Skip to main content
SpringerLink
Log in

Commercial Aircraft Trajectory Optimization to Reduce Flight Costs and Pollution: Metaheuristic Algorithms

  • Chapter
  • First Online:
Advances in Visualization and Optimization Techniques for Multidisciplinary Research

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Abstract

Aircraft require significant quantities of fuel in order to generate the power required to sustain a flight. Burning this fuel causes the release of polluting particles to the atmosphere and constitutes a direct cost attributed to fuel consumption. The optimization of various aircraft operations in different flight phases such as cruise and descent, as well as terminal area movements, have been identified as a way to reduce fuel requirements, thus reducing pollution. The goal of this chapter is to briefly explain and apply different metaheuristic optimization algorithms to improve the cruise flight phase cost in terms of fuel burn. Another goal is to present an overview of the most popular commercial aircraft models. The algorithms implemented for different optimization strategies are genetic algorithms, the artificial bee colony, and the ant colony algorithm. The fuel burn aircraft model used here is in the form of a Performance Database. A methodology to create this model using a Level D aircraft research flight simulator is briefly explained. Weather plays an important role in flight optimization, and so this work explains a method for incorporating open source weather. The results obtained for the optimization algorithms show that every optimization algorithm was able to reduce the flight consumption, thereby reducing the pollution emissions and contributing to airlines’ profit margins.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Abbreviations

h (ft):

Altitude

Pij:

Ants decision parameter

Bg (ft, Mach or degrees):

Best global trajectory’s position

P:

Bilinear interpolation weight

va (kts or Kelvin):

Bilinear value to interpolate

Dr (N):

Drag

Rm (m):

Earth radio

eij (hrs):

Flight Time difference

F (kg):

Fuel burn

Fij (kg):

Fuel burn for a given segment ij

Cons (kg):

Fuel consumption

ff (kg/hr):

Fuel flow

g (m/s2):

Gravity

GS (kts):

Ground Speed

L (N):

Lift

m (kg):

Mass

c1:

Particle influence towards the global leader

c2:

Particle influence towards the local leader

D (Mach, degrees, ft):

Particle’s displacement

X (Mach, degrees, ft):

Particle’s position

C:

Pheromone

R2:

Random parameter related to the global leader

R1:

Random parameter related to the local leader

Rω:

Random parameter related to the particle’s inertia

v (kts):

South wind

Bl (ft, Mach or degrees):

Best local trajectory’s position

Th (N):

Thrust

VTAS (kts):

True Air Speed

w (kts):

Vertical wind

u (kts):

West wind

wd (kts):

Wind rates parallel to the aircraft

χHDG (deg):

Aircraft azimuth

α:

Algorithm convergence parameter

β:

Algorithm convergence parameter

ϕ (deg):

Latitude

λ (deg):

Longitude

ω:

Particle’s inertia

γ:

Pheromone evaporation rate

γTAS (deg):

Pitch

μTAS (deg):

Roll

η:

Thrust-specific fuel consumption

References

  1. ATAG (2016) Aviation benefits beyond borders. Air Transport Action Group, Geneva, Switzerland, July (2016). https://aviationbenefits.org/

  2. Crutzen PJ (1970) The influence of nitrogen oxides on the atmospheric ozone content. QJR Meteorol Soc 96:320–325. http://dx.doi.org/10.1002/qj.49709640815

    Article  Google Scholar 

  3. Robinson E (1978) Hydrocarbons in the atmosphere. Pure appl Geophys 116:372–384. https://doi.org/10.1007/bf01636892

    Article  Google Scholar 

  4. Black DA, Black JA, Issarayangyun T, Samuels SE (2007) Aircraft noise exposure and resident’s stress and hypertension: a public health perspective for airport environmental management. J Air Transp Manag 13:264–276. https://doi.org/10.1016/j.jairtraman.2007.04.003

