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Constraint programming for air traffic management: a survey1

In memory of Pascal Brisset

Published online by Cambridge University Press:  26 July 2012

Cyril Allignol ,
Nicolas Barnier ,
Pierre Flener  and
Justin Pearson
Cyril Allignol*
Affiliation:
École Nationale de l'Aviation Civile, 7 Avenue Édouard Belin, F—31055 Toulouse, France; e-mail: allignol@recherche.enac.fr, barnier@recherche.enac.fr
Nicolas Barnier*
Affiliation:
École Nationale de l'Aviation Civile, 7 Avenue Édouard Belin, F—31055 Toulouse, France; e-mail: allignol@recherche.enac.fr, barnier@recherche.enac.fr
Pierre Flener*
Affiliation:
Department of Information Technology, Uppsala University, Box 337, SE—751 05 Uppsala, Sweden; e-mail: Pierre.Flener@it.uu.se, Justin.Pearson@it.uu.se
Justin Pearson*
Affiliation:
Department of Information Technology, Uppsala University, Box 337, SE—751 05 Uppsala, Sweden; e-mail: Pierre.Flener@it.uu.se, Justin.Pearson@it.uu.se
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Abstract

Air traffic management (ATM) under its current paradigm is reaching its structural limits considering the continuously growing demand. The need for a decrease in traffic workload opens numerous problems for optimization, from capacity balancing to conflict solving, using many different degrees of freedom, such as re-routing, flight-level changes, or ground-holding schemes. These problems are usually of a large dimension (there are 30 000 daily flights in Europe in the year 2012) and highly combinatorial, hence challenging for current problem solving technologies. We give brief tutorials on ATM and constraint programming (CP), and survey the literature on deploying CP technology for modelling and solving combinatorial problems that occur in an ATM context.

Type
Articles
Information
The Knowledge Engineering Review , Volume 27 , Special Issue 3: Constraint Programming for Air Traffic Management , 26 July 2012 , pp. 361 - 392
Copyright
Copyright © Cambridge University Press 2012

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References

Aggoun, A., Beldiceanu, N. 1993. Extending CHIP in order to solve complex scheduling and placement problems. Mathematical and Computer Modelling 17(7), 57–73.CrossRefGoogle Scholar
Alliot, J.-M., Colin de Verdière, D. 2003. ATM: 20 ans d'effort et perspectives. In Symposium de l'Académie Nationale de l'Air et de l'Espace: vers l'automatisation du vol et sa gestion. Available at http://pom.tls.cena.fr/papers/articles/anae03.pdfGoogle Scholar
Alliot, J.-M., Durand, N., Granger, G. 2001. A statistical analysis of the influence of vertical and ground speed errors on conflict probe. In Proceedings of ATM'01, the 4th USA/Europe R&D Seminar on Air Traffic Management. Available at http://www.atmseminar.org/seminarContent/seminar4/papers/p_118_DSTCDM.pdfGoogle Scholar
Apt, K. R., Wallace, M. 2006. Constraint Logic Programming using ECLiPSe. Cambridge University Press.CrossRefGoogle Scholar
Artiouchine, K., Baptiste, P., Dürr, C. 2008a. Runway sequencing with holding patterns. European Journal of Operational Research 189 (3), 1254–1266. (Early version in Proceedings of the 2nd International Workshop on Discrete Optimization Methods in Production and Logistics, 96–101. Omsk–Irkutsk, Russia, 2004.).CrossRefGoogle Scholar
Artiouchine, K., Baptiste, P., Mattioli, J. 2008b. The k king problem, an abstract model for computing aircraft landing trajectories: on modeling a dynamic hybrid system with constraints. INFORMS Journal on Computing 20(2), 222–233.CrossRefGoogle Scholar
Baptiste, P., Le Pape, C., Nuijten, W. 2001. Constraint-based scheduling: applying constraint programming to scheduling problems. Kluwer Academic Publishers.CrossRefGoogle Scholar
Barnhart, C., Belobaba, P., Odoni, A. R. 2003. Applications of operations research in the air transport industry. Transportation Science 37(4), 368–391. Available at http://cassi.nuaa.edu.cn/download/paper/1148801073.pdfCrossRefGoogle Scholar
