Call For Papers
Contact Us

  Hopfield Neural Networks for Aircrafts’ Enroute Sectoring: KRISHAN-HOPES  
  Authors : Dr. Krishan Kumar
  Cite as:


Air traffic controlling is a very complex task for the air port personnel. Hence the emphasis on some new advance computing techniques had always been a great and important area of research. Hopfield neural networks or simply Hopfield nets, a widely used popular category of feedback neural network or recurrent neural networks may play a very important role in handling issues related to air traffic control. As Hopfield nets provide a model for the memory of human brain and therefore they can memorize the input patterns of any real life problem. Hence these nets can be efficiently and effectively used for the air space sectoring problem. In this paper, a way to divide the existing space scenario in different sectors using Hopfield nets is presented. It is found that this method is appropriate for making the sectors of a congested busy air space. The result shows that algorithm gives the near optimal solution for 48 nodes or aircrafts.


Published In : IJCSN Journal Volume 5, Issue 1

Date of Publication : February 2016

Pages : 149-156

Figures :07

Tables : 01

Publication Link : Hopfield Neural Networks for Aircrafts’ Enroute Sectoring: KRISHAN-HOPES




Dr Krishan Kumar : is Assistant Professor in the Department of Computer Science, Faculty of Technology, Gurukula Kangri University, Haridwar, Uttarakhand, India. His area of interest is artificial neural networks (ANN) and its applications. He obtained his M.C.A degree from IMS Ghaziabad, India and Ph. D.(CS & IT) from Institute of Engineering & Technology, M.J.P.Rohilkhand University, Bareilly. He has also qualified National Eligibility Test (UGC-NET) in Computer Science and Application. Dr. Kumar has authored more than 30 research papers in international/national Journals/ Conferences. Presently he is vice chairman of Computer Society of India, Haridwar Chapter and elected Chairman for the session 2016- 17. He has also been working as reviewer for many reputed journals like Elsevier, Springer etc. for last 10 years.








Artificial Neural Network

Hopfield Network

Air Space

Collision Avoidance


Consequently I have simulated the results for the 48 aircrafts flying in the air at same height and same horizontal plane. In “Table 1” only 24 binary patterns are shown. Next 24 patterns i.e from 25 to 48 shall be converted on the same pattern. Earlier they were in congestion due to crossing the limit of maximum possible aircrafts in a sector. Hopfield neural net has been successfully applied and implemented using MATLAB; and It seems suitable for solving the aircrafts’ space congestion problem. The problem of enroute congestion is similar to the most popular operation research travelling salesman problem (TSP). Hence the division of aircrafts into different sectors on the basis of their positions can also be done.










[1] Bowers, Peter M., Boeing Aircraft since 1916, ISBN 0-85177-804-6, London: Putnam Aeronautical Books, 1989. [2] E.P Gilbo, “Optimizing airport capacity utilization in air traffic flow management subject to constraints at arrival and departure fixes”, IEEE Transactions on Control Systems Technology, Vol. 5, no. 5, sep. 1997. [3] K. Kumar, R. Singh, Z. Khan, and A. Indian, “Air Traffic Runway Allocation Problem Using ARTMAP (ART1)”, Ubiquitous Computing and Communication International Journal, Korea, Vol. 3, No 3, July, 2008, pp. 130-136. [4] Min Xue, “Airspace Sector Redesign Based on Voronoi Diagrams”, University of California at Santa Cruz, Moffett Field, CA 94035, 2008. [5] Daniel Delahaye, Jean-Marc Alliot, Marc Schenauer, and Jean-Loup Farges, “Genetic algorithms for partitioning air space”, Proceedings of the 10th Conference on Artificial Intelligence and Application, IEEE, 1-4 Mar 1994, pp. 291 – 297. [6] D. Delahaye, M. Schoenauer and J. M. Alliot, “Airspace sectoring by evolutionary computation”, Evolutionary Computation Proceeding by IEEE World Congress on Computational Intelligence, IEEE International Conference on Vol., Issue, 4-9 May 1998. [7] B. Pesic and D. Delahaye, Daily Operational airspace sector grouping. April 27, 1999. [8] O babic and T Kristic, “Airspace daily operational Sectorization by fuzzy logic”, Elsevier, 2000. [9] Riley, V. Chatterji, G. Johnson, W. Mogford, R. Kopardekar, P. Sieira, E. Landing, and M. Lawton, G. “Pilot Perceptions of Airspace Complexity”, Part-2, Digital Avionics Systems Conference. DASC 04, IEEE, 2004. [10] Laurene Fausett, Fundamentals of Neural networks: Architecture, Algorithm and Applications, Pearson Education, ISBN 978-81-317-0053, 1994. [11] Krishan Kumar, “ART1 Neural Networks for Air Space Sectoring”, International Journal of Computer Applications, USA, 2012, pp. 20 – 24. [12] Krishan Kumar, “Self Organizing Map (SOM) Neural Networks For Air Space Sectoring”, in IEEE International Conference Computational Intelligence & Communication Networks, Udaipur, India, 17-18, Nov’2014. [13] K. Kumar, R. Singh, Z. Khan, “Air Traffic Enroute Conflict Detection Using Adaptive Resonance Theory Map Neural Networks (ART1)”, Ubiquitous Computing and Communication International Journal, Korea, Vol. 3, No 3, July, 2008, pp. 28-35. [14] D. Klingman and J. M. Mulvey editors, Network models and associated applications, North Holland, ISBN: 0-444-86203-X, 1981. [15] Gilbert Saporta, Probabilistic analysis of statistic techniques, 1990. [16] P.L. Tuan, H.S. Procter, and G.J. Couluris, “Advanced productivity analysis methods for air traffic control operations”, FAA report RD-76-164, Standford Research Institute, Mento Park CA 94025. December 1976. [17] Chung-Kuan Cheng, “The optimal partitioning of networks”, Networks, 22:297-315, 1992. [18] Lester Ingber and Bruce Rosen, “Genetic Algorithm and fast simulated re-annealing: a comparison”, Mathematical and Computer Modeling, 16(1):87-100, 1992. [19] Kevin, An Introduction to Neural Networks: Routledge. ISBN 1857285034, 2002. [20] “Neural networks and physical systems with emergent collective computational abilities”, Proceedings of the National Academy of Sciences, 1982, pp. 2554-2558. [21] “Neurons with graded response have collective computational properties like those of two-state neurons”, Proceedings of the National Academy of Sciences, 1984, pp. 81:3088-3092.