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A mixed 0-1 nonlinear optimization model and algorithmic approach for the collision avoidance in ATM: velocity changes through a time horizon. (English) Zbl 1349.90641
Comput. Oper. Res. 39, No. 12, 3136-3146 (2012); addendum ibid. 40, No. 1, 520 (2013).
Summary: In this paper a mixed 0-1 nonlinear model for the Collision Avoidance problem in Air Traffic Management is presented. The aim of the problem consists of deciding the best strategy for an arbitrary aircraft configuration such that all conflicts in the airspace are avoided where a conflict is the loss of the minimum safety distance that two aircraft have to keep in their flight plans. The optimization model is based on geometric constructions. It requires knowing the initial flight plan (coordinates, angles and velocities in each period). The objective is the minimization of the acceleration variations when the aircraft are forced to return to the original flight plan once there is no aircraft in conflict. A linear approximation by using iteratively Taylor polynomials is presented to solve the problem in mixed 0-1 linear terms. An extensive computational experience for a testbed of large-scale instances is reported.

MSC:
90C11 Mixed integer programming
90C30 Nonlinear programming
90B20 Traffic problems in operations research
90C10 Integer programming
90C90 Applications of mathematical programming
Software:
CPLEX
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References:
[1] Almiñana, M.; Escudero, L.F.; Landete, M.; Monge, J.F.; Rabasa, A.; Sánchez-Soriano, J., On a mixed 0-1 separable nonlinear approach for water irrigation scheduling, IIE transactions, 44, 4, 398-405, (2008)
[2] Alonso-Ayuso, A.; Escudero, L.F.; Martín-Campo, F.J., Collision avoidance in the air traffic management: a mixed integer linear optimization approach, IEEE transactions on intelligent transportation systems, 12, 1, 47-57, (2011)
[3] Alonso-Ayuso A, Escudero LF, Olaso P, Pizarro C. Conflict avoidance: 0-1 linear models for conflict detection resolution. TOP, doi:10.1007/s11750-011-0224-6, in press. · Zbl 1276.90015
[4] Cafieri S, Brisset P, Durand N. A mixed-integer optimization model for air traffic deconfliction. In: Proceedings of TOGO (Toulouse Global Optimization). Toulouse, France; 2010. p. 27-30.
[5] Christodoulou MA, Costoulakis C. Nonlinear mixed integer programming for aircraft collision avoidance in free flight. In: IEEE Melecon 2004, Dubrovnik, Croacia, vol. 1; 2004. p. 327-30.
[6] Dell’Olmo, P.; Lulli, G., A new hierarchical architecture for air traffic management: optimization of airway capacity in a free flight scenario, European journal of operational research, 144, 179-193, (2003) · Zbl 1037.90536
[7] EUROCONTROL. Fasti ATC manual, \(\langle\)http://www.eurocontrol.int/fasti〉; 2011 [accessed January 2011].
[8] IBM ILOG. CPLEX v12.1. User’s Manual for CPLEX, 2009.
[9] Kuchar, J.K.; Yang, L.C., A review of conflict detection and resolution modeling methods, IEEE transactions on intelligent transportation systems, 1, 4, 179-189, (2000)
[10] Martín-Campo FJ. The collision avoidance problem: methods and algorithms. PhD thesis. Móstoles, Madrid, Spain: Department of Statistics and Operations Research, Rey Juan Carlos University; 2010.
[11] Pallottino, L.; Feron, E.; Bicchi, A., Conflict resolution problems for air traffic management systems solved with mixed integer programming, IEEE transactions on intelligent transportation systems, 3, 1, 3-11, (2002)
[12] Richards AG, How JP. Aircraft trajectory planning with collision avoidance using mixed integer linear programming. In: American control conference, Anchorage, Alaska, USA; 2002.
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