Barnier, N. 2002. Application de la programmation par contraintes à des problèmes de gestion du trafic aérien. PhD thesis, Institut National Polytechnique de Toulouse, France. Available at http://pom.tls.cena.fr/papers/thesis/barnier.pdfGoogle Scholar
Barnier, N., Allignol, C. 2009. 4D-trajectory deconfliction through departure time adjustment. In Proceedings of ATM'09, the 8th USA/Europe R&D Seminar on Air Traffic Management, Saunders-Hodge, S. & Duong, V. (eds). Available at http://www.atmseminar.org/seminarContent/seminar8/papers/p_143_NSTFO.pdfGoogle Scholar
Barnier, N., Allignol, C. 2011. Combining flight level allocation with ground holding to optimize 4D-deconfliction. In Proceedings of ATM'11, the 9th USA/Europe R&D Seminar on Air Traffic Management, Saunders-Hodge, S. & Duong, V. (eds). Available at http://www.atmseminar.org/seminarContent/seminar9/papers/157-Barnier-Final-Paper-4-5-11.pdfGoogle Scholar
Barnier, N., Allignol, C. 2012. Trajectory deconfliction with constraint programming. Knowledge Engineering Review 27, 291–307. Special Issue on Constraint Programming for Air Traffic Management.CrossRefGoogle Scholar
Barnier, N., Brisset, P. 2004. Graph coloring for air traffic flow management. Annals of Operations Research 130(1–4), 163–178.Google Scholar
Barnier, N., Brisset, P., Rivière, T. 2001. Slot allocation with constraint programming: models and results. In Proceedings of ATM'01, the 4th USA/Europe R&D Seminar on Air Traffic Management, McLaurin, H. (ed). Available at http://www.atmseminar.org/seminarContent/seminar4/papers/p_119_ITFODM.pdfGoogle Scholar
Bayen, A. M., Tomlin, C. J., Ye, Y., Zhang, J. 2004. An approximation algorithm for scheduling aircraft with holding time. In Proceedings of CDC'04, the 43rd IEEE Conference on Decision and Control, 3, 2760–2767. IEEE.CrossRefGoogle Scholar
Beldiceanu, N., Carlsson, M., Petit, T. 2004. Deriving filtering algorithms from constraint checkers. In Proceedings of CP'04, the 10th International Conference on Principles and Practice of Constraint Programming, LNCS, 3258, Wallace, M. (ed), 107–122. Springer-Verlag.Google Scholar
Beldiceanu, N., Carlsson, M., Rampon, J. X. 2007. Global constraint catalogue: past, present, and future. Constraints 12(1), 21–62. . Available at http://www.emn.fr/z-info/sdemasse/gccatCrossRefGoogle Scholar
Berge, M. E., Haraldsdottir, A., Scharl, J. 2006. The multiple runway planner (MRP): modeling and analysis for arrival planning. In Proceedings of DASC'06, the 25th Digital Avionics Systems Conference, 1–11. IEEE.CrossRefGoogle Scholar
Bertsimas, D., Stock Patterson, S. 1998. The air traffic flow management problem with enroute capacities. Operations Research 46(3), 406–422. Available at http://www.mit.edu/~dbertsim/papers/AirTransportation/The%20air%20traffic%20flow%20management%20problem%20with%20enroute%20capacities.pdfCrossRefGoogle Scholar
Bichot, C. E., Durand, N. 2007. A tool to design functional airspace blocks. In Proceedings of ATM'07, the 7th USA/Europe R&D Seminar on Air Traffic Management, Saunders-Hodge, S. & Duong, V. (eds). Available at http://www.atmseminar.org/seminarContent/seminar7/papers/p_169_DAM.pdfGoogle Scholar
Bleuzen-Guernalec, N., Colmerauer, A. 1997. Narrowing a 2n-block of sorting in O(n log n). In Proceedings of CP'97, the 3rd International Conference on Principles and Practice of Constraint Programming, LNCS, 1330, Smolka, G. (ed). Springer-Verlag.CrossRefGoogle Scholar
Bontemps, C., Guittet, K. 2004. Commentaires sur l’étude de l'Université de Westminster portant sur les coûts des délais ATC. Note technique, Centre d’Études de la Navigation Aérienne.Google Scholar
Boussemart, F., Hemery, F., Lecoutre, C., Sais, L. 2004. Boosting systematic search by weighting constraints. In Proceedings of ECAI'04, the 16th European Conference on Artificial Intelligence, López de Mántaras, R. & Saitta, L. (ed), 146–150. IOS Press.Google Scholar
