Deconfliction with Constraint Programming Nicolas Barnier and Cyril Allignol [email protected],[email protected]ENAC – DTI/R&D International Workshop on Constraint Technology for Air Traffic Control & Management INO’08 12/02/2008 N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 1 / 23
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Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol [email protected],[email protected]
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2 Pre-tactical (a few days to a few hours) : Air Traffic FlowManagement (ATFM), sector openings and capacities, flow regulationby delaying and rerouting (Central Flow Management Unit)
3 Tactical (5-15 min) : Air Traffic Control (ATC), surveillance,coordination, conflict resolution
2 Pre-tactical (a few days to a few hours) : Air Traffic FlowManagement (ATFM), sector openings and capacities, flow regulationby delaying and rerouting (Central Flow Management Unit)
3 Tactical (5-15 min) : Air Traffic Control (ATC), surveillance,coordination, conflict resolution
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 4 / 23
Context Ground-Holding
Ground-Holding
Pre-tactical Flow Regulation
Safest than handling the traffic while airborne
Costly for airlines and passengers, snowball effect
Sector Capacity and Regulation
Air Traffic Control Centres (ATCC) opening schedules : designed byexperts (FMP)
Open sectors capacities : hourly entry rate
Regulation on flows crossing overloaded sectors : Computer AssistedSlot Allocation (CASA) at CFMU
CASA
Greedy algorithm : optimality, consistency
“First-come, first-served” questionable principle
Operational setting, real-time updates
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 5 / 23
Context Ground-Holding
Ground-Holding
Pre-tactical Flow Regulation
Safest than handling the traffic while airborne
Costly for airlines and passengers, snowball effect
Sector Capacity and Regulation
Air Traffic Control Centres (ATCC) opening schedules : designed byexperts (FMP)
Open sectors capacities : hourly entry rate
Regulation on flows crossing overloaded sectors : Computer AssistedSlot Allocation (CASA) at CFMU
CASA
Greedy algorithm : optimality, consistency
“First-come, first-served” questionable principle
Operational setting, real-time updates
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 5 / 23
Context Ground-Holding
Ground-Holding
Pre-tactical Flow Regulation
Safest than handling the traffic while airborne
Costly for airlines and passengers, snowball effect
Sector Capacity and Regulation
Air Traffic Control Centres (ATCC) opening schedules : designed byexperts (FMP)
Open sectors capacities : hourly entry rate
Regulation on flows crossing overloaded sectors : Computer AssistedSlot Allocation (CASA) at CFMU
CASA
Greedy algorithm : optimality, consistency
“First-come, first-served” questionable principle
Operational setting, real-time updates
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 5 / 23
Context Ground-Holding
Slot Allocation with CP
Optimize upon CASA Solutions
SHAMAN : CP model over 30 min periods (CENA/RFM)ISA : CP and LP [Junker et al]Marabout : sort constraint with FaCiLe to smooth the entry rate[ATM’01]
“Complexity” of Traffic
Relevance of sector capacity to model controller workload ?Discrepancies between planned schedule and actual openingsMore pertinent metrics w.r.t. real-time merge/split decision[Giannazza, Guittet 06]
Prior Opening Schedule Optimization
Optimize upon FMP’s opening scheduleMultiple partitioning problem, possibly with side transition constraints[Barnier 02]Lower cost for slot allocationWith other workload metrics [Giannazza 07]
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 6 / 23
Context Ground-Holding
Slot Allocation with CP
Optimize upon CASA Solutions
SHAMAN : CP model over 30 min periods (CENA/RFM)ISA : CP and LP [Junker et al]Marabout : sort constraint with FaCiLe to smooth the entry rate[ATM’01]
“Complexity” of Traffic
Relevance of sector capacity to model controller workload ?Discrepancies between planned schedule and actual openingsMore pertinent metrics w.r.t. real-time merge/split decision[Giannazza, Guittet 06]
Prior Opening Schedule Optimization
Optimize upon FMP’s opening scheduleMultiple partitioning problem, possibly with side transition constraints[Barnier 02]Lower cost for slot allocationWith other workload metrics [Giannazza 07]
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 6 / 23
Context Ground-Holding
Slot Allocation with CP
Optimize upon CASA Solutions
SHAMAN : CP model over 30 min periods (CENA/RFM)ISA : CP and LP [Junker et al]Marabout : sort constraint with FaCiLe to smooth the entry rate[ATM’01]
“Complexity” of Traffic
Relevance of sector capacity to model controller workload ?Discrepancies between planned schedule and actual openingsMore pertinent metrics w.r.t. real-time merge/split decision[Giannazza, Guittet 06]
Prior Opening Schedule Optimization
Optimize upon FMP’s opening scheduleMultiple partitioning problem, possibly with side transition constraints[Barnier 02]Lower cost for slot allocationWith other workload metrics [Giannazza 07]
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 6 / 23
Context Ground-Holding
ResultsStandard Model
