Combining Flight Level Allocation with Ground Holdingto Optimize 4D-Deconfliction
Cyril Allignol and Nicolas [email protected]
DSNA – ENAC
Ninth USA/Europe ATM R&D Seminar 2011Berlin, 15/06/2011
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 1 / 22
Outline
1 Introduction
2 ContextGround Holding in Europe4D-Trajectory Deconfliction
3 Combining Flight Level Allocation with Ground HoldingVariablesConflict DetectionFL Allocation ConstraintsGround Holding Constraints
4 ResultsFL Allocation StageGround Holding Stage
5 Further Works
6 Conclusion
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 2 / 22
Introduction
Introduction
Congested European Sky
Regulation delays mainly due to en-route sector capacities
Structural limits of the sector-based ATC system reached
Optimization of airspace structure and ATFM regulations: SESAR
Two-Stage ATM Optimization
1 Flight Level Allocation
Vertical separation of 2D + time-intersecting flightsGraph Coloring, but minimization of discrepancy to requested FL
2 Ground Holding
Deconfliction by departure time adjustmentGraph Coloring as special case, minimization of delays
Solved by Constraint Programming (CP)
Versatile modelling tool for combinatorial optimization problem
Optimality proof for feasibility stageC. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 3 / 22
Introduction
Introduction
Congested European Sky
Regulation delays mainly due to en-route sector capacities
Structural limits of the sector-based ATC system reached
Optimization of airspace structure and ATFM regulations: SESAR
Two-Stage ATM Optimization
1 Flight Level Allocation
Vertical separation of 2D + time-intersecting flightsGraph Coloring, but minimization of discrepancy to requested FL
2 Ground Holding
Deconfliction by departure time adjustmentGraph Coloring as special case, minimization of delays
Solved by Constraint Programming (CP)
Versatile modelling tool for combinatorial optimization problem
Optimality proof for feasibility stageC. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 3 / 22
Introduction
Introduction
Congested European Sky
Regulation delays mainly due to en-route sector capacities
Structural limits of the sector-based ATC system reached
Optimization of airspace structure and ATFM regulations: SESAR
Two-Stage ATM Optimization
1 Flight Level Allocation
Vertical separation of 2D + time-intersecting flightsGraph Coloring, but minimization of discrepancy to requested FL
2 Ground Holding
Deconfliction by departure time adjustmentGraph Coloring as special case, minimization of delays
Solved by Constraint Programming (CP)
Versatile modelling tool for combinatorial optimization problem
Optimality proof for feasibility stageC. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 3 / 22
Context Ground Holding in Europe
Ground Holding in Europe
Pre-tactical Flow Regulation
Safer than handling the traffic while airborne
Costly for airspace users, network effect
Sector Capacity and Regulation
Air Traffic Control Centres opening schedules: designed by experts,based on previous traffic and demand
Open sectors capacities: hourly entry rate
Regulation on flows crossing overloaded sectors: Computer AssistedSlot Allocation (CASA/ETFMS) at CFMU
Accuracy and Effectiveness of the Model?
Relevance of sector capacity to model controller workload?
Discrepancies between planned schedule and actual openings
CASA: greedy algorithm (optimality, soundness?)
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 4 / 22
Context Ground Holding in Europe
Ground Holding in Europe
Pre-tactical Flow Regulation
Safer than handling the traffic while airborne
Costly for airspace users, network effect
Sector Capacity and Regulation
Air Traffic Control Centres opening schedules: designed by experts,based on previous traffic and demand
Open sectors capacities: hourly entry rate
Regulation on flows crossing overloaded sectors: Computer AssistedSlot Allocation (CASA/ETFMS) at CFMU
Accuracy and Effectiveness of the Model?
Relevance of sector capacity to model controller workload?
Discrepancies between planned schedule and actual openings
CASA: greedy algorithm (optimality, soundness?)
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 4 / 22
Context Ground Holding in Europe
Ground Holding in Europe
Pre-tactical Flow Regulation
Safer than handling the traffic while airborne
Costly for airspace users, network effect
Sector Capacity and Regulation
Air Traffic Control Centres opening schedules: designed by experts,based on previous traffic and demand
Open sectors capacities: hourly entry rate
Regulation on flows crossing overloaded sectors: Computer AssistedSlot Allocation (CASA/ETFMS) at CFMU
Accuracy and Effectiveness of the Model?
Relevance of sector capacity to model controller workload?
Discrepancies between planned schedule and actual openings
CASA: greedy algorithm (optimality, soundness?)
