Ramazan Kürşat ÇEÇEN

Uçak Çakışma Saptama ve Çözümleme Problemi için Karma Tam Sayılı Doğrusal Programlama Modeli Yaklaşımı

Hava taşımacılığındaki talep artışı gerek hava sahalarında gerekse havaalanlarında ciddi trafik yoğunluğuna neden olmaktadır. Bu yoğunluk hem gecikmelere hem de uçaklar arasında çakışmalara neden olabilmektedir. Bu çalışmada, uçaklar arasında oluşacak çakışmaların önlenmesi amacıyla uçak çakışma saptama ve çözümleme konusu ele alınmış ve problemin çözümü için karma tam sayılı doğrusal programlama modeli önerilmiştir. Önerilen matematiksel modelin test edilmesi için bir referans durum üretilmiştir. Bu referans durum hava sahasında ilk gelen ilk hizmet alır prensibi ile çakışmaların çözümlenmesini sağlamaktadır. Önerilen model ile toplam gecikme süresi ve gecikmeden kaynaklı toplam yakıt tüketiminin en küçüklemesi amaçlanmıştır. Bu amaç fonksiyonları hem tek başlarına hem de birlikte ele alınarak oluşturulan referans durum ile karşılaştırılmıştır. Test problemlerinden elde edilen sonuçlara göre gecikmeden kaynaklı toplam yakıt tüketiminde ve toplam gecikme süresinde referans duruma göre %17,3 ve %3,2 oranlarında iyileşmeler meydana gelmiştir. Her iki amaç fonksiyonun birlikte ele alındığı durumda ise yakıt tüketiminde %15,2 oranında bir azalma saptanmıştır.

Anahtar Kelimeler:

Uçak çakışma saptama ve çözümleme, Hava trafik yönetimi, karma tam-sayılı doğrusal programlama, yakıt tüketimi, gecikme süresi

A Mixed Integer Linear Programming Approach for Aircraft Conflict Detection and Resolution Problem

An increasing demand in air transportation leads to a significant rise in traffic density both at airspaces and at airports. This rise in air traffic density may cause both delays and conflicts between aircraft pairs. Aircraft conflict detection and resolution problem is discussed in this study and a mixed integer linear programming model is proposed for this problem. A baseline case was generated to test the proposed mathematical model. The baseline case decides which aircraft receive delay for the resolution of conflicts, with the principle of the first come first served. The proposed model minimizes total delay time and total fuel consumption due to delay. These objectives were compared with the baseline considering the functions both individually and together. According to the results, the enhancement of the total fuel consumption due to delay and total delay duration are 17.3% and 3.2% compared to the baseline cases. When the two functions are considered together, 15.2% reduction in fuel consumption was obtained.

Keywords:

Aircraft conflict detection and resolution, air traffic management, mixed integer linear programming, fuel consumption, airborne delay,

PDF

___

Alonso-Ayuso, A., Escudero, L. F., & Martín-Campo, F. J. (2012). A mixed 0–1 nonlinear optimization model and algorithmic approach for the collision avoidance in ATM: Velocity changes through a time horizon. Computers & Operations Research, 39(12), 3136-3146.
Alonso-Ayuso, A., Escudero, L. F., & Martín-Campo, F. J. (2016). Exact and approximate solving of the aircraft collision resolution problem via turn changes. Transportation Science, 50(1), 263-274.
Alonso-Ayuso, A., Escudero, L. F., & Martín-Campo, F. J. (2016). An exact multi-objective mixed integer nonlinear optimization approach for aircraft conflict resolution. Top, 24(2), 381-408.
Cafieri, S., & Durand, N. (2014). Aircraft deconfliction with speed regulation: new models from mixed-integer optimization. Journal of Global Optimization, 58(4), 613-629.
Cafieri, S., & Omheni, R. (2017). Mixed-integer nonlinear programming for aircraft conflict avoidance by sequentially applying velocity and heading angle changes. European journal of operational research, 260(1), 283-290.
Cafieri, S., & Rey, D. (2017). Maximizing the number of conflict-free aircraft using mixed-integer nonlinear programming. Computers & Operations Research, 80, 147-158.
Cai, J., & Zhang, N. (2019). Mixed Integer Nonlinear Programming for Aircraft Conflict Avoidance by Applying Velocity and Altitude Changes. Arabian Journal for Science and Engineering, 44(10), 8893-8903.
Campo FJ. (2010). The collision avoidance problem: methods and algorithms. PhD Thesis, Universidad Rey Juan Carlos, Madrid, Spain
Carlier, J., Nace, D., Duong, V., & Nguyen, H. H. (2003). Using disjunctive scheduling for a new sequencing method in multiple-conflicts solving. In Proceedings of the 2003 IEEE International Conference on Intelligent Transportation Systems, Vol (1), 708-714.
Cecen, R. K., & Cetek, C. (2019). A Two-Step Approach for Airborne Delay Minimization Using Pretactical Conflict Resolution in Free-Route Airspace. Journal of Advanced Transportation, 2019.
Cecen, R. K., & Cetek, C. (2020). Conflict-free en-route operations with horizontal resolution manoeuvers using a heuristic algorithm. The Aeronautical Journal, 124(1275), 767-785.
Center, E. E. (2013). User manual for the base of aircraft data (BADA) revison 3.11. Brussels: Eurocontrol.
Christodoulou, M., & Costoulakis, C. (2004). Nonlinear mixed integer programming for aircraft collision avoidance in free flight. In Proceedings of the 12th IEEE Mediterranean Electrotechnical Conference, Vol (1), 327-330.
Hong, Y., Choi, B., Oh, G., Lee, K., & Kim, Y. (2017). Nonlinear conflict resolution and flow management using particle swarm optimization. IEEE Transactions on Intelligent Transportation Systems, 18(12), 3378-3387.
ICAO. Rules of the Air and Air Traffic Services, Air Traffic Management. 15th ed. (2007) Montreal, Canada: International Civil Aviation Organization Publications.
Kuchar, J. K., & Yang, L. C. (2000). A review of conflict detection and resolution modelling methods. IEEE Transactions on intelligent transportation systems, 1(4), 179-189.
Pallottino, L., Feron, E. M., & Bicchi, A. (2002). Conflict resolution problems for air traffic management systems solved with mixed integer programming. IEEE transactions on intelligent transportation systems, 3(1), 3-11.
Richards, A., & How, J. P. (2002). Aircraft trajectory planning with collision avoidance using mixed integer linear programming. In Proceedings of the 2002 American Control Conference, (3), 1936-1941.
Vela, A., Solak, S., Singhose, W. &Clarke, J.P. (2009). A mixed integer program for flight-level assignment and speed control for conflict resolution, In Proceedings of the 48th IEEE Conference on Decision and Control, 5219–5226