Lateral Reference Trajectory Algorithm Using Ant Colony - AIAA ARC

Lateral Reference Trajectory Algorithm Using Ant Colony Optimization Alejandro Murrieta-Mendoza1, Antoine Hamy2, Ruxandra Mihaela Botez3 Université du Québec – École de Technologie Supérieure – LARCASE, Montreal Canada

The aeronautical industry requires important quantities of fossil fuel to sustain flights. Fuel burn releases pollution particles to the atmosphere such as carbon dioxide. The aeronautical industry has set itself the goal of diminishing CO2 emissions for the forthcoming years. A way of reducing fuel consumption is by improving en-route operations. For long haul flights, cruise is the flight stage that requires the most fuel consumption. Taking advantage of tailwinds reduces the flight time, thus reducing the fuel requirements. In this paper, an algorithm based on the Ant Colony Optimization was developed to optimize the lateral navigation reference trajectory of a commercial aircraft. Following a constant flight level, the algorithm was able to identify favorable wind areas, and to lead the aircraft to take advantage of these winds to optimize the flight cost. The aircraft model was a numerical performance model constructed from experimental flight data, where weather information was obtained by using information from Weather Canada. Results showed important fuel savings for different long haul flights.

Nomenclature CDA CDG CI LNAV NRT Pheromi PDB Pi PTP TOC TOD VNAV WA WS YUL γ

= = = = = = = = = = = = = = = =

Continuous Descent Approach Paris Charles De Gaulle International airport (France) Cost Index Lateral Navigation Tokyo Narita International Airport (Japan) Pheromone level at a given path. Performance Database Waypoint Selection Probability International Airport of Point à Pitre (Guadeloupe) Top of climb Top of decent Vertical Navigation Wind Azimuth Wind Speed Montreal Pierre Eliot Trudeau International Airport (Canada) Pheromone evaporation rate

I. Introduction

T

HE aeronautical industry is responsible of around 2% of the dioxide carbon (CO2) released to the atmosphere [1]. CO2 is known for its effects on global warming, and it has been pointed out to contribute to the average wind speed incrementing the flight times [2]. Not only CO2, but also Nitrogen Oxides (NOx), and hydrocarbons were released to the atmosphere due to fuel burn. An important percentage of these emissions were released in the stratosphere as discussed in [3]. Other environmental types of pollution generated by aircraft are noise and contrails formation. Noise may lead to stress to population [4], and contrails were believed to contribute more to global warming than CO 2 [5]. 1

PhD Student, ETS/LARCASE, 1110 Rue Notre-Dame West, Montreal, Canada. Undergraduated Assitant Research, ETS/LARCASE, 1110 Rue Notre-Dame West, Montreal, Canada. 3 Full Profesor, ETS/ LARCASE, 1110 Rue Notre-Dame West, Monteral, Canada. 1 American Institute of Aeronautics and Astronautics 2

By reducing fuel consumption to fly a given mission, the emissions released to the atmosphere are as consequence reduced. Another advantage is that by diminishing the fuel requirements, the flight cost is reduced. Airlines have implemented different techniques to reduce fuel consumption without bringing important aircraft modifications as discussed in [6]. From operations perspective, optimizing trajectories can bring important fuel savings. A successful implementation was the Continuous Descent Approach (CDA), where the aircraft descends with engines in IDLE following a constant slope instead of the conventional step descend fashion. This procedure has been studied at different airports [7-9] proving to reduce the fuel consumption and noise. To execute this procedure, the Top of Descent (ToD) has to be estimated, as well as the aircraft weight for its correct execution [10, 11], and to avoid traffic control vectoring and the execution of missed approach procedures [12]. Although different algorithms have been developed to lead aircraft to fly at their most efficient trajectories, different studies have pointed out that aircraft did not fly at their optimal altitudes and speeds [13, 14]. The set of altitudes and speeds that compose a flight is called the vertical reference trajectory. Algorithms optimizing the vertical reference trajectory have been developed by using Optimal control [15-19], Mixed-Integer Linear Programming [20, 21], and Dynamic Programming [22, 23]. Most of these techniques use the point-mass equations of motion and the BADA database provided by Eurocontrol to compute the aircraft fuel burn. Other algorithms have been developed by using a numerical performance model obtained from experimental flight test data. Using this database, the vertical reference trajectory optimization has been solved by using search space reduction techniques [24, 25], golden section search [26], fuel estimators [27], genetic algorithms [28, 29], and branch and bound inspired techniques [30, 31]. All these algorithms have shown the vertical optimization opportunities. Weather has an important influence in flight cost. It is desired to identify places where the wind is favorable and lead the aircraft to travel there. Different algorithms have been developed to take advantage of weather to reduce flight cost. The techniques used for this algorithms are the Dijkstra’s algorithm [32, 33], and the genetic algorithms. The possibility of optimizing the lateral and vertical reference trajectories at the same time has been explored [17, 34]. In this paper, the Ant Colony Optimization (ACO) algorithm has been implemented to optimize the lateral fight trajectory for a fixed altitude by taking into account winds and flight plan information. The paper is organized as follows. Firstly the flight cost of a given trajectory is described, secondly the ACO implementation is described, and finally results and conclusions are presented.