    Article  Google Scholar 

  5. Clarke JP, Brooks J, Nagle G, Scacchioli A, White W, Liu SR (2013) Optimized profile descent arrivals at los angeles international airport. J Aircr 50(2):360–369. http://dx.doi.org/10.2514/1.c031529

    Article  Google Scholar 

  6. Kwok-On T, Anthony W, John B (2003) Continuous descent approach procedure development for noise abatement tests at louisville international airport, KY. In: AIAA’s 3rd annual aviation technology, integration, and operations (ATIO) Forum

    Google Scholar 

  7. ICAO (2010) Aviation’s contribution to climate change. International Civil Aviation Organization, Montreal

    Google Scholar 

  8. IATA (2009) Beginner’s guide to aviation biofuels. International Air Transport Association, Geneva, Switzerland

    Google Scholar 

  9. McConnachie D, Wollersheim C, Hansman RJ (2013) The impact of fuel price on airline fuel efficiency and operations. In: Aviation Technology, Integration, and Operations Conference, Los Angeles, CA

    Google Scholar 

  10. Jensen L, Tran H, Hansman JR (2015) Cruise fuel reduction potential from altitude and speed optimization in global airline operations. Presented at the Eleventh USA/Europe air traffic management research and development seminar (ATM2015), Lisbon, Portugal,

    Google Scholar 

  11. Jensen L, Hansman JR, Venuti J, Reynolds T (2014) Commercial airline altitude optimization strategies for reduced cruise fuel consumption. In: 14th AIAA aviation technology, integration, and operations conference, Atlanta, GA. http://dx.doi.org/10.2514/6.2014-3006

  12. Jensen L, Hansman JR, Venuti JC, Reynolds T (2013) Commercial airline speed optimization strategies for reduced cruise fuel consumption. Presented at the 2013 aviation technology, integration, and operations conference, Los Angeles, USA. http://dx.doi.org/10.2514/6.2013-4289

  13. Turgut ET, Cavcar M, Usanmaz O, Canarslanlar AO, Dogeroglu T, Armutlu K, et al (2014) Fuel flow analysis for the cruise phase of commercial aircraft on domestic routes. Aerosp Sci Technol 37:1–9. http://dx.doi.org/10.1016/j.ast.2014.04.012

    Article  Google Scholar 

  14. Murrieta-Mendoza A, Botez RM, Ford S (2016) New method to compute the missed approach fuel consumption and its emissions. Aeronaut J 120(1228):910–929. http://dx.doi.org/10.1017/aer.2016.37

    Article  Google Scholar 

  15. Lovegren JA (2011) Quantification of fuel burn reduction in cruise via speed and altitude optimization strategies. Massachusetts Institute of Technology Cambridge, MA 02139 USA. https://dspace.mit.edu/handle/1721.1/97360

  16. Bonami P, Olivares A, Soler M, Staffetti E (2014) Multiphase mixed-integer optimal control approach to aircraft trajectory optimization. J Guid Control Dyn 36(5):1267–1277. https://doi.org/10.2514/1.60492

    Article  Google Scholar 

  17. Cobano JA, Alejo D, Heredia G, Ollero A (2013) 4D trajectory planning in ATM with an anytime stochastic approach. In: Proceedings of the 3rd international conference on application and theory of automation in command and control systems, Naples, Italy. 978-1-4503-2249-2, http://dx.doi.org/10.1145/2494493.2494494

  18. Korn B, Helmke H, Kuenz A (2006) 4D trajectory management in the extended TMA: coupling AMAN And 4D FMS for optimized approach trajectoreis. In: 25th congress of international council of the aeronautical sciences, Hamburg, Germany. 0-9533991-7-6

    Google Scholar 

  19. Soler-Arnedo M, Hansen M, Zou B, Contrail sensitive 4D trajectory planning with flight level allocation using multiphase mixed-integer optimal control. In: AIAA guidance, navigation, and control (GNC) conference, 2013. Los Angeles, CA, http://dx.doi.org/10.2514/6.2013-5179