Brisset, P., Rivière, T. 2005. Shortest path in planar graph and air route network. In Proceedings of INO'05, the 4th EUROCONTROL Innovative Research Workshop & Exhibition. Available at http://inoworkshop.eurocontrol.fr/Previous/index-53745.pdfGoogle Scholar
Carlsson, M., Ottosson, G., Carlson, B. 1997. An open-ended finite domain constraint solver. In Proceedings of PLILP'97, Glaser, H., Hartel, P. & Kuchen, H. (eds), LNCS, 1292, 191–206. Springer-Verlag.CrossRefGoogle Scholar
Central Flow Management Unit (CFMU). 2011. Basic CFMU Handbook—General & CFMU Systems, 15.0 edition. EUROCONTROL/Central Flow Management Unit. Available at http://www.cfmu.eurocontrol.int/cfmu/gallery/content/public/library/handbook_supplements/basic_handbook/docu_general_systems_latest.pdfGoogle Scholar
Chemla, D., Diaz, D., Kerlirzin, P., Manchon, S. 1995. Using CLP(FD) to support air traffic flow management. In Proceedings of PAP'95, the 3rd International Conference on Practical Applications of Prolog, Paris, France, Roth, A. & Marien, A. (eds). Alinmead Software Ltd.Google Scholar
Choco Team. 2010. Choco: An Open Source Java Constraint Programming Library. Research report 10-02-INFO, École des Mines de Nantes. Available at http://choco.emn.fr/Google Scholar
Central Office for Delay Analysis (CODA). 2009. CODA Digest—Delays to Air Transport in Europe. Technical report, EUROCONTROL—Central Office for Delay Analysis. Available at http://www.eurocontrol.int/sites/default/files/content/documents/official-documents/facts-and-figures/coda-reports/coda-reports-2009.zipGoogle Scholar
Cook, A. J., Tanner, G. 2009. The challenge of managing airline delay costs. In Summer School/Workshop on Air Traffic Management Economics, Belgrade, Serbia. Available at http://www.garsonline.de/Downloads/090910/Papers/Paper_Cook%20%20Tanner.pdfGoogle Scholar
Cook, A. J., Tanner, G., Anderson, S. 2004. Evaluating the true cost to airlines of one minute of airborne or ground delay: final report. Technical report, EUROCONTROL and University of Westminster. Available at http://westminsterresearch.wmin.ac.uk/17/1/Cook%2CTanner%2CAnderson_2004_final.pdfGoogle Scholar
Dalichampt, M., Petit, E., Junker, U., Lebreton, J. 2001. Innovative Slot Allocation: an overview. EEC Note No. 10/01, EUROCONTROL Experimental Centre, Brétigny, France. Available at http://www.eurocontrol.int/eec/gallery/content/public/document/eec/report/2001/016_Innovative_Slot_Allocation.pdfGoogle Scholar
Deau, R., Gotteland, J.-B., Durand, N. 2009. Airport surface management and runways scheduling. In Proceedings of ATM'09, the 8th USA/Europe R&D Seminar on Air Traffic Management, Saunders-Hodge, S. & Duong, V. (eds). Available at http://www.atmseminar.org/seminarContent/seminar8/papers/p_081_AO.pdfGoogle Scholar
Degrand, J., Mercier, E. 2000. Load Capacity Constraint Regulation. EEC Note 02/2000, EUROCONTROL Experimental Centre. Available at http://www.eurocontrol.int/eec/gallery/content/public/document/eec/report/2000/003_Load_Capacity_Constraint_Regulation.pdfGoogle Scholar
Delahaye, D., Alliot, J.-M., Schoenauer, M., Farges, J.-L. 1995. Genetic algorithms for automatic regroupment of air traffic control sectors. In Proceedings of the 4th Annual Conference on Evolutionary Programming (EP'95). Available at http://pom.tls.cena.fr/papers/articles/ep95.pdfGoogle Scholar
Delahaye, D., Schoenauer, M., Alliot, J.-M. 1998. Airspace sectoring by evolutionary computation. In Proceedings of the IEEE International Congress on Evolutionary Computation, 218–223. IEEE.Google Scholar
Duong, V., Gawinowski, G., Nicolaon, J.-P., Smith, D. 2001. Sector-less air traffic management. In Proceedings of ATM'01, the 4th USA/Europe R&D Seminar on Air Traffic Management, McLaurin, H. (ed). Available at http://www.atmseminar.org/seminarContent/seminar4/papers/p_158_NC.pdfGoogle Scholar
