Merging Flows in Terminal Maneuvering Area using Time Decomposition Approach

Transcription

1 Merging Flows in Terminal Maneuvering Area using Time Decomposition Approach Ji MA Daniel DELAHAYE, Mohammed SBIHI, Marcel MONGEAU MAIAA Laboratory in Applied Mathematics, Computer Science and Automatics for Air Transport. ENAC École Nationale de l Aviation Civile ICRAT conference, 23 June 2016 Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

2 Outline 1 Background and problem description 2 Problem modeling 3 Solution approaches 4 Simulation results 5 Conclusions and perspectives Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

3 Outline 1 Background and problem description 2 Problem modeling 3 Solution approaches 4 Simulation results 5 Conclusions and perspectives Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

4 Air traffic forecast According to Airbus global market forecast , air traffic will double in the next 15 years. 39 out of the 47 aviation mega cities are largely congested today. airport infrastructure is adequate airports with potential for congestion airports where conditions make it impossible to meet demand Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

5 Terminal Maneuvering Area (TMA) (1/2) ICAO DOC 4444 : TMA is a control area normally established at the confluence of ATS routes in the vicinity of one or more major aerodromes. TMA of Paris region Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

6 Terminal Maneuvering Area (TMA) (2/2) TMA is one of the most complex types of airspace. Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

7 Merging and sequencing problem Merging and organizing arrival aircraft from different entry points into an orderly stream in a short time horizon. Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

8 Outline 1 Background and problem description 2 Problem modeling 3 Solution approaches 4 Simulation results 5 Conclusions and perspectives Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

9 Given data (1/2) A set of flights F = { } 1,..., N f For each flight f F, e f : initial entering point number at TMA ; ts f : initial entering time at TMA ; vs f : initial entering speed at TMA ; c f : wake turbulence category (Heavy, Medium, Light). Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

10 Given data (2/2) A set of routes R = {r k k N, 1 k R} where R is the number of routes and r k is one route with entering point k One route is composed of several links, the first one starts from the entering point and the last link ends at the runway ; Each link is defined by two nodes (waypoint) and constitutes a part of the route. Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

11 Speed change model Figure : Real aircraft speed profile with respect to time Figure : Speed change model Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

12 Decision variables Two kinds of decision variables associated with the problem : t f T f entering time at TMA of aircraft f (in second), where T f = {t f s + j δt j Z, t min /δt j t max /δt} v f V f speed of aircraft f at the entering point of TMA, where V f = {v f min + jδ f v j Z, j (v f max v f min )/δ f v } Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

13 Decision variables Two kinds of decision variables associated with the problem : t f T f entering time at TMA of aircraft f (in second), where T f = {t f s + j δt j Z, t min /δt j t max /δt} v f V f speed of aircraft f at the entering point of TMA, where Decision vector : x = (t, v) V f = {v f min + jδ f v j Z, j (v f max v f min )/δ f v } Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

14 Separation requirements Minimum horizontal separation of 3 NM in TMA Wake turbulence separation Category Leading Aircraft Heavy Medium Light Heavy Trailing Aircraft Medium Light Table : Separation minima for two successive aircraft, in NM Single-runway separation requirements Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

15 Three kinds of conflicts (1/3) Link conflicts Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

16 Three kinds of conflicts (2/3) Node conflicts Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

17 Three kinds of conflicts (3/3) Runway conflicts Table : Single-runway separation requirements, in seconds. 1 Category Trailing Aircraft, g Leading Aircraft, f Heavy Medium Light Heavy Medium Light R. De Neufville, A. Odoni, P. Belobaba, and T. Reynolds, Airport systems : planning, design and management, Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

18 Objective function We minimize the total number of node conflicts S (x) = λ f,g F f g n r f r g N n f g (x) + f,g F f g l r f r g L l f g (x) + f,g F f g P f g (x) + γ D(x) Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

19 Objective function We minimize the total number of node conflicts S (x) = λ f,g F f g n r f r g N n f g (x) + f,g F f g l r f r g L l f g (x) + f,g F f g P f g (x) + γ D(x) the total number of link conflicts Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

20 Objective function We minimize the total number of node conflicts S (x) = λ f,g F f g n r f r g N n f g (x) + f,g F f g l r f r g L l f g (x) + f,g F f g P f g (x) + γ D(x) the total number of link conflicts the total number of runway conflicts Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