  20. Tsotskas C, Kipouros T, Savill M, Biobjective optimisation of preliminary aircraft trajectories. In: Evolutionary multi-criterion optimization vol 7811. Springer Berlin Heidelberg, 2013 pp. 741–755

    Google Scholar 

  21. Valenzuela A, Rivas D (2014) Optimization of aircraft cruise procedures using discrete trajectory patterns. J Aircr 51:1632–1640. https://doi.org/10.2514/1.C032041

    Article  Google Scholar 

  22. Rippel E, Bar-Gill A, Shimkin N (2005) Fast graph-search algorithms for general-aviation flight trajectory generation. J Guid Control Dyn 28:801–811. https://doi.org/10.2514/1.7370

    Article  Google Scholar 

  23. Dicheva S, Bestaoui Y (2014) Three-Dimensional A* dynamic mission planning for an airborne launch vehicle. J Aerosp Inf Syst 11:98–106. http://dx.doi.org/10.2514/1.I010070

    Article  Google Scholar 

  24. Felix Patron RS, Botez RM, Labour D (2013) New altitude optimisation algorithm for the flight management system CMA-9000 improvement on the A310 and L-1011 aircraft. Aeronaut J 117(117):787–805. https://doi.org/10.1017/S0001924000008459

    Article  Google Scholar 

  25. Gagné J, Murrieta-Mendoza A, Botez R, Labour D (2013) New method for aircraft fuel saving using flight management system and its validation on the L-1011 aircraft. In: 2013 Aviation Technology, Integration, and Operations Conference, Los Angeles, CA. http://dx.doi.org/10.2514/6.2013-4290

  26. Murrieta-Mendoza A, Botez RM (2014) Vertical navigation trajectory optimization algorithm for a commercial aircraft. AIAA/3AF Aircraft Noise and Emissions Reduction Symposium, June 16–20 http://dx.doi.org/10.2514/6.2014-3019

  27. Dancila B, Botez RM, Labour D (2013) Fuel burn prediction algorithm for cruise, constant speed and level flight segments. Aeronaut J 117(1191):491–504

    Article  Google Scholar 

  28. Murrieta-Mendoza A, Beuze B, Ternisien L, Botez R (2015) Branch & bound-based algorithm for aircraft VNAV profile reference trajectory optimization. In: 15th AIAA aviation technology, integration, and operations conference, aviation forum, Dallas, TX, USA. 978-1-5108-0818-8. http://dx.doi.org/10.2514/6.2015-2280

  29. Murrieta-Mendoza A, Botez RM (2015) Aircraft vertical route optimization deterministic algorithm for a flight management system. Presented at the SAE AeroTech Congress & Exhibition, Seattle, USA. http://dx.doi.org/10.4271/2015-01-2541

  30. Ng HK, Sridhar B, Grabbe S (2014) Optimizing aircraft trajectories with multiple cruise altitudes in the presence of winds. J Aerosp Inf Syst 11:35–47. https://doi.org/10.2514/1.I010084

    Article  Google Scholar 

  31. Hagelauer P, Mora-Camino F (1998) A soft dynamic programming approach for on-line aircraft 4D-trajectory optimization. Eur J Oper Res 107:87–95. https://doi.org/10.1016/S0377-2217(97)00221-X

    Article  MATH  Google Scholar 

  32. Miyazawa Y, Wickramasinghe NK, Harada A, Miyamoto Y (2013) Dynamic programming application to airliner four dimensional optimal flight trajectory. In: AIAA guidance, navigation, and control (GNC) conference, Boston, USA (2013). http://dx.doi.org/10.2514/6.2013-4969

  33. Bronsvoort J (2014) Contributions to trajectory prediction theory and its application to arrival management for air traffic control. Ph. D. Escuela Tecnica Superior de Ingenieros de Telecomunicacion, Universidad Politecnica de Madrid