Duong, V. N., Hoffman, E., Nicolaon, J.-P. 1997. Initial results of investigation into autonomous aircraft concept (freer-1). In Proceedings of ATM'97, the 1st USA/Europe R&D Seminar on Air Traffic Management, Fron, X. & McLaurin, H. (eds). Available at http://www.atmseminar.org/seminarContent/seminar1/papers/p_018_ASSP.pdfGoogle Scholar
EUROCONTROL. 2011. As the Crow Flies—Free Route Airspace Maastricht. Available at http://www.eurocontrol.int/system/files/sites/default/files/content/documents/2011march-free-route-airspace-maastricht.pdfGoogle Scholar
FAA. 2011. NextGen Implementation Plan. Technical Report 202-493-4939, Federal Aviation Administration. Available at http://www.faa.gov/nextgen/media/ng2011_implementation_plan.pdfGoogle Scholar
Feydy, T., Barnier, N., Brisset, P., Durand, N. 2005. Mixed conflict model for air traffic control. In Interval Analysis, Constraint Propagation, Applications (IntCP 2005), a workshop of CP 2005. Available at http://pom.tls.cena.fr/papers/articles/intcp2005.pdfGoogle Scholar
Flener, P., Pearson, J., Ågren, M., Garcia Avello, C., Çeliktin, M., Dissing, S. 2007a. Air-traffic complexity resolution in multi-sector planning using constraint programming. In Proceedings of ATM'07, the 7th USA/Europe R&D Seminar on Air Traffic Management, Pusch, C. & Saunders-Hodge, S. (eds). Available at http://www.atmseminar.org/seminarContent/seminar7/papers/p_023_IAC.pdfGoogle Scholar
Flener, P., Pearson, J., Ågren, M., Garcia Avello, C., Çeliktin, M., Dissing, S. 2007b. Air-traffic complexity resolution in multi-sector planning. Journal of Air Transport Management 13(6), 323–328.Google Scholar
Freuder, E. C., Wallace, M. 2000. Constraint technology and the commercial world. IEEE Intelligent Systems 15(1), 20–23. Special Issue on Constraints.Google Scholar
Garcia de la Banda, M., Marriott, K., Rafeh, R., Wallace, M. 2006. The modelling language Zinc. In F. Benhamou, editor, Proceedings of CP'06, the 12th International Conference on Principles and Practice of Constraint Programming, LNCS, 4204, 700–705. Springer-Verlag.Google Scholar
Gecode Team. 2006. Gecode: a generic constraint development environment. Available at http://www.gecode.org/Google Scholar
Gianazza, D., Guittet, K. 2006. Selection and evaluation of air traffic complexity metrics. In Proceedings of DASC'06, the 25th Digital Avionics Systems Conference. IEEE. Available at http://pom.tls.cena.fr/papers/articles/dasc25_307giana.pdfGoogle Scholar
Gianazza, D., Alliot, J.-M., Granger, G. 2002. Optimal combinations of air traffic control sectors using classical and stochastic methods. In The 2002 International Conference on Artificial Intelligence IC-AI'02. Available at http://pom.tls.cena.fr/papers/articles/intl02_gianazza_alliot2.pdfGoogle Scholar
Glover, F., Laguna, M. 1993. Tabu search. In Modern Heuristic Techniques for Combinatorial Problems, Colin R. Reeves (ed). 70–150, John Wiley & Sons.Google Scholar
Gotlieb, A. 2012. TCAS software verification using constraint programming. Knowledge Engineering Review, this issue. Special Issue on Constraint Programming for Air Traffic Management.CrossRefGoogle Scholar
Granger, G., Durand, N., Alliot, J.-M. 2001. Optimal resolution of en route conflicts. In Proceedings of ATM'01, the 4th USA/Europe R&D Seminar on Air Traffic Management. Available at http://pom.tls.cena.fr/papers/articles/atm2001geraud.pdfGoogle Scholar
Granvilliers, L., Benhamou, F. 2006. Algorithm 852: RealPaver: an interval solver using constraint satisfaction technique. ACM Transactions on Mathematical Software 32(1), 138–156.CrossRefGoogle Scholar
Hassani Bijarbooneh, F., Flener, P., Pearson, J. 2009. Dynamic demand-capacity balancing for air traffic management using constraint-based local search: first results. In Proceedings of LSCS'09, the 6th International Workshop on Local Search Techniques in Constraint Satisfaction, Electronic Proceedings in Theoretical Computer Science, 5, Deville, Y. & Solnon, C. (eds), 27–40. Available at http://dx.doi.org/10.4204/EPTCS.5.3. (Also in: Schaefer, D. (ed), Proceedings of INO'09, the 8th EUROCONTROL Innovative Research Workshop & Exhibition, 2009).Google Scholar