II. Methodology A. The Flight Cost The fuel consumption required for the aircraft to fly a given trajectory is computed using a numerical performance model. This model is a database that was created and validated using experimental flight data. Due to the database nature, interpolations are required to obtain data that is not directly available by providing the discrete inputs. A complete flight can be computed by a series of Lagrange linear interpolations with remarkably accuracy as studied in [35, 36]. This method has been used in this paper. The numerical performance model can alternatively be created using a Level D flight simulator as showed in [37]. Normally, a numerical performance database contains different flight phases. For this paper, as the climb and descent phases are not taken into account, only the cruise phase is computed. The PDB for the cruise takes the form as seen in Fig 1. Inputs Mach number Gross Weight (kg) ISA deviation temperature (°C) Altitude (ft)

Output

}

Fuel flow (kg/hr)

Figure. 1 Numerical Performance Database Inputs and Outputs for the Cruise Phase The relationship that provides the fuel cost is generally defined in eq. (1): (1) 2 American Institute of Aeronautics and Astronautics

Where Flight Cost and Fuel Burn are given in Kg, Flight Time is given in hours and the Cost Index (CI) is given in Kg/hr. The CI is a relationship defined by every airline which “converts” hours to fuel burn cost. Flight Time is computed as shown in Eq. (2). (2) ( ) ( ) Mach number is the speed either set by the pilot or selected by the algorithm as explained below. Speed SoundAlt is the speed sound at a given altitude, Wind Speed (WS) is the wind speed obtained in knots and Wind Angle (WA) is the wing angle (in degrees) at the aircraft particular location. As it can be seen in the Eq. (2) divisor, the ground speed is taken into account for the flight time. Fuel burn was computed using information given by the PDB as follows. (3) The flight considered for this research takes place at a fixed flight level. If the search space is discretized in waypoints by taking the ToC as the departure point, and the ToD as the destination point, the lateral navigation can be seen as a shortest path problem. The solution is provided by the combination of waypoints that links the ToC to the ToD. The final cost is the flight cost sum of those waypoints as shown in Eq. (4). ∑

(4)

B. Weather Conditions Besides aircraft weight, speed, and flight altitude, weather is the other factor that directly affects flight fuel cost The weather parameters taken into account in this paper are the temperature and the wind. Wind is of special importance since identifying headwinds and tailwinds impact the flight time, thus the fuel burn. It is desired to follow tailwinds, and to avoid headwinds. For this paper, weather information was obtained from Weather Canada. Weather is provided under the form of a grid of 600 x 300 points spaced at every 0.6 degrees (66 km). These conditions are available for different latitudes and longitudes for different pressure levels, for 3 hours blocks during one day. The aircraft is rarely located exactly at an altitude and geographical position of the grid provided by Environment Canada as it can be seen in Fig 2. For this reason, interpolations are required to obtain the weather values at the aircraft location as pointed out in [34].