    Google Scholar 

  34. Murrieta-Mendoza A, Demange S, George F, Botez RM (2015) Performance database creation using a flight D simulator for cessna citation X aircraft in cruise regime. In: The 34th IASTED international conference on modelling, identification, and control (MIC2015), Innsbruck, Austria. http://dx.doi.org/10.2316/P.2015.826-028

  35. Ghazi G, Botez RM, Tudor M (2015) Performance database creation for cessna citation X aircraft in climb regime using an aero-propulsive model developed from flight tests. Presented at the AHS sustainability, Montreal, Canada

    Google Scholar 

  36. Kimlberlin R (2003) Flight testing of fixed-wing aircraft, 1st edn. AIAA, Reston, Virginia

    Book  Google Scholar 

  37. Ghazi G, Tudor M, Botez R (2015) Identification of a cessna citation X aero-propulsive model in climb regime from flight tests. Presented at the international conference on air transport INAIR, Amsterdam, the Netherlands

    Google Scholar 

  38. Murrieta-Mendoza A, Botez RM (2014) Method to calculate aircraft VNAV trajectory cost using a performance database. In: International mechanical engineering congress & exposition, montreal, Canada. 978-0-7918-4642-1, http://dx.doi.org/10.1115/IMECE2014-37568

  39. Murrieta-Mendoza A, Botez RM (2015) Methodology for vertical-navigation flight-trajectory cost calculation using a performance database. J Aerosp Inf Syst 12:519–532. https://doi.org/10.2514/1.I010347

    Article  Google Scholar 

  40. Félix Patrón RS, Schindler M, Botez RM (2015) Aircraft trajectories optimization by genetic algorithms to reduce flight cost using a dynamic weather model. In: 15th AIAA aviation technology, integration, and operations conference, Dallas, TX

    Google Scholar 

  41. Félix-Patrón RS, Kessaci A, Botez R (2014) Horizontal flight trajectories optimisation for commercial aircraft through a flight management system. Aeronaut J 118(1210):1499–1518. https://doi.org/10.1017/S0001924000010162

    Article  Google Scholar 

  42. Sridhar B, Ng H, Chen N (2013) Aircraft trajectory optimization and contrails avoidance in the presence of winds. J Guid Control Dyn 34:1577–1584. https://doi.org/10.2514/1.53378

    Article  Google Scholar 

  43. Murrieta-Mendoza A (2013) Vertical and lateral flight optimization algorithm and missed approach cost calculation. Master, École de Technologie Supérieure, Montreal

    Google Scholar 

  44. Félix-Patrón RS, Botez RM (2015) Flight trajectory optimization through genetic algorithms for lateral and vertical integrated navigation. J Aerosp Inf Syst 12:533–544. http://dx.doi.org/10.2514/1.I010348

    Article  Google Scholar 

  45. Félix-Patrón RS, Berrou Y, Botez RM (2014) New methods of optimization of the flight profiles for performance database-modeled aircraft. Proceedings of the institution of mechanical engineers, Part G: J Aerosp Eng 229(10):1853–1867. http://dx.doi.org/10.1177/0954410014561772

    Article  Google Scholar 

  46. Sidibe S, Botez RM (2013) Trajectory optimization of FMS-CMA 9000 by dynamic programming. Presented at the ASI AÉRO 2013 conference, 60th Aeronautics Conference and AGM, Toronto, Canada

    Google Scholar 

  47. Felix-Patron RS, Botez RM, Labour D (2012) Vertical profile optimization for the flight management system CMA-9000 using the golden section search method. Presented at the IECON 2012—38th Annual Conference on IEEE, Montreal, QC. https://doi.org/10.1109/iecon.2012.6389517

  48. Murrieta-Mendoza A, Félix-Patrón RS, Botez RM (2015) Flight Altitude Optimization Using Genetic Algorithms Considering Climb and Descent Costs in Cruise with Flight Plan Information,” presented at the SAE AeroTech Congress & Exhibition, Seattle, USA, 2015. http://dx.doi.org/10.4271/2015-01-2542