Hildum, D. W., Smith, S. F. 2007. Constructing conflict-free schedules in space and time. In Proceedings of ICAPS'07, the 17th International Conference on Automated Planning and Scheduling, Boddy, M. S., Fox, M. & Thiébaux, S. (eds), 184–191. AAAI Press (Extended version in this volume).Google Scholar
Hildum, D. W., Smith, S. F. 2012. Scheduling safe movement of air traffic in crowded air spaces. Knowledge Engineering Review 27, 307–331. Special Issue on Constraint Programming for Air Traffic Management.Google Scholar
Hooker, J. N. 2007. Integrated Methods for Optimization. Springer-Verlag.Google Scholar
Hoos, H. H., Stützle, T. 2004. Stochastic Local Search: Foundations & Applications. Elsevier/Morgan Kaufmann.Google Scholar
International Civil Aviation Organization (ICAO). 1996. Procedures for air navigation services—rules of the air and air traffic services. Document 4444, International Civil Aviation Organization. Current edition available at http://store1.icao.int/documentItemView.ch2?ID=7139Google Scholar
ITA. 2000. Cost of Air Transport Delay in Europe, Paris, France. Available at http://www.eurocontrol.int/sites/default/files/content/documents/single-sky/pru/publications/other/cost-of-air-transport-delay-in-eu-ita.pdfGoogle Scholar
Jägare, P. 2011. Airspace Sectorisation Using Constraint Programming. Master's thesis, Uppsala University, Sweden, Report IT 11 021, Faculty of Science and Technology. Available at http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-155783Google Scholar
Junker, U. 2012. Air traffic flow management with heuristic repair. Knowledge Engineering Review, this issue. Special Issue on Constraint Programming for Air Traffic Management.Google Scholar
Kameugne, R., Fotso, L. P., Scott, J., Ngo-Kateu, Y. 2011. A quadratic edge-finding filtering algorithm for cumulative resource constraints. In Proceedings of CP'11, the 17th International Conference on Principles and Practice of Constraint Programming, LNCS, 6876, Lee, J. (ed), 478–492. Springer-Verlag.Google Scholar
Kerlirzin, P., Manchon, S., Plusquellec, C., Gotteland, J.-B. 2000. Building and evaluating a minimal regulation scheme. In Proceedings of ATM'00, the 3rd USA/Europe R&D Seminar on Air Traffic Management, Napoli, Italy, Saunders-Hodge, S. & Duong, V. (eds). Available at http://www.atmseminar.org/seminarContent/seminar3/papers/p_035_AMSMP.pdfGoogle Scholar
Kirkpatrick, S., Gelatt, C. D. Jr, Vecchi, M. P. 1983. Optimization by simulated annealing. Science 220(4598), 671–680.Google Scholar
Leal de Matos, P., Ormerod, R. 2000. The application of operational research to European air traffic flow management—understanding the context. European Journal of Operational Research 123(1), 125–144.Google Scholar
Leal de Matos, P., Powell, P. 2003. Decision support for flight re-routing in Europe. Decision Support Systems 34(4), 397–412.Google Scholar
Musialek, B., Munafo, C. F., Ryan, H., Paglione, M. 2010. Literature Survey of Trajectory Predictor Technology. Technical Report DOT/FAA-AJP-661, Federal Aviation Administration. Available at http://acy.tc.faa.gov/cpat/docs/SepMgmtResearchSurveyTechNoteFinalDeliveryNov2010.pdfGoogle Scholar
Pesant, G. 2004. A regular language membership constraint for finite sequences of variables. In Proceedings of CP'04, the 10th International Conference on Principles and Practice of Constraint Programming, LNCS, 3258, Wallace, M. (ed), 482–495. Springer-Verlag.Google Scholar
QinetiQ. 2004. Complexity Algorithm Development: the Algorithm. Technical report, EUROCONTROL EATMP Infocentre and QinetiQ.Google Scholar
