejor.2014.10.064
[7]Hillier, F.S., Lieberman, G.J. (1995). Introduction to Operations Research, 6th ed., New York: McGraw-Hill.
[8]Hwang, F.J. and Huang, Y.H. (2021). An effective logarithmic formulation for piecewise linearization requiring no inequality constraint. Computational Optimization and Applications 79(3), 601-631. doi: 10.1007/s10589-021-00285-4
[9]Irion, J., Lu, J.C., Al-Khayyal, F., Tsao, Y.C. (2012). A piecewise linearization framework for retail shelf space management models. European Journal of Operational Research 222(1), 122-136. doi: 10.1016/j.ejor.2012.04.021
[10]Lieder, A., Briskorn, D., Stolletz R. (2015). A dynamic programming approach for the aircraft landing problem with aircraft classes. European Journal of Operational Research 243(1), 61-69. doi: 10.1016/j.ejor.2014.11.027
[11]Liu, Y.H. (2011). A genetic local search algorithm with a threshold accepting mechanism for solving the runway dependent aircraft landing problem. Optimization Letters 5(2), 229-245. doi: 10.1007/s11590-010-0203-0
[12]Pinol, H., Beasley, J.E. (2006). Scatter search and bionomic algorithms for the aircraft landing problem. European Journal of Operational Research 171(2), 439-462. doi: 10.1016/j.ejor.2004.09.040
[13]Tavakkoli-Moghaddam, R., Yaghoubi-Panah, M., Radmehr, F. (2012). Scheduling the sequence of aircraft landings for a single runway using a fuzzy programming approach. Journal of Air Transport Management 25, 15-18. doi: 10.1016/j.jairtraman.2012.03.004
[14]Vielma, J.P., Nemhauser, G.L. (2011). Modeling disjunctive constraints with a logarithmic number of binary variables and constraints. Mathematical Programming 128(1), 49–72. doi: 10.1007/s10107-009-0295-4
[15]Xie, J., Zhou, Y., Zheng, H. (2013). A hybrid metaheuristic for multiple runways aircraft landing problem based on bat algorithm. Journal of Applied Mathematics 2013, 742653. doi: 10.1155/2013/742653

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