  49. Murrieta-Mendoza A, Botez RM (2014) Lateral navigation optimization considering winds and temperatures for fixed altitude cruise using The Dijkstra’s algorithm. In: International mechanical engineering congress & exposition, Montreal, Canada. http://dx.doi.org/10.1115/IMECE2014-37570

  50. Murrieta-Mendoza A, Romain C, Botez RM (2016) Commercial aircraft lateral flight reference trajectory optimization. In: 20th IFAC symposium on automatic control in aerospace ACA 2016, 19(17):1–6. 2405–8963, Sherbrooke, QC, Canada. http://dx.doi.org/10.1016/j.ifacol.2016.09.001

    Article  MathSciNet  Google Scholar 

  51. Murrieta-Mendoza A, Hamy A, Botez RM (2016) Lateral reference trajectory algorithm using ant colony optimization. In: 16th AIAA aviation technology, integration, and operations conference, Washington, D.C. http://dx.doi.org/10.2514/6.2016-4209

  52. Murrieta-Mendoza A, Ruiz S, Kessaci S, Botez RM (2017) Vertical reference flight trajectory optimization with the particle swarm optimisation. In The 36th IASTED international conference on modelling, identification and control (MIC 2017), Innsbruck, Austria

    Google Scholar 

Download references

Acknowledgements

We would like to thank the team of the Business-led Network of Centres of Excellence Green Aviation Research & Development Network (GARDN), and in particular Mr. Sylvan Cofsky for the funds received for this project (GARDN II—Project: CMC-21). This research was conducted at the Research Laboratory in Active Controls, Avionics and Aeroservoelasticity (LARCASE) in the framework of the global project “Optimized Descent and Cruise”. For more information please visit http://larcase.etsmtl.ca. We would like to thank Mr. Rex Haygate, Mr. Oussama Abdul-Baki, Mr. Reza Neshat and Mr. Yvan Blondeau from CMC-Electronics—Esterline. We would also like to thank Mr. Antoine Hamy, Mr. Audric Bunel, Mr. Charles Romain, Mr. Paul Mugnier, Mr. Jocelyn Gagné, Mr. Roberto Felix- Patron, Mr. Hugo Ruiz, Ms. Sonya Kessaci, and Mr. Oscar Carranza from LARCASE for their invaluable contributions. We also would like to thank the CONACYT (Mexico) and the FQRNT (Quebec, Canada) for their financial support.

Author information

Authors and Affiliations

  1. Laboratory of Research in Active Controls, Avioncis and Aeroservoelasticity (LARCASE), Université Du Québec/École de Technologie Supérieure, Montreal, H2J 3L6, Canada

    Alejandro Murrieta-Mendoza & Ruxandra Mihaela Botez

Authors
  1. Alejandro Murrieta-Mendoza
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ruxandra Mihaela Botez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ruxandra Mihaela Botez .

Editor information

Editors and Affiliations

  1. Vesalius College (VeCo), Vrije Universiteit Brussel (VUB), Brussels, Belgium

    Dean Vucinic

  2. Mechanical Engineering Department, Universidade Federal Fluminense, Niterói—Rio de Janeiro, Brazil

    Fabiana Rodrigues Leta

  3. Department of Mechanical Engineering, SCMS School of Engineering and Technology, Karukutty, Ernakulam, Kerala, India

    Sheeja Janardhanan

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Murrieta-Mendoza, A., Botez, R.M. (2020). Commercial Aircraft Trajectory Optimization to Reduce Flight Costs and Pollution: Metaheuristic Algorithms. In: Vucinic, D., Rodrigues Leta, F., Janardhanan, S. (eds) Advances in Visualization and Optimization Techniques for Multidisciplinary Research. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-13-9806-3_2

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-9806-3_2

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-9805-6

  • Online ISBN: 978-981-13-9806-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation