Skip to main content

Flight Gate Assignment with a Quantum Annealer

  • Conference paper
  • First Online:
Quantum Technology and Optimization Problems (QTOP 2019)


Optimal flight gate assignment is a highly relevant optimization problem from airport management. Among others, an important goal is the minimization of the total transit time of the passengers. The corresponding objective function is quadratic in the binary decision variables encoding the flight-to-gate assignment. Hence, it is a quadratic assignment problem being hard to solve in general. In this work we investigate the solvability of this problem with a D-Wave quantum annealer. These machines are optimizers for quadratic unconstrained optimization problems (QUBO). Therefore the flight gate assignment problem seems to be well suited for these machines. We use real world data from a mid-sized German airport as well as simulation based data to extract typical instances small enough to be amenable to the D-Wave machine. In order to mitigate precision problems, we employ bin packing on the passenger numbers to reduce the precision requirements of the extracted instances. We find that, for the instances we investigated, the bin packing has little effect on the solution quality. Hence, we were able to solve small problem instances extracted from real data with the D-Wave 2000Q quantum annealer.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 64.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others


  1. Bonabeau, E.: Agent-based modeling: methods and techniques for simulating human systems. Natl. Acad. Sci. 99, 7280–7287 (2002)

    Article  Google Scholar 

  2. Cai, J., Macready, W.G., Roy, A.: A practical heuristic for finding graph minors. arXiv preprint, June 2014.

  3. Classen, A.B., Rudolph, F.: Proactive passenger management with a total airport management perspective. In: Transportation Research Forum - TRF 2015, pp. 1–19, März 2015.

  4. Do, T.T.T.M., et al.: A hybrid quantum-classical approach to solving scheduling problems. In: Ninth Annual Symposium on Combinatorial Search (2016)

    Google Scholar 

  5. Garey, M.R., Johnson, D.S.: Computers and Intractability, vol. 29. WH Freeman, New York (2002)

    Google Scholar 

  6. Gleixner, A., et al.: The SCIP optimization suite 5.0. Technical report, Optimization Online, December 2017.

  7. Haghani, A., Chen, M.C.: Optimizing gate assignments at airport terminals. Transp. Res. Part A: Policy Pract. 32(6), 437–454 (1998)

    Google Scholar 

  8. Hammer, P.L., Rudeanu, S.: Boolean Methods in Operations Research and Related Areas, vol. 7. Springer, New York (2012).

    Book  MATH  Google Scholar 

  9. Jung, M., Classen, A.B., Rudolph, F., Pick, A., Noyer, U.: Simulating a multi-airport region to foster individual door-to-door travel. In: Winter Simulation Conference, pp. 2518–2529. IEEE (2017).

  10. Kim, S.H., Feron, E., Clarke, J.P., Marzuoli, A., Delahaye, D.: Airport gate scheduling for passengers, aircraft, and operations. J. Air Transp. 25(4), 109–114 (2017).

    Article  Google Scholar 

  11. Kügel, A.: Improved exact solver for the weighted max-sat problem. Pos@ sat 8, 15–27 (2010).

  12. Mangoubi, R., Mathaisel, D.F.: Optimizing gate assignments at airport terminals. Transp. Sci. 19(2), 173–188 (1985)

    Article  Google Scholar 

  13. McGeoch, C.C., Wang, C.: Experimental evaluation of an adiabiatic quantum system for combinatorial optimization. In: Proceedings of the ACM International Conference on Computing Frontiers, p. 23. ACM (2013)

    Google Scholar 

  14. Rieffel, E.G., Venturelli, D., O’Gorman, B., Do, M.B., Prystay, E.M., Smelyanskiy, V.N.: A case study in programming a quantum annealer for hard operational planning problems. Quant. Inf. Process. 14(1), 1–36 (2015)

    Article  Google Scholar 

  15. Stollenwerk, T., et al.: Quantum annealing applied to de-conflicting optimal trajectories for air traffic management. arXiv preprint (2017).

  16. Venturelli, D., Marchand, D.J.J., Rojo, G.: Quantum annealing implementation of job-shop scheduling. arXiv preprint, June 2015.

Download references


The authors would like to thank NASA Ames Quantum Artificial Intelligence Laboratory for their support during performing the experiments on the D-Wave 2000Q system, for many valuable discussions and the opportunity to use the D-Wave 2000Q machine at NASA Ames.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Tobias Stollenwerk .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Stollenwerk, T., Lobe, E., Jung, M. (2019). Flight Gate Assignment with a Quantum Annealer. In: Feld, S., Linnhoff-Popien, C. (eds) Quantum Technology and Optimization Problems. QTOP 2019. Lecture Notes in Computer Science(), vol 11413. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-14081-6

  • Online ISBN: 978-3-030-14082-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics