Optimization of Arrival and Departure Routes in Terminal Maneuvering Area Jun Zhou MAIAA – Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l’Aérien ENAC – École Nationale de l’Aviation Civile UPS – Université Toulouse III - Paul Sabatier Toulouse, France International Conference on Research in Air Transportation (ICRAT) – Doctoral Symposium 31 May 2014 Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 1 / 33
Outline Context and problem description 1 Problem modeling 2 Solution approach 3 Simulation results 4 Conclusions and perspectives 5 Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 2 / 33
Outline Context and problem description 1 Problem modeling 2 Solution approach 3 Simulation results 4 Conclusions and perspectives 5 Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 3 / 33
Air tra ffi c growth BOEING long-term market forecast Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 4 / 33
Airports capacity Airport is both the starting and ending point of air tra ffi c. air tra ffi c flow increases ⇓ airports surrounding areas capacity insu ffi ciency Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 5 / 33
Terminal Maneuvering Area (TMA) (1 / 2) A designated area of controlled airspace surrounding one or several airports Designed to handle aircraft arriving to and departing from airports TMA of the Paris region Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 6 / 33
Terminal Maneuvering Area (TMA) (2 / 2) TMA is one of the most complex types of airspace. Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 7 / 33
SID / STAR Standard Instrument Departure (SID) route: Standard Terminal Arrival Route (STAR): A flight route followed by aircraft after A route which connects the last enroute takeo ff from an airport. way-point to the Initial Approach Fix. Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 8 / 33
SID / STAR towards automatic design Currently, SID / STAR are designed manually based on the airport layout, existing Navaid infrastructures and nearby constraints. This study considers the automation of SID / STAR design - at a strategic level in 3D - based on RNAV concept Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 9 / 33
SID / STAR towards automatic design Currently, SID / STAR are designed manually based on the airport layout, existing Navaid infrastructures and nearby constraints. This study considers the automation of SID / STAR design - at a strategic level in 3D - based on RNAV concept ⇓ Optimization problem Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 9 / 33
Outline Context and problem description 1 Problem modeling 2 Solution approach 3 Simulation results 4 Conclusions and perspectives 5 Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 10 / 33
Model parameters (1 / 2) We consider TMA surrounding one airport , designed in a circular configuration centered on the airport. Two concentric circles C 1 and C 2 , with radius R 1 and R 2 , with altitude H 1 and H 2 Entry / Exit points located on C 1 O = { O 1 , . . . , O n in , O n in + 1 , . . . , O n in + n out } - the first n in points are entry points - the remaining n out points are exit points Arrival / Departure points located on C 2 I = { I 1 , . . . , I n arr , I n arr + 1 , . . . , I n arr + n dep } - the first n arr points are arrival points - the remaining n dep points are departure points Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 11 / 33
Model parameters (2 / 2) Subset K ⊆ O × I , containing the pairs of points to be connected Total amount of flights N , arriving at and departing from the airport Proportion of flights associated with each pair of points Two parallel runways, available for all types of aircraft - O = { O 1 , O 2 , O 3 , O 4 } - I = { I 1 , I 2 , I 3 } - K = { ( O 1 , I 1 ) , ( O 1 , I 2 ) , ( O 2 , I 2 ) , ( I 3 , O 3 ) , ( I 3 , O 4 ) } Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 12 / 33
Decision variables Routes connecting points ( O i , I j ) ∈ K : γ ij : [0 , 1] → R 3 where γ ij (0) = O i if 1 ≤ i ≤ n in and 1 ≤ j ≤ n arr γ ij (1) = I j γ ij (0) = I i if n arr + 1 ≤ i ≤ n arr + n dep and n in + 1 ≤ j ≤ n in + n out γ ij (1) = O j ( γ ijx , γ ijy , γ ijz ) are the components of γ ij in axis ( x , y , z ). Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 13 / 33
Constraints Two main constraints are considered: forbidden areas and minimum separation . Forbidden areas: mountains, cities, Minimum separation between routes: military areas, etc. ∀ ( O i , I j ) , ( O k , I l ) ∈ K , ∀ ( µ 1 , µ 2 ) ∈ [0 , 1] Let Ω be a forbidden area. ( γ ijx ( µ 1 ) − γ klx ( µ 2 )) 2 + ( γ ijy ( µ 1 ) − γ kly ( µ 2 )) 2 ≥ 6 NM , � ∀ ( O i , I j ) ∈ K , ∀ µ ∈ [0 , 1] γ ij ( µ ) � Ω | γ ijz ( µ 1 ) − γ klz ( µ 2 ) | ≥ 1200 ft Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 14 / 33
Objective function Minimizing the total distance flown by all flights during a certain period. � L = w ij N l ij ( i , j ) where - l ij is the length of route γ ij - w ij is the proportion of flights on route γ ij Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 15 / 33
Outline Context and problem description 1 Problem modeling 2 Solution approach 3 Simulation results 4 Conclusions and perspectives 5 Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 16 / 33
Solution approach The problem is solved in three steps. 1. Compute an individual route by Fast Marching Method (FMM) and Gradient Descent method, where we take into consideration the forbidden areas. Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 17 / 33
Solution approach The problem is solved in three steps. 1. Compute an individual route by Fast Marching Method (FMM) and Gradient Descent method, where we take into consideration the forbidden areas. 2. Given a fixed order of route designing, compute sequentially the routes taking into account the minimum separation constraints. Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 17 / 33
Solution approach The problem is solved in three steps. 1. Compute an individual route by Fast Marching Method (FMM) and Gradient Descent method, where we take into consideration the forbidden areas. 2. Given a fixed order of route designing, compute sequentially the routes taking into account the minimum separation constraints. 3. Find an order minimizing the objective function by applying Simulated Annealing (SA) . Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 17 / 33
1 st step: designing one route (1 / 3) Given ( O i , I j ) ∈ K , searching for an optimal route by seeking the minimal travel time route from γ ij (0) to γ ij (1). The minimal-time optimal trajectory problem can be modelled by a wave front propagation problem. ( J. A. Sethian , 1999, adapted by B. Girardet , 2012) �∇ u ( x ) � F ( x ) = 1 where u ( x ) is the time at which the front reaches the point x . Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 18 / 33
1 st step: designing one route (2 / 3) Choosing the front propagation speed at point x F ( x ) = (1 − α ( x )) F where - F is a constant value - α ( x ) ∈ [0 , 1[ α ( x ) = 0 . 99 in forbidden area α ( x ) = 0 in free area Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 19 / 33
1 st step: designing one route (3 / 3) Fast Marching Method (FMM) Solving the wave front propagation problem in isotropic case (no wind) Obtaining the minimum time to reach any point in space starting from γ ij (0) Gradient Descent - starting from γ ij (1) Generating the route - moving towards γ ij (0) - taking steps proportional to −∇ u Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 20 / 33
2 nd step: generating all routes with fixed order Fix an order , computing sequentially the routes: Once a route is computed, this route and its protection zone are considered as additional forbidden area constraints for the remaining routes, by selecting an adapted propagation speed F ( x ). Example Jun Zhou (ENAC) Optimization of Arrival and Departure Routes in Terminal Maneuvering Area May 31, 2014 21 / 33
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