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 4 / 22
Context 4D-Trajectory Deconfliction
4D-Trajectory Deconfliction
4D-Trajectory Planning
“Strategic” deconfliction (EC project Episode 3)
Several opportunities: flight level, rerouting, delay, speed...
Large scale combinatorial optimization problems
Conflict Model
Finest grain (conflicts) vs aggregated model (sector capacity)
Sliding time windows to handle uncertainty
Two-Stage Trajectory Deconfliction
1 Flight Level AllocationDetection in the horizontal planeVertical separation (Graph Coloring) minimizing discrepancy to RFL
2 Ground HoldingDifference of delays (O
(n2)!) constrained outside conflicting intervals
Minimization of delays
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 5 / 22
Context 4D-Trajectory Deconfliction
4D-Trajectory Deconfliction
4D-Trajectory Planning
“Strategic” deconfliction (EC project Episode 3)
Several opportunities: flight level, rerouting, delay, speed...
Large scale combinatorial optimization problems
Conflict Model
Finest grain (conflicts) vs aggregated model (sector capacity)
Sliding time windows to handle uncertainty
Two-Stage Trajectory Deconfliction
1 Flight Level AllocationDetection in the horizontal planeVertical separation (Graph Coloring) minimizing discrepancy to RFL
2 Ground HoldingDifference of delays (O
(n2)!) constrained outside conflicting intervals
Minimization of delays
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 5 / 22
Context 4D-Trajectory Deconfliction
4D-Trajectory Deconfliction
4D-Trajectory Planning
“Strategic” deconfliction (EC project Episode 3)
Several opportunities: flight level, rerouting, delay, speed...
Large scale combinatorial optimization problems
Conflict Model
Finest grain (conflicts) vs aggregated model (sector capacity)
Sliding time windows to handle uncertainty
Two-Stage Trajectory Deconfliction
1 Flight Level AllocationDetection in the horizontal planeVertical separation (Graph Coloring) minimizing discrepancy to RFL
2 Ground HoldingDifference of delays (O
(n2)!) constrained outside conflicting intervals
Minimization of delays
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 5 / 22
Combining Flight Level Allocation with Ground Holding Variables
Conflict Model
Data
Flight plans and airspace data for one day of traffic
Simulation with CATS [Alliot,Durand 97]
Trajectories sampled every 15 s (catch shortest conflicts)
Notation: flight i at point pki at time tki if not delayed
Variables and Constraints
Decision variables: flight level FLi ∈ [RFLi − devmax,RFLi + devmax]and delay δi ∈ [0, δmax] for each flight i
Auxilliary variables: θki = tki + δi dij = δj − δiConstraints: two flights cannot be at two conflicting points of theirtrajectories at the same time
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 6 / 22
Combining Flight Level Allocation with Ground Holding Variables
Conflict Model
Data
Flight plans and airspace data for one day of traffic
Simulation with CATS [Alliot,Durand 97]
Trajectories sampled every 15 s (catch shortest conflicts)
Notation: flight i at point pki at time tki if not delayed
Variables and Constraints
Decision variables: flight level FLi ∈ [RFLi − devmax,RFLi + devmax]and delay δi ∈ [0, δmax] for each flight i
Auxilliary variables: θki = tki + δi dij = δj − δiConstraints: two flights cannot be at two conflicting points of theirtrajectories at the same time
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 6 / 22
Combining Flight Level Allocation with Ground Holding Conflict Detection
Conflict Detection
ijd
0
i
j
−2w 2w
tki ∈ [1000, 1180], t lj ∈ [600, 750]
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 7 / 22
Combining Flight Level Allocation with Ground Holding Conflict Detection
Conflict Detection
ijd
0
i
j
−2w 2w
t1i = 1000
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 7 / 22
Combining Flight Level Allocation with Ground Holding Conflict Detection
Conflict Detection
ijd
0
i
j
−2w 2w
t2i = 1015
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 7 / 22
Combining Flight Level Allocation with Ground Holding Conflict Detection
Conflict Detection
ijd
0
i
j
−2w 2w370 400
t3i = 1030, [t3
j = 630, t5j = 660], dij 6∈ [370, 400]
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 7 / 22