Figure 2. Grid Example from Environment Canada C. The Optimization Algorithm The objective of the optimization algorithm is to minimize the flight cost expressed in Eq. (1). In general terms, the problem is treated as the shortest path problem. This kind of problem can be solved using swarm intelligence algorithms such as the Ant Colony Optimization (ACO) algorithm. 1. The Ant Colony Optimization The (ACO) mimics the search of food sources performed by ants. Evolution has provided ants with a mechanism to identify previously visited places. As ants explore the search space, they release a substance called pheromone which evaporates over time. Pheromone plays an important role in the way ants select a given path. The stronger the pheromone concentration is in a given path, the most probable a given ant will follow that path. When different ants find a given food source different pheromone trails between the source and the food are created. As ants do round 3 American Institute of Aeronautics and Astronautics

trips from the food source to the colony, the concentration of pheromone deposited in the shortest path gets higher. This takes place because over time, pheromone is added more often in the shortest path than in longer paths. A stronger pheromone concentration attracts more ants, which increment even more the pheromone concentration. Over time, almost all ants will follow this path. However, some ants will always wonder around looking for a new route for the known food source or looking for new food sources. If the shortest path followed by ants is blocked, then the same procedure is repeated to find the new shortest path. 2. Optimization Algorithm In order to implement the ACO algorithm for the trajectory optimization problem, a decision grid is required as the one shown in Fig. 3.

Figure 3. Search Space for the Ant Colony This decision grid represents the search space, which for the shortest path problem is a set of waypoints (latitude, longitude). The first waypoint in the grid is the ToC (ant colony) and the last point is the ToD (food source). To link the ToD to the ToC, ants select one trajectory among all possibilities. An ant can only travel to the next three waypoints to which it is connected. One waypoint is directly in front of the preceding waypoint, and the other waypoints are located at a maximum angle of ±15°. The ant algorithm using here is built following three main modules. Module 1: The algorithm creates one random trajectory linking waypoints to connect the ToC to the ToD. Fuel consumption, flight time, and flight cost are computed from that random trajectory. Figure 4 shows the grid from which a trajectory is randomly selected and its parameters such as flight cost, fuel burn, and flight time are computed in equations (1) - (3). A quantity of pheromone is deposited on the edges that the ant visited. In other words, this step emulates a given ant that found a food source for the first time.

Figure 4. Search Space Representation with “Optimal” and “Optimal Candidates”. Module 2: This module serves to mimic that ants tend to retake the route where there is more pheromone, normally the shortest route as described above. Since the Module One will be executed many times, there will be many different trajectories. Among all the available trajectories, the five most economical trajectories according with Eq. (1) are selected. In these five trajectories, the pheromone concentration is incremented following Eq. (5). For the other routes, no pheromone is 4 American Institute of Aeronautics and Astronautics

added, but the previously deposited pheromone evaporates over time. In this way, the algorithm tries to converge to the optimal solution. (5) ( ) ( )( ) Pheromi is the pheromone concentration on the trajectory i. The pheromone evaporation rate is expressed as γ, while the pheromone concentration deposited by the ant only at one waypoint across the route is expressed by C. Module 3: In this module, one ant is placed at the ToC and it is left free to find its own trajectory to the ToD. The algorithm takes decision at every waypoint to where to head next. The ant decision is influenced only by the pheromone concentration coefficient P that is computed with Eq. (6). The ant selects the path to follow using the highest coefficient P . ∑(

(6)

)

In Pi, α is the value that influences the system convergence. Pheromi is the pheromone concentration from the current to the next waypoint, and Pheromk represents the sum of pheromone in the three possible waypoint selection. During the execution of this module, the pheromone concentration on the complete ant grid is updated, following Eq. (4). On Fig. 5, the waypoint with the highest coefficient Pi obtained from Eq. (6) is selected as the next waypoint to compose the trajectory.