Régin, J.-C. 1994. A filtering algorithm for constraints of difference in CSPs. In Proceedings of AAAI'94, the 12th (US) National Conference on Artificial Intelligence, Hayes-Roth, B. & Korf, R. E. (eds), 362–367. AAAI Press.Google Scholar
Régin, J.-C. 1996. Generalized arc-consistency for global cardinality constraint. In Proceedings of AAAI'96, the 13th (US) National Conference on Artificial Intelligence, Weld, D. & Clancey, B. (eds), 209–215. AAAI Press.Google Scholar
Rossi, F., van Beek, P., Walsh, T. 2006. Handbook of Constraint Programming. editors. Elsevier, 2006.Google Scholar
Schiex, T., Verfaillie, G. 1993. Nogood recording for static and dynamic constraint satisfaction problems. International Journal of Artificial Intelligence Tools 3, 48–55.Google Scholar
SESAR Consortium. 2007. SESAR Concept of Operations. Technical Report DLT-0612-222-01-00, SESAR Consortium. Available at http://www.eurocontrol.int/sites/default/files/content/documents/sesar/20070717-sesar-conops.pdfGoogle Scholar
STATFOR. 2010. EUROCONTROL Long-term Forecast: IFR Flight Movements 2010–2030. Technical Report 10/11/22-134, EUROCONTROL—Air Traffic Statistics and Forecasts, Brussels, Belgium. Available at https://www.eurocontrol.int/sites/default/files/content/documents/official-documents/forecasts/long-term-forecast-2010-2030.pdfGoogle Scholar
Sundequist Blomdahl, K., Flener, P., Pearson, J. 2010a. Contingency plans for air traffic management. In Proceedings of CP'10, the 16th International Conference on Principles and Practice of Constraint Programming, LNCS, 6308, Cohen, D. (ed), 643–657. Springer-Verlag.CrossRefGoogle Scholar
Sundequist Blomdahl, K., Flener, P., Pearson, J. 2010b. Contingency plans for air traffic flow and capacity management. In Proceedings of INO'10, the 9th EUROCONTROL Innovative Research Workshop & Exhibition, Schaefer, D. (ed). Available at http://inoworkshop.eurocontrol.fr/2010/download.php?pid=147_21277Google Scholar
Sundequist Blomdahl, K., Flener, P., Pearson, J. 2012. Contingency plans for air traffic flow and capacity management using constraint programming. Journal of Aerospace Operations 1, 249–266. IOS Press.CrossRefGoogle Scholar
Tran Dac, H., Baptiste, P., Duong, V. 2005. Airspace sectorization with constraints. RAIRO Operations Research 39(2), 105–122.Google Scholar
Van Hentenryck, P., Bent, R. 2006. Online Stochastic Combinatorial Optimization. MIT Press.Google Scholar
Van Hentenryck, P., Carillon, J.-P. 1988. Generality versus specificity: an experience with AI and OR techniques. In Proceedings of AAAI'88, the 7th (US) National Conference on Artificial Intelligence, Mitchell, T. & Smith, R. (eds), 660–664. AAAI Press.Google Scholar
Van Hentenryck, P., Michel, L. 2005. Constraint-Based Local Search. The MIT Press.Google Scholar
van Leeuwen, P., van Hanxleden Houwert, N. 2003. Scheduling aircraft using constraint relaxation. In Proceedings of the 22nd Workshop of the UK Planning and Scheduling Special Interest Group. Available at http://planning.cis.strath.ac.uk/plansig/pastsigs/glasgow-22/PimVanLeeuwen.pdf.gzGoogle Scholar
Vela, A., Solak, S., Féron, E., Feigh, K., Singhose, W., Clarke, J.-P. 2009. A fuel optimal and reduced controller workload optimization model for conflict resolution. In Proceedings of DASC'09, the 28th Digital Avionics Systems Conference. IEEE.Google Scholar
Villiers, J. 2004. Automatisation du contrôle de la circulation aérienne : ERASMUS—Une voie conviviale pour franchir le mur de la capacité, ITA études & documents, 58. Institut du Transport Aérien.Google Scholar
Wallace, M. 2007a. Hybrid algorithms in constraint programming. In Selected and Invited Papers of CSCLP'06 LNAI, 4651, Azevedo, F., Barahona, P., Fages, F. & Rossi, F. (eds), Springer-Verlag, 1–32.Google Scholar
Wallace, M. 2007b. Constraint programming—the paradigm to watch. Constraint Programming Letters 1, 7–13. Special Issue on the Next 10 Years of Constraint Programming. Available at http://www.constraint-programming.org/letters/Papers/v1/wallace.pdfGoogle Scholar