Combining Flight Level Allocation with Ground Holding Conflict Detection
Conflict Detection
ijd
0
i
j
−2w 2w415370
t4i = 1045, [t3
j = 630− t6j = 675], dij 6∈ [370, 415] ⊆ [370, 415]
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 7 / 22
Combining Flight Level Allocation with Ground Holding Conflict Detection
Conflict Detection
ijd
0
i
j
−2w 2w430370
t5i = 1060, [t3
j = 630− t7j = 690], dij 6∈ [370, 430] ⊆ [370, 430]
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 7 / 22
Combining Flight Level Allocation with Ground Holding Conflict Detection
Conflict Detection
ijd
0
i
j
−2w 2w430370
t6i = 1075, [t4
j = 645− t8j = 705], dij 6∈ [370, 430] ⊆ [370, 430]
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 7 / 22
Combining Flight Level Allocation with Ground Holding Conflict Detection
Conflict Detection
ijd
0
i
j
−2w 2w445370 385
t7i = 1090, [t4
j = 645− t8j = 705], dij 6∈ [385, 445] ⊆ [370, 445]
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 7 / 22
Combining Flight Level Allocation with Ground Holding Conflict Detection
Conflict Detection
ijd
0
i
j
−2w 2w370 385 445
t8i = 1105, [t5
j = 660− t9j = 720], dij 6∈ [385, 445] ⊆ [370, 445]
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 7 / 22
Combining Flight Level Allocation with Ground Holding Conflict Detection
Conflict Detection
ijd
0
i
j
−2w 2w370 385 460
t9i = 1120, [t5
j = 660− t10j = 735], dij 6∈ [385, 460] ⊆ [370, 460]
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 7 / 22
Combining Flight Level Allocation with Ground Holding Conflict Detection
Conflict Detection
ijd
0
i
j
−2w 2w370 400 460
t10i = 1135, [t6
j = 675− t10j = 735], dij 6∈ [400, 460] ⊆ [370, 460]
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 7 / 22
Combining Flight Level Allocation with Ground Holding Conflict Detection
Conflict Detection
ijd
0
i
j
−2w 2w370 415 460
t i11 = 1150, [t7j = 690− t10
j = 735], dij 6∈ [415, 460] ⊆ [370, 460]
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 7 / 22
Combining Flight Level Allocation with Ground Holding Conflict Detection
Conflict Detection
ijd
0
i
j
−2w 2w370 415 460430
t i12 = 1165, [t9j = 720− t10
j = 735], dij 6∈ [415, 430] ⊆ [370, 460]
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 7 / 22
Combining Flight Level Allocation with Ground Holding Conflict Detection
Conflict Detection
ijd
0
i
j
−2w 2w370 460
dij = δj − δi 6∈ [370, 460]
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 7 / 22
Combining Flight Level Allocation with Ground Holding Conflict Detection
Multiply-Conflicting Flight Pair
-10000 -5000 0 5000 10000 15000 20000 25000-20000
-15000
-10000
-5000
0
5000
10000
15000
0 50
100 150 200 250 300 350
45034589
900
910
920
930
940
950
960
970
dij = δj − δi 6∈ Cij = [lb1ij ..ub1
ij ] ∪ · · · ∪ [lbkij ..ubk
ij ]
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 8 / 22
Combining Flight Level Allocation with Ground Holding Conflict Detection
Flight Conflicting with Many Other
Constraint Graph of High Degree
Highest degree > 650
Large cliques > 150
One single large connected component
-40000
-30000
-20000
-10000
0
10000
20000
30000
-50000
-40000
-30000
-20000
-10000
0
10000
20000 0 50
100 150 200 250 300 350 400 450
500
550
600
650
700
750
800
850
900
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 9 / 22
Combining Flight Level Allocation with Ground Holding FL Allocation Constraints
2D+Time Conflicts
For each pair of flights i 6= j
∀k, l , such that dh(pki , p
li ) < 5 NM (horizontal plane only):
θki 6= θlj
tki + δi 6= t lj + δj
dij 6= tki − t lj
Therefore: dij /∈ CHij = [lb1ij ..ub1
ij ] ∪ · · · ∪ [lbmij ..ubm
ij ]
We note: conflictH(i , j) ⇔ [−δmax, δmax] ∩ CHij 6= ∅
Trajectories truncated to their largest possible level part(below RFL− devmax)
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 10 / 22
Combining Flight Level Allocation with Ground Holding FL Allocation Constraints
FL Allocation: Flows Model
Model
Flights sharing the same route and (almost) same RFL aggregatedinto flows Fk
Extension of conflicts to flows:
conflict(Fk ,Fl)⇔ ∃(i , j) ∈ Fk ×Fl s.t. conflictH(i , j)
Constraints: conflict(Fk ,Fl) ⇒ FLk 6= FLl
Cost: costFL =∑i
|RFLi − FLi |
Limits
Few variables, but very dense constraint graph
Does not solve catch-up conflicts
It was abandoned for the single flight model.