Figure. 5. Optimal Path Selection Following the Probability Having described the three basic modules, the ACO algorithm is able to find the most economical trajectory from the ToC to the ToD by taking into account weather conditions. The modules are executed in the algorithm as shown in Fig 6. Start

M1 xm

xn

M1 M2 X4

M2 M3

M3

End

Figure 6. Search Space Representation with “Optimal” and “Optimal Candidates”. 5 American Institute of Aeronautics and Astronautics

At the beginning of the algorithm, trajectories are randomly created, pheromone is deposited, and parameters such as flight cost, flight time, and fuel burn are computed (M1). The next step is the sorting of the trajectories, and the selection of a first efficient route to join ToC to ToD (M2 & M3). Finally, modules M2 and M3 are executed four times, and for each time, module M1 is executed. This research is done in order for the algorithm to converge to the most efficient trajectory. In this last step, few ants travel on different paths to search for a better trajectory than the trajectories already known. For this reason, the module M1 is briefly executed in order to not remain at a local minimum as random trajectories are generated which allow the exploration of the search space.

III. Results Different simulations were executed to measure the algorithm optimization capabilities. The commercial aircraft used for these tests was a 2-engine long-haul, wide-body able to carry up to 275 passengers plus crew. The test procedure was to run the flight test at a given hour following the geodesic trajectory (shortest path in a sphere), the fuel consumption and the flight time were recorded. The same flight, under the same conditions (flight profile, take-off time, and weather) was run with the flight proposed by the Ant Colony Optimization (ACO) algorithm developed in this paper. The fuel burn, and flight time were recorded and compared against the fuel burn and flight time of the geodesic route flight. In Fig. 1, a solution provided by the ACO for the cruise phase from Montreal to Paris is shown. Note how the trajectory slightly deviates from the geodesic trajectory. First, the ACO proposed to deviate north from the trajectory of reference, to then converge with the trajectory of reference and deviate south from the trajectory to finally converge to the destination point. These deviations from the geodesic are due to favourable winds. The algorithm was able to identify them and guide the aircraft as function of those favourable wind currents.

Figure. 7. Geodesic and ACO Trajectories from YUL to CDG In Fig. 7 and Fig. 8, the fuel consumption and the flight time for the geodesic trajectory versus the optimization obtained for different flights are respectively shown. All flights were evaluated at a fixed flight level corresponding to 35,000 ft at a constant Mach number of 0.8. The evaluated flights took place from Montreal (YUL) to Paris (CDG), Vancouver (YVR) to YUL, CDG to New York (JFK), Chicago (ORD) to CDG, YUL to Reykjavík (RVK), and CDG to ORD.

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4.00+04

1.88%

3.50E+04

1.01% 1.63%

3.00E+04

2.05%

1.21%

Flight Cost (kg)

2.50E+04

1.27%

0.56%

2.00E+04 1.50E+04 1.00E+04 5.00E+03 0.00E+00

ORD

C - CDG DG - ORD YUL - CDG CDG - JFK CDG - YUL YVR - YUL YUL - RVK Geodesic

ACO

Figure. 8. Geodesic and ACO Trajectories from YUL to CDG 9

1.41%

8

1.01% 1.47%

Flight Time (hr)

7

1.95%

1.17%

6 1.45%

5

0.29%

4 3 2 1 0 ORD - CDG

CDG - ORD

YUL - CDG

CDG - JFK

Geodesic

CDG - YUL

YVR - YUL

YUL - RVK

ACO

Figure. 9. Geodesic and ACO Trajectories from YUL to CDG Results showed that it was possible to reduce the fuel consumption and the flight time using the ACO. The advantages of reducing the flight cost, and the polluting emissions released to the atmosphere. Important quantities of fuel reductions, up to 714 kg were recoded (ORD-CDG). Flight time reductions of up to 8 minutes (CDG - JFK) were recorded. Finally, using Eq. (1), the flight cost was computed for each trajectory, its reduction on terms of % was compared as shown in Fig. 9.

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40000,00

1.90%

35000,00

1.64%

30000,00

Flight Cost (Kg)

1.01% 2.06%

1.22%

25000,00

1.26%

20000,00

0.57%

15000,00 10000,00 5000,00 0,00

ORD

C - CDG DG - ORD YUL - CDG CDG - JFK CDG - YUL YVR - YUL YUL - RVK Geodesic

ACO

Figure. 10. Geodesic and ACO Trajectories from YUL to CDG It was possible to optimize all flights. However, as the optimization depends fully on weather, it is possible that the algorithm will not find a more economical trajectory as the geodesic route (or any reference route), in the case when weather conditions would not be favourable enough as in the flights here presented.

