Skip to main content
SpringerLink
Log in

An exact multi-objective mixed integer nonlinear optimization approach for aircraft conflict resolution

  • Original Paper
  • Published:
TOP Aims and scope Submit manuscript

Abstract

An exact mixed integer nonlinear optimization (MINO) model is presented for tackling the aircraft conflict detection and resolution problem in air traffic management. Given a set of flights and their configurations, the aim of the problem was to provide new configurations such that all conflict situations are avoided, with conflict situation understood to mean an event in which two or more aircraft violate the minimum safety distances that must be maintained in flight. The proposed model solves the problem using both horizontal (velocity and angle turn change) and vertical (altitude level change) maneuvers. As a special case, another model is presented in which only horizontal maneuvers are used. The models proposed are based on a geometric construction which involves trigonometric functions, so the constraint system is included via a large set of trigonometric and nonconvex inequalities. A multicriteria approach is presented to provide useful information to air traffic control officers about the maneuvers to be performed. The main results of an extensive computational experiment are reported in which the performance of the state-of-the-art nonconvex MINO solver Minotaur is studied.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Alonso-Ayuso A, Escudero LF, Martín-Campo FJ (2011) Collision avoidance in the air traffic management: a mixed integer linear optimization approach. IEEE Trans Intell Transp Syst 12(1):47–57

    Article  Google Scholar 

  • Alonso-Ayuso A, Escudero LF, Martín-Campo FJ (2012) A mixed 0–1 nonlinear optimization model and algorithmic approach for the collision avoidance in ATM: velocity changes through a time horizon. Comput Oper Res 12(39):3136–3146

    Article  Google Scholar 

  • Alonso-Ayuso A, Escudero LF, Olaso P, Pizarro C (2013) Conflict avoidance: 0–1 linear models for conflict detection & resolution. TOP 21(3):485–504

    Article  Google Scholar 

  • Alonso-Ayuso A, Escudero LF, Martín-Campo FJ (2014) Exact and approximate solving of the aircraft collision resolution problem by turn changes. Transp Sci. doi:10.1287/trsc.2014.0557

    Google Scholar 

  • Alonso-Ayuso A, Escudero LF, Martín-Campo FJ (2014b) On modeling the air traffic control coordination in the collision avoidance problem by mixed integer linear optimization. Ann Oper Res 1(222):89–105

    Article  Google Scholar 

  • Alonso-Ayuso A, Escudero LF, Martín-Campo FJ, Mladenović N (2014c) A VNS metaheuristic for solving the aircraft conflict detection and resolution problem by performing turn changes. J Glob Optim. doi:10.1007/s10898-014-0144-8

    Google Scholar 

  • Alonso-Ayuso A, Escuedro LF, Martín-Campo FJ (2015) Multiobjective optimization for aircraft conflict resolution. A metaheuristic approach. Eur J Oper Res. doi:10.1016/j.ejor.2015.07.049

  • Bonini D, Dupré C, Granger G (2009) How ERASMUS can support an increase in capacity in 2020. In: Proceedings of the 7th international conference on computing, communications and control technologies, Orlando, USA

  • Cafieri S, Durand N (2013) Aircraft deconfliction with speed regulation: new models from mixed-integer optimization. J Glob Optim. doi:10.1007/s10898-013-0070-1

    Google Scholar 

  • Cetek C (2009) Realistic speed change maneuvers for air traffic conflict avoidance and their impact on aircraft economics. Int J Civ Aviat 1(1):62–73

    Google Scholar 

  • Chankong V, Haimes Y (1983) Multiobjective decision making: theory and methodology. North-Holland, New York

    Google Scholar 

  • Charnes A, Cooper W, Ferguson R (1955) Optimal estimation of executive compensation by linear programming. Manag Sci 1(2):138–151

    Article  Google Scholar 

  • Christodoulou MA, Costoulakis C (2004) Nonlinear mixed integer programming for aircraft collision avoidance in free flight. In: IEEE Melecon 2004, Dubrovnik, Croacia, vol 1, pp 327–330

  • Cochrane J, Zeleny M (1973) Multiple criteria decision making. University of South Carolina Press, Columbia

    Google Scholar 

  • Cohon J (1978) Multiobjective programming and planning. Academic Press, New York

    Google Scholar 

  • Dell’Olmo P, Lulli G (2003) A new hierarchical architecture for air traffic management: optimization of airway capacity in a free flight scenario. Eur J Oper Res 144:179–193

    Article  Google Scholar 

  • Durand N, Alliot J, Mèdioni F (2000) Neural nets trained by genetic algorithms for collision avoidance. Appl Intell 13:205–213

  • Escudero L (1995) Robust portfolios for mortgage-backed securities. In: Zenios SA (ed.) Quantitative methods, AI and supercomputers in finance, pp 201–228. Unicom, London