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 11 / 22
Combining Flight Level Allocation with Ground Holding FL Allocation Constraints
FL Allocation: Flows Model
Model
Flights sharing the same route and (almost) same RFL aggregatedinto flows Fk
Extension of conflicts to flows:
conflict(Fk ,Fl)⇔ ∃(i , j) ∈ Fk ×Fl s.t. conflictH(i , j)
Constraints: conflict(Fk ,Fl) ⇒ FLk 6= FLl
Cost: costFL =∑i
|RFLi − FLi |
Limits
Few variables, but very dense constraint graph
Does not solve catch-up conflicts
It was abandoned for the single flight model.
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 11 / 22
Combining Flight Level Allocation with Ground Holding FL Allocation Constraints
FL Allocation: Single Flight Model
For each pair of flights i 6= j
conflictH(i , j) ⇔ [−δmax, δmax] ∩ CHij 6= ∅
Constraints: conflictH(i , j) ⇒ FLi 6= FLj
Cost: costFL =∑i
|RFLi − FLi |
Temporal Relaxation
Very dense graph with costly solutions for feasible values of δmax
Most flights won’t be delayed (or by a very small amount)
Detection with dij = 0 ∈ CHij : solutions with low devmax and costFL
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 12 / 22
Combining Flight Level Allocation with Ground Holding FL Allocation Constraints
FL Allocation: Single Flight Model
For each pair of flights i 6= j
conflictH(i , j) ⇔ [−δmax, δmax] ∩ CHij 6= ∅
Constraints: conflictH(i , j) ⇒ FLi 6= FLj
Cost: costFL =∑i
|RFLi − FLi |
Temporal Relaxation
Very dense graph with costly solutions for feasible values of δmax
Most flights won’t be delayed (or by a very small amount)
Detection with dij = 0 ∈ CHij : solutions with low devmax and costFL
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 12 / 22
Combining Flight Level Allocation with Ground Holding Ground Holding Constraints
Ground Holding Conflict Constraints
For each pair of flights i 6= j after FL allocation
∀k, l , such that dh(pki , p
li ) < 5 NM ∧ dv (pk
i , pli ) < 1000 ft:
θki 6= θlj
Therefore: dij /∈ Cij = [lb1ij ..ub1
ij ] ∪ · · · ∪ [lbmij ..ubm
ij ]
Cost: costmaxGH = max
iδi
costsumGH =
∑i
δi
NP-hard problem
Non European Flights
Flights originating outside the ECAC zone cannot be delayed byEurocontrol instances (≈ 10%): δi = 0
Conflicts between two such flights discarded (a few dozens)
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 13 / 22
Combining Flight Level Allocation with Ground Holding Ground Holding Constraints
Ground Holding Conflict Constraints
For each pair of flights i 6= j after FL allocation
∀k, l , such that dh(pki , p
li ) < 5 NM ∧ dv (pk
i , pli ) < 1000 ft:
θki 6= θlj
Therefore: dij /∈ Cij = [lb1ij ..ub1
ij ] ∪ · · · ∪ [lbmij ..ubm
ij ]
Cost: costmaxGH = max
iδi
costsumGH =
∑i
δi
NP-hard problem
Non European Flights
Flights originating outside the ECAC zone cannot be delayed byEurocontrol instances (≈ 10%): δi = 0
Conflicts between two such flights discarded (a few dozens)
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 13 / 22
Results
Results
Instance Figures
Traffic within French airspace in 2008 (time step: 1 min)
Demand up to 8 700 flights
Up to 37 000 intersecting flights during FL allocation
Up to 315 000 during ground holding
Resolution
All instances solved down to FL0 (except TMA)
Max optimality proof for most of them
A few seconds for FL allocation and about 1 min for ground holding
No optimization of the mean/sum but minimizing search heuristic
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 14 / 22
Results
Results
Instance Figures
Traffic within French airspace in 2008 (time step: 1 min)
Demand up to 8 700 flights
Up to 37 000 intersecting flights during FL allocation
Up to 315 000 during ground holding
Resolution
All instances solved down to FL0 (except TMA)
Max optimality proof for most of them
A few seconds for FL allocation and about 1 min for ground holding
No optimization of the mean/sum but minimizing search heuristic
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 14 / 22
Results FL Allocation Stage
Reduction of the Number of Conflicts After FL Allocation
0
500
1000
1500
2000
2500
3000
3500
4000
0812 0813 0814 1006 1007 1008 1010
RFLAFL
Cannot take climb/descent phase into account (≈ 75% of all conflicts)
All cruising phase conflicts solved for devmax = FL30
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 15 / 22