IV. Conclusion and Future Work In this paper, an algorithm to reduce the fuel burn for a given flight was developed. Reducing the fuel burn brings the benefits of reducing the flight cost and reducing the pollution released to the atmosphere. To make it possible, the new methodology implemented the ACO algorithm. This algorithm was able to reduce fuel burn for different destinations. As expected, it was observed that the level of optimization depended on the weather. The encouraging results suggest performing more tests for different trajectories to have a better insight of the level of optimization that can be obtained. It is as well of interest to implement the vertical reference trajectory optimization in the current work to observe the optimization potential for a 3D trajectory. With this improvement the algorithm will decide the waypoints in which it should perform changes in altitude. Significant flight cost reduction is expected using this future algorithm. The availability of real current flight plans provided by a European airline could lead to a more realistic comparison.

Acknowledgments The Research here presented was conducted at the Research Laboratory in Active Controls, Avionics and Aeroservoelasticity (LARCASE) in the frame of the global project “Optimized Descent and Cruise” with funds from the Business-led Network of Centers of Excellence Green Aviation Research & Development Network (GARDN). For more information please visit http://larcase.etsmtl.ca. The authors would like to thank Rex Haygate, Dominique Labour and Yvan Blondeau from CMC-Electronics – Esterline, and Oscar Carranza from LARCASE. The authors would like to thank CONACYT in Mexico and the FQRNT in Quebec, Canada.

References 1. 2. 3.

4.

5.

ICAO. "Aviation's contribution to climate change." International Civil Aviation Organization, Montreal, 2010, p. 260. Paul, D. W. "Transatlantic flight times and climate change," Environmental Research Letters Vol. 11, No. 2, 2016, p. 024008. doi: 10.1088/1748-9326/11/2/024008 Sheng, H., Marais, K., and Landry, S. "Assessment of stratospheric fuel burn by civil commercial aviation," Transportation Research Part D: Transport and Environment Vol. 34, 2015, pp. 1-15. doi: http://dx.doi.org/10.1016/j.trd.2014.10.008 Black, D. A., Black, J. A., Issarayangyun, T., and Samuels, S. E. "Aircraft Noise Exposure and Resident's Stress and Hypertension: A public Health Perspective for Airport Environmental Management," Journal of Air Transport Management Vol. 13, No. 5, 2007, pp. 264-276. doi: http://dx.doi.org/10.1016/j.jairtraman.2007.04.003 Campbell, S. E., Bragg, M. B., and Neogi, N. A. "Fuel-Optimal Trajectory Generation for Persistent Contrail Mitigation," Journal of Guidance, Control, and Dynamics Vol. 36, No. 6, 2013, pp. 1741-1750. doi: 10.2514/1.55969

8 American Institute of Aeronautics and Astronautics

6.

7.

8.

9.

10.

11. 12.

13.

14.

15. 16.

17. 18. 19. 20.

21.

22.

23.

24.

25. 26.

27.