  • Eurocontrol (2010) Eurocontrol long-term forecast: IFR flight 2010–2030. Technical report, Eurocontrol-Air Traffic Statistics and Forecast

  • Frazzoli E, Mao ZH, Oh JH, Feron E (2001) Resolution of conflicts involving many aircraft via semidefinite programming. AIAA J Guid Control Dyn 24(1):79–86

    Article  Google Scholar 

  • Ignizio J (1985) Introduction to linear goal programming. Sage Publishing, Beverly Hills

    Google Scholar 

  • Jardin MR (2003) Toward real-time en route air traffic control optimization. PhD thesis, Stanford University, Palo Alto (CA), USA

  • Krozel J, Peters M (1997) Strategic conflict detection and resolution for free flight. In: Proceedings of the 36th conference on decision and control, pp 1822–1828

  • Kuchar JK, Yang LC (2000) A review of conflict detection and resolution modeling methods. IEEE Trans Intell Transp Syst 1(4):179–189

    Article  Google Scholar 

  • Leyffer S, Linderoth J, Luedtke J, Mahajan A, Munson T (2011) Minotaur solver. http://wiki.mcs.anl.gov/minotaur/index.php/MINOTAUR. Last Accessed October 2013

  • Martín-Campo FJ (2012) The collision avoidance problem: methods and algorithms. Lambert Academic Publishing, Germany

    Google Scholar 

  • Mavrotas G (2009) Effective implementation of the \(\varepsilon \)-constraint method in multi-objective mathematical programming problems. Appl Math Comput 213(2):455–465

    Google Scholar 

  • Omer J (2015) A space-discretized mixed-integer linear model for air-conflict resolution with speed and heading maneuvers. Comput Oper Res 58:75–86

    Article  Google Scholar 

  • Omer J, Farges J (2013) Hybridization of nonlinear and mixed-integer linear programming for aircraft separation with trajectory recovery. IEEE Trans Intell Transp Syst 14(3):1218–1230

    Article  Google Scholar 

  • Pallottino L, Feron E, Bicchi A (2002) Conflict resolution problems for air traffic management systems solved with mixed integer programming. IEEE Trans Intell Transp Syst 3(1):3–11

    Article  Google Scholar 

  • Peyronne C, Conn A, Mongeau M, Delahaye D (2015) Solving air-traffic conflict problems via local continuous optimization. Eur J Oper Res 241(2):502–512

    Article  Google Scholar 

  • Rey D, Rapine C, Fondacci R, Faouzi NE (2012) Minimization of potentials air conflicts through speed regulation. Transp Res Rec J Transp Res Board 2300:59–67

    Article  Google Scholar 

  • Richards AG, How JP (2002) Aircraft trajectory planning with collision avoidance using mixed integer linear programming. In: American control conference, Anchorage (Alaska), USA

  • Romero C (1991) Handbook of critical issues in goal programming. Pergamon Press, Oxford

    Google Scholar 

  • Sigurd K, How J (2003) Uav trajectory design using total field collision avoidance. In: AIAA guidance, navigation and control conference

  • Vela A, Solak S, Singhose W, Clarke J (2009) A mixed-integer program for flight level assignment and speed control for conflict resolution. In: Proceedings of the joint 48th IEEE conference on decision and control and 28th Chinese control conference, Shanghai. IEEE

  • Zeleny M (1982) Multicriteria decision making. McGraw-Hills, New York

    Google Scholar 

Download references

Acknowledgments

The authors gratefully acknowledge the help of Sven Leyffer of the Mathematics and Computer Science Division of the National Laboratory, Chicago, USA, in making available to us the latest version of his nonconvex MINO Minotaur engine. They would like to express their thanks to the two anonymous reviewers for their helpful and constructive comments and suggestions which clearly improved the final version of the paper. This research is partially supported by the projects OPTIMOS3 MTM2012-36163-C06-06 and PCDASO MTM2012-31514, both funded by the Spanish Ministry of Economy Affairs and Competitiveness.

Author information

Authors and Affiliations

  1. Área de Estadística e Investigación Operativa, Universidad Rey Juan Carlos, Móstoles, Madrid, Spain

    Antonio Alonso-Ayuso & Laureano F. Escudero

  2. Dpto. de Estadística e Investigación Operativa II (Métodos de Decisión), Universidad Complutense de Madrid, Madrid, Spain

    F. Javier Martín-Campo

Authors
  1. Antonio Alonso-Ayuso
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Laureano F. Escudero
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. Javier Martín-Campo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. Javier Martín-Campo.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alonso-Ayuso, A., Escudero, L.F. & Martín-Campo, F.J. An exact multi-objective mixed integer nonlinear optimization approach for aircraft conflict resolution. TOP 24, 381–408 (2016). https://doi.org/10.1007/s11750-015-0402-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11750-015-0402-z

Keywords

Mathematics Subject Classification

Search

Navigation