21 Objective function We minimize the total number of node conflicts S (x) = λ f,g F f g n r f r g N n f g (x) + f,g F f g l r f r g L l f g (x) + f,g F f g P f g (x) + γ D(x) the total number of link conflicts the total number of runway conflicts decision deviation : D(x) = { f F t f (x) t f s or v f (x) v f s } Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

22 Outline 1 Background and problem description 2 Problem modeling 3 Solution approaches 4 Simulation results 5 Conclusions and perspectives Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

23 Solution approaches Two resolution approaches Resolve the complete problem with an optimization algorithm Using time decomposition approach combined with the optimization algorithm Sliding window approach Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

24 Sliding window approach (1/2) W : the length of the sliding window T s (k) : the beginning time of the k th sliding window T e (k) : the ending time of the k th sliding window Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

25 Sliding window approach (1/3) W : the length of the sliding window ; T s (k) : the beginning time of the k th sliding window ; T e (k) : the ending time of the k th sliding window ; S : time shift of the sliding window. Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

26 Sliding window approach (2/3) For each aircraft f F, t f s : the earliest entering (start) time at TMA ; t f s : the latest entering (start) time at TMA ; t f e : the earliest landing (end) time ; t f e : the latest landing (end) time. Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

27 Sliding window approach (3/3) Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

28 Sliding window approach (3/3) Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

29 Sliding window approach (3/3) Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

30 Sliding window approach (3/3) Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

31 Simulated annealing (1/3) Temperature Stopping criterion Objective function Neighborhood Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

32 Simulated annealing (2/3) Stopping criterion Maximal number of transitions ; Maximal running time of algorithm ; No more improvement after a certain number of transitions (or time) ; Final temperature T f = T init ɛ. Temperature Linear Law : T i = T 0 β i, β > 0 ; Logarithmic law : T i = T 0 /log(i) ; Decrease by tier ; Geometric law : T i+1 = T i α 0 < α < 1. Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

33 Simulated annealing (3/3) Neighborhood Roulette wheel selection Example : Flight Number of conflicts S F = 34, random value σ = 0.5 S F σ = 17 Recalculate the sum until S f 17, then stop and get f = 4 change v f or t f of flight f Random generation Generate a random flight f change v f or t f of flight f Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

34 Outline 1 Background and problem description 2 Problem modeling 3 Solution approaches 4 Simulation results 5 Conclusions and perspectives Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

35 Case study Traffic flow proportion Scenario 1 Scenario 2 Scenario 3 Entry node OKIPA 31.8% 35.5% 36.1% Entry node BANOX 19.7% 20% 20.1% Entry node LORNI 33% 27% 25.9% Entry node MOPAR 15.5% 17.5% 17.9% Total Arrivals Table : Daily Traffic flow Characteristics of Paris CDG runway 26L Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

36 Sliding window approach + Simulated annealing Figure : Computational time of the two methods Table : Conflicts comparison of the two methods Scenario Initial conflicts SA residual conflicts SA+sliding-window residual conflicts Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

37 Sliding window approach + Simulated annealing Table : Comparison of the two methods for scenario 2 Method SA algorithm SA+sliding-window Average delay of entrance time at TMA 86 s 81 s Entrance delay standard deviation 177 s 160 s Average speed change in % Speed change standard deviation in % Figure : Computational time of the two methods Table : Conflicts comparison of the two methods Scenario Initial conflicts SA residual conflicts SA+sliding-window residual conflicts Figure : Number of flights without decision changes Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

38 Sliding window approach + Simulated annealing Figure : Delay at TMA entrance comparison of different objectives Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

39 Outline 1 Background and problem description 2 Problem modeling 3 Solution approaches 4 Simulation results 5 Conclusions and perspectives Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

40 Conclusions A mathematical formulation of the aircraft merging problem in TMA Novel approach by time decomposition Generating a less CPU time and less aircraft deviations solution compared to the simulated annealing applied to the full problem Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

41 Perspectives Balance the runway capacity Integration of TMA and airport Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34

42 Thank you for your attention! Ji MA (ENAC) Merging flows using Time Decomposition Approach 23 June / 34