McConnachie, D., Wollersheim, C., and Hansman, R. J. "The Impact of Fuel Price on Airline Fuel Efficiency and Operations," 2013 Aviation Technology, Integration, and Operations Conference. American Institute of Aeronautics and Astronautics, 2013. Kwok-On, T., Daniel, B., and Anthony, W. "Development of Continuous Descent Arrival (CDA) Procedures for DualRunway Operations at Houston Intercontinental," 6th AIAA Aviation Technology, Integration and Operations Conference (ATIO). American Institute of Aeronautics and Astronautics, 2006. Kwok-On, T., Anthony, W., and John, B. "Continuous Descent Approach Procedure Development for Noise Abatement Tests at Louisville International Airport, KY," AIAA's 3rd Annual Aviation Technology, Integration, and Operations (ATIO) Forum. American Institute of Aeronautics and Astronautics, 2003. De Lépinay, I., Dimitriu, D., and Melrose, A. "Environmental impact assessment of Continuous Descent Approaches at Manchester and Bucharest airports," 35th International Congress and Exposition on Noise Control Engineering, INTER-NOISE 2006. Vol. 6, Institute of Noise Control Engineering of the USA -, Honolulu, HI, United states, 2006, pp. 3856-3863. Stell, L. "Predictability of Top of Descent Location for Operational Idle-Thrust Descents," 10th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference. American Institute of Aeronautics and Astronautics, Fort Worth USA, 2010. Johnson, C. M. "Analysis of Top of Descent (TOD) uncertainty," Digital Avionics Systems Conference (DASC), 2011 IEEE/AIAA 30th. Seattle, WA, 2011, pp. 2E3-1-2E3-10. Murrieta-Mendoza, A., Botez, R., and Ford, S. "Estimation of Fuel Consumption and Polluting Emissions Generated during the Missed Approach Procedure," The 33nd IASTED International Conference on Modelling, Identification, and Control (MIC 2014) ACTA Press, Innsbruck, Austria, 2014. Jensen, L., Hansman, J. R., Venuti, J. C., and Reynolds, T. "Commercial Airline Speed Optimization Strategies for Reduced Cruise Fuel Consumption," 2013 Aviation Technology, Integration, and Operations Conference. American Institute of Aeronautics and Astronautics, Los Angeles, USA, 2013. Jensen, L., Hansman, J. R., Venuti, J., and Reynolds, T. "Commercial Airline Altitude Optimization Strategies for Reduced Cruise Fuel Consumption," 14th AIAA Aviation Technology, Integration, and Operations Conference. American Institute of Aeronautics and Astronautics, 2014. Tsotskas, C., Kipouros, T., and Savill, M. "Biobjective Optimisation of Preliminary Aircraft Trajectories," Evolutionary Multi-Criterion Optimization. Vol. 7811, Springer Berlin Heidelberg, 2013, pp. 741-755. Celis, C., Sethi, V., Zammit-Mangion, Singh, R., and Pilidis, P. "Theoretical Optimal Trajectories for Reducing the Environmental Impact of Commercial Aircraft Operations," Journal of Aerospace Technology And Management Vol. 6, No. 1, 2014, pp. 29-42. doi: 10.5028/jatm.v6i1.288 Ng, H. K., Sridhar, B., and Grabbe, S. "Optimizing Aircraft Trajectories with Multiple Cruise Altitudes in the Presence of Winds," Journal of Aerospace Information Systems Vol. 11, No. 1, 2014, pp. 35-47. doi: 10.2514/1.I010084 Valenzuela, A., and Rivas, D. "Optimization of Aircraft Cruise Procedures Using Discrete Trajectory Patterns," Journal of Aircraft Vol. 51, No. 5, 2014, pp. 1632-1640. doi: 10.2514/1.C032041 Franco, A., and Rivas, D. "Optimization of Multiphase Aircraft Trajectories Using Hybrid Optimal Control," Journal of Guidance, Control, and Dynamics, 2015, pp. 1-16. doi: 10.2514/1.G000688 Soler-Arnedo, M., Hansen, M., and Zou, B. "Contrail Sensitive 4D Trajectory Planning with Flight Level Allocation Using Multiphase Mixed-Integer Optimal Control," AIAA Guidance, Navigation, and Control (GNC) Conference. American Institute of Aeronautics and Astronautics, 2013. Bonami, P., Olivares, A., Soler, M., and Staffetti, E. "Multiphase Mixed-Integer Optimal Control Approach to Aircraft Trajectory Optimization," Journal of Guidance, Control, and Dynamics Vol. 36, No. 5, 2014, pp. 1267-1277. doi: 10.2514/1.60492 Miyazawa, Y., Wickramasinghe, N. K., Harada, A., and Miyamoto, Y. "Dynamic Programming Application to Airliner Four Dimensional Optimal Flight Trajectory," AIAA Guidance, Navigation, and Control (GNC) Conference. American Institute of Aeronautics and Astronautics, Boston, USA, 2013. Hagelauer, P., and Mora-Camino, F. "A Soft Dynamic Programming Approach for On-Line Aircraft 4D-Trajectory Optimization," European Journal of Operational Research Vol. 107, No. 1, 1998, pp. 87-95. doi: http://dx.doi.org/10.1016/S0377-2217(97)00221-X Gagné, J., Murrieta-Mendoza, A., Botez, R., and Labour, D. "New Method for Aircraft Fuel Saving Using Flight Management System and Its Validation on the L-1011 aircraft," 2013 Aviation Technology, Integration, and Operations Conference, 2013. doi: 10.2514/6.2013-4290 Murrieta-Mendoza, A., and Botez, R. M. "Vertical Navigation Trajectory Optimization Algorithm For A Commercial Aircraft," AIAA/3AF Aircraft Noise and Emissions Reduction Symposium, 2014. doi:10.2514/6.2014-3019 Felix Patron, R. S., Botez, R. M., and Labour, D. "New Altitude Optimisation Algorithm for the Flight Management System CMA-9000 Improvement on the A310 and L-1011 Aircraft," The Aeronautical Journal Vol. 117, No. 1194, 2013, pp. 787-805. Dancila, B., Botez, R. M., and Labour, D. "Fuel Burn Prediction Algorithm for Cruise, Constant Speed and Level Flight Segments," The Aeronatuical Journal Vol. 117, No. 1191, 2013.