Results FL Allocation Stage
Distribution of Discrepancies from RFL After Allocation
0
2000
4000
6000
8000
10000
0812 0813 0814 1006 1007 1008 1010
0 10 20 30
0
2000
4000
6000
8000
10000
0812 0813 0814 1006 1007 1008 1010
0 10 20 30
Flows Model Single Flight Model
Cost with Single Flight Model 55% better than with Flows Model
All instances solved with devmax = FL30, costFL = 16 000− 20 000
80% at their RFL, 20% at FL10, 1% at FL20 and a couple at FL30
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 16 / 22
Results Ground Holding Stage
Optimal Max Cost Before and After FL Allocation
0
20
40
60
80
100
0812 0813 0814 1006 1007 1008 1010
RFLAFL
Reduction up to 40% (average 25%)
But max criterion does not reflect the overall amount of delay
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 17 / 22
Results Ground Holding Stage
Sum of delays before and after FL allocation
0
2000
4000
6000
8000
10000
12000
14000
16000
0812 0813 0814 1006 1007 1008 1010
RFLAFL
Reduced by 25% on average (up to 36%)
More consistent than max delay
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 18 / 22
Results Ground Holding Stage
Percentage of delayed flights before and after FL allocation
0
10
20
30
40
50
0812 0813 0814 1006 1007 1008 1010
RFLAFL
Reduced by 5% on average (up to 8%)
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 19 / 22
Further Works
Further Works
More Realistic Modelling
Temporal uncertainties taken into account in real time withiterative resolution over a sliding time window
Side constraints: aircraft rotation (easy to implement but lack ofdata)...
Handling remaining conflicts with CATS resolution modules [Granger,Durand, Alliot 2001] (horizontal manœuvres, speed adjustment)
European Instances
Up to 30 000 flights a day
More RAM or other search paradigms (LS, meta-heuristics,combination with CP)
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 20 / 22
Further Works
Further Works
More Realistic Modelling
Temporal uncertainties taken into account in real time withiterative resolution over a sliding time window
Side constraints: aircraft rotation (easy to implement but lack ofdata)...
Handling remaining conflicts with CATS resolution modules [Granger,Durand, Alliot 2001] (horizontal manœuvres, speed adjustment)
European Instances
Up to 30 000 flights a day
More RAM or other search paradigms (LS, meta-heuristics,combination with CP)
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 20 / 22
Further Works
Handling Uncertainties with Sliding Time Window
T3
4T
Tw
2σ
3σ
initT
2T
t = 0
t =
t =
t =
1Tσ
uncertainty on take−off time
frozen zone
modifiable zone
σ
Flights with departure time between t − σ and t are “noised”
If the uncertainty brings them back to the “modifiable zone”, they aretaken into account again for allocation
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 21 / 22
Conclusion
Conclusion
ATM
Flight level allocation and ground holding combined
Deconfliction vs aggregated regulation
FL allocation with very low discrepancies to RFL
Amount of allocated delay compatible with typical CFMU figures
Large problem but optimality proof (w.r.t. max) obtained with CP
Has to be combined with other strategies (e.g. sliding windows)when managing uncertainties
CP
Versatile technology: quick prototyping, various search strategies,incremental refinement of the model, side constraints...
CP technology scalable to such LSCOP, even with ECAC instances?
May be combined with other search paradigms: LS to solve CSP, CPto speed up LS...
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 22 / 22
Conclusion
Conclusion
ATM
Flight level allocation and ground holding combined
Deconfliction vs aggregated regulation
FL allocation with very low discrepancies to RFL
Amount of allocated delay compatible with typical CFMU figures
Large problem but optimality proof (w.r.t. max) obtained with CP
Has to be combined with other strategies (e.g. sliding windows)when managing uncertainties
CP
Versatile technology: quick prototyping, various search strategies,incremental refinement of the model, side constraints...
CP technology scalable to such LSCOP, even with ECAC instances?
May be combined with other search paradigms: LS to solve CSP, CPto speed up LS...
C. Allignol, N. Barnier (DSNA – ENAC) 4D-Deconfliction ATM 2011 22 / 22