Quantum Variational Algorithms for the Aircraft Deconfliction Problem
Pages 307 - 320
Abstract
Tactical deconfliction problem involves resolving conflicts between aircraft to ensure safety while maintaining efficient trajectories. Several techniques exist to safely adjust aircraft parameters such as speed, heading angle, or flight level, with many relying on mixed-integer linear or nonlinear programming. These techniques, however, often encounter challenges in real-world applications due to computational complexity and scalability issues. This paper proposes a new quantum approach that applies the Quantum Approximate Optimization Algorithm (QAOA) and the Quantum Alternating Operator Ansatz (QAOAnsatz) to address the aircraft deconfliction problem. We present a formula for designing quantum Hamiltonians capable of handling a broad range of discretized maneuvers, with the aim of minimizing changes to original flight schedules while safely resolving conflicts. Our experiments show that a higher number of aircraft poses fewer challenges than a larger number of maneuvers. Additionally, we benchmark the newest IBM quantum processor and show that it successfully solves four out of five instances considered. Finally, we demonstrate that incorporating hard constraints into the mixer Hamiltonian makes QAOAnsatz superior to QAOA. These findings suggest quantum algorithms could be a valuable algorithmic candidate for addressing complex optimization problems in various domains, with implications for enhancing operational efficiency and safety in aviation and other sectors.
References
[1]
Airports council international europe | aci europe - media 2024 (2024). https://www.aci-europe.org/media-room/477-passenger-traffic-reaches-nearly-95-of-pre-pandemic-levels-in-2023.html
[2]
Abbas, A., et al.: Quantum optimization: Potential, challenges, and the path forward. arXiv preprint arXiv:2312.02279 (2023)
[3]
Alonso-Ayuso A, Escudero LF, and Martín-Campo FJ Collision avoidance in air traffic management: a mixed-integer linear optimization approach IEEE Trans. Intell. Transp. Syst. 2010 12 1 47-57
[4]
Alonso-Ayuso A, Escudero LF, and Martín-Campo FJ Exact and approximate solving of the aircraft collision resolution problem via turn changes Transp. Sci. 2016 50 1 263-274
[5]
Bilimoria, K.: A geometric optimization approach to aircraft conflict resolution. In: 18th Applied Aerodynamics Conference, p. 4265 (2000)
[6]
Born M and Fock V Beweis des adiabatensatzes Z. Phys. 1928 51 3–4 165-180
[7]
Cafieri S and Durand N Aircraft deconfliction with speed regulation: new models from mixed-integer optimization J. Global Optim. 2014 58 613-629
[8]
Cafieri S and Omheni R Mixed-integer nonlinear programming for aircraft conflict avoidance by sequentially applying velocity and heading angle changes Eur. J. Oper. Res. 2017 260 1 283-290
[9]
Cerulli M, d’Ambrosio C, Liberti L, and Pelegrín M Detecting and solving aircraft conflicts using bilevel programming J. Global Optim. 2021 81 529-557
[10]
Chai, Y., Epifanovsky, E., Jansen, K., Kaushik, A., Kühn, S.: Simulating the flight gate assignment problem on a trapped ion quantum computer. arXiv preprint arXiv:2309.09686 (2023)
[11]
Farhi, E., Goldstone, J., Gutmann, S.: A quantum approximate optimization algorithm. arXiv preprint arXiv:1411.4028 (2014)
[12]
Grönkvist, M.: The tail assignment problem. Citeseer (2005)
[13]
Hadfield S On the representation of Boolean and real functions as Hamiltonians for quantum computing ACM Trans. Quantum Comput. 2021 2 4 1-21
[14]
Hadfield, S., Wang, Z., O’gorman, B., Rieffel, E.G., Venturelli, D., Biswas, R.: From the quantum approximate optimization algorithm to a quantum alternating operator ansatz. Algorithms 12(2), 34 (2019)
[15]
He Z et al. Alignment between initial state and mixer improves QAOA performance for constrained optimization NPJ Quantum Inf. 2023 9 1 121
[16]
Kuchar JK and Yang LC A review of conflict detection and resolution modeling methods IEEE Trans. Intell. Transp. Syst. 2000 1 4 179-189
[17]
Lehouillier T, Omer J, Soumis F, and Desaulniers G Two decomposition algorithms for solving a minimum weight maximum clique model for the air conflict resolution problem Eur. J. Oper. Res. 2017 256 3 696-712
[18]
Martins, L.N., Rocha, A.P., Castro, A.J.: A QUBO model to the tail assignment problem. In: ICAART (2), pp. 899–906 (2021)
[19]
Mohammadbagherpoor, H., et al.: Exploring airline gate-scheduling optimization using quantum computers. arXiv preprint arXiv:2111.09472 (2021)
[20]
Omer J A space-discretized mixed-integer linear model for air-conflict resolution with speed and heading maneuvers Comput. Oper. Res. 2015 58 75-86
[21]
Pallottino L, Feron EM, and Bicchi A Conflict resolution problems for air traffic management systems solved with mixed integer programming IEEE Trans. Intell. Transp. Syst. 2002 3 1 3-11
[22]
Pelegrín M and d’Ambrosio C Aircraft deconfliction via mathematical programming: review and insights Transp. Sci. 2022 56 1 118-140
[23]
Rey, D., Hijazi, H.: Complex number formulation and convex relaxations for aircraft conflict resolution. In: 2017 IEEE 56th Annual Conference on Decision and Control (CDC), pp. 88–93. IEEE (2017)
[24]
Spall JC An overview of the simultaneous perturbation method for efficient optimization J. Hopkins APL Tech. Dig. 1998 19 4 482-492
[25]
Stollenwerk T, Lobe E, and Jung M Feld S and Linnhoff-Popien C Flight gate assignment with a quantum annealer Quantum Technology and Optimization Problems 2019 Cham Springer 99-110
[26]
Stollenwerk T et al. Quantum annealing applied to de-conflicting optimal trajectories for air traffic management IEEE Trans. Intell. Transp. Syst. 2019 21 1 285-297
[27]
Vela, A., Solak, S., Singhose, W., Clarke, J.P.: A mixed integer program for flight-level assignment and speed control for conflict resolution. In: Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly with 2009 28th Chinese Control Conference, pp. 5219–5226. IEEE (2009)
[28]
Vikstål P, Grönkvist M, Svensson M, Andersson M, Johansson G, and Ferrini G Applying the quantum approximate optimization algorithm to the tail-assignment problem Phys. Rev. Appl. 2020 14 3
Recommendations
Applying the quantum approximate optimization algorithm to the minimum vertex cover problem
AbstractThe minimum vertex cover problem belongs to a NP- complete problem, which is difficult to obtain the near-optimal solution in the polynomial time range using classical algorithms. In this paper, a quantum circuit solution scheme based ...
Highlights- For MVCP, the QAOA-based quantum circuit solution scheme is proposed.
- The ...
Comments
Information & Contributors
Information
Published In
Jul 2024
433 pages
ISBN:978-3-031-63777-3
DOI:10.1007/978-3-031-63778-0
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
Publisher
Springer-Verlag
Berlin, Heidelberg
Publication History
Published: 02 July 2024
Author Tags
Qualifiers
- Article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 06 Oct 2024
Other Metrics
Citations
View Options
View options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in