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28.

29.

30.

31.

32.

33. 34. 35. 36.

37.

Felix Patron, R. S., Oyono Owono, A. C., Botez, R. M., and Labour, D. "Speed and Altitude Optimization on the FMS CMA-9000 for the Sukhoi Superjet 100 Using Genetic Algorithms," 2013 Aviation Technology, Integration, and Operations Conference. American Institute of Aeronautics and Astronautics, 2013. Murrieta-Mendoza, A., Félix-Patrón, R. S., and Botez, R. M. "Flight Altitude Optimization Using Genetic Algorithms Considering Climb and Descent Costs in Cruise with Flight Plan Information," SAE 2015 AeroTech Congress & Exhibition. SAE International, Seattle, USA, 2015, p. 9. Murrieta-Mendoza, A., Beuze, B., Ternisien, L., and Botez, R. "Branch & Bound-Based Algorithm for Aircraft VNAV Profile Reference Trajectory Optimization," 15th AIAA Aviation Technology, Integration, and Operations Conference, Aviation Forum. AIAA, Dallas, TX, USA, 2015. Murrieta-Mendoza, A., and Botez, R. "Aircraft Vertical Route Optimization Deterministic Algorithm for a Flight Management System," SAE 2015 AeroTech Congress & Exhibition. Vol. SAE Technical Paper 2015-01-2541, SAE International, Seattle, USA, 2015, p. 13. Murrieta-Mendoza, A., and Botez, R. M. "Lateral Navigation Optimization Considering Winds And Temperatures For Fixed Altitude Cruise Using The Dijkstra’s Algorithm," International Mechanical Engineering Congress & Exposition. Montreal, Canada, 2014. Rippel, E., Bar-Gill, A., and Shimkin, N. "Fast Graph-Search Algorithms for General-Aviation Flight Trajectory Generation," Journal of Guidance, Control, and Dynamics Vol. 28, No. 4, 2005, pp. 801-811. doi: 10.2514/1.7370 Murrieta-Mendoza, A. "Vertical and Lateral Flight Optimization Algorithm and Missed Approach Cost Calculation.." Vol. Master, École de Technologie Supérieure, Montreal, 2013, p. 114. Murrieta-Mendoza, A., and Botez, R. M. "Method to Calculate Aircraft VNAV Trajectory Cost Using a Performance Database," International Mechanical Engineering Congress & Exposition. Montreal, Canada, 2014. Murrieta-Mendoza, A., and Botez, R. M. "Methodology for Vertical-Navigation Flight-Trajectory Cost Calculation Using a Performance Database," Journal of Aerospace Information Systems Vol. 12, No. 8, 2015, pp. 519-532. doi: 10.2514/1.I010347 Murrieta Mendoza, A., Demange, S., George, F., and Botez, R. M. "Performance Database Creation Using a Flight D Simulator For Cessna Citation X Aircraft in Cruise Regime," The 34th IASTED International Conference on Modelling, Identification, and Control (MIC2015). IASTED, Innsbruck, Austria, 2015.

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