15
30
35
20
25
10
5
00 200 400 600 800 1000 1200 1400
Non régulé
50
45
40
Standard
Entries within the next δ min
Flights in the sector
Marabout
00
5
10
15
20
25
30
35
40
45
50
400 600 800 1000 1200200 1400
Non réguléTri
30
0
Standard
200 400 600 800 1000 1200 1400
25
20
15
10
5
0
Tri
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 7 / 23
Context Ground-Holding
ResultsStandard Model
15
30
35
20
25
10
5
00 200 400 600 800 1000 1200 1400
Non régulé
50
45
40
Standard
Entries within the next δ min
Flights in the sector
Marabout
00
5
10
15
20
25
30
35
40
45
50
400 600 800 1000 1200200 1400
Non réguléTri
30
0
Standard
200 400 600 800 1000 1200 1400
25
20
15
10
5
0
Tri
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 7 / 23
Context Ground-Holding
ResultsStandard Model
15
30
35
20
25
10
5
00 200 400 600 800 1000 1200 1400
Non régulé
50
45
40
Standard
Entries within the next δ min
30
0
25
20
15
10
5
0200 400 600 800 1000 1200 1400
Flights in the sector
Marabout
00
5
10
15
20
25
30
35
40
45
50
400 600 800 1000 1200200 1400
Non réguléTri
30
0
Standard
200 400 600 800 1000 1200 1400
25
20
15
10
5
0
Tri
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 7 / 23
Context Ground-Holding
ResultsStandard Model
15
30
35
20
25
10
5
00 200 400 600 800 1000 1200 1400
Non régulé
50
45
40
Standard
Entries within the next δ min
30
0
25
20
15
10
5
0200 400 600 800 1000 1200 1400
Flights in the sector
Marabout
00
5
10
15
20
25
30
35
40
45
50
400 600 800 1000 1200200 1400
Non réguléTri
30
0
Standard
200 400 600 800 1000 1200 1400
25
20
15
10
5
0
Tri
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 7 / 23
Context Ground-Holding
ResultsStandard Model
15
30
35
20
25
10
5
00 200 400 600 800 1000 1200 1400
Non régulé
50
45
40
Standard
Entries within the next δ min
30
0
25
20
15
10
5
0200 400 600 800 1000 1200 1400
Flights in the sector
Marabout
00
5
10
15
20
25
30
35
40
45
50
400 600 800 1000 1200200 1400
Non réguléTri
30
0
Standard
200 400 600 800 1000 1200 1400
25
20
15
10
5
0
Tri
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 7 / 23
Context Ground-Holding
ResultsStandard Model
15
30
35
20
25
10
5
00 200 400 600 800 1000 1200 1400
Non régulé
50
45
40
Standard
Entries within the next δ min
30
0
25
20
15
10
5
0200 400 600 800 1000 1200 1400
Flights in the sector
Marabout
00
5
10
15
20
25
30
35
40
45
50
400 600 800 1000 1200200 1400
Non réguléTri
30
0
Standard
200 400 600 800 1000 1200 1400
25
20
15
10
5
0
Tri
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 7 / 23
Context Ground-Holding
Conflict-Free 4D Tubes
4D Trajectory Planning
European Commission Episode 3 project (WP3)
4D trajectory planning to reduce conflicts number and controllerworkload
Many opportunities : flight level, speed, rerouting...
Large scale combinatorial optimization problem
Deconfliction by Ground-Holding
Finest grain vs aggregated model (sector capacity)
Same degree of freedom than slot allocation
Solve all conflicts above a given FL by delaying flights only
Standard (flight plan) and direct routes considered
Assumption : aircraft able to follow their 4D trajectories precisely...
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 8 / 23
Context Ground-Holding
Conflict-Free 4D Tubes
4D Trajectory Planning
European Commission Episode 3 project (WP3)
4D trajectory planning to reduce conflicts number and controllerworkload
Many opportunities : flight level, speed, rerouting...
Large scale combinatorial optimization problem
Deconfliction by Ground-Holding
Finest grain vs aggregated model (sector capacity)
Same degree of freedom than slot allocation
Solve all conflicts above a given FL by delaying flights only
Standard (flight plan) and direct routes considered
Assumption : aircraft able to follow their 4D trajectories precisely...
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 8 / 23
Deconfliction by Ground-Holding Model
Model
Data
Flight plans and airspace data for one day of traffic
Simulation with CATS [Alliot,Durand 97]
Trajectories sampled every 15s (shortest conflicts not missed) overFrench controlled airspace
Notation : flight i at point pki at time tk
i if not delayed
Variables and Constraints
Decision variables : delay δi for each flight i
Auxilliary variables : θki = tk
i + δi dij = δj − δiConstraints : two flights cannot be at two conflicting points of theirtrajectories at the same time
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 9 / 23
Deconfliction by Ground-Holding Model
Model
Data
Flight plans and airspace data for one day of traffic
Simulation with CATS [Alliot,Durand 97]
Trajectories sampled every 15s (shortest conflicts not missed) overFrench controlled airspace
Notation : flight i at point pki at time tk
i if not delayed
Variables and Constraints
Decision variables : delay δi for each flight i
Auxilliary variables : θki = tk
i + δi dij = δj − δiConstraints : two flights cannot be at two conflicting points of theirtrajectories at the same time
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 9 / 23
Deconfliction by Ground-Holding Model
Constraints
Conflict Constraints
∀i 6= j ,∀k, l , such that dh(pki , p
li ) < 5 NM ∧ dv (pk
i , pli ) < 1000 ft :
θki 6= θl
j
tki + δi 6= t l
j + δj
dij 6= tki − t l
j
Note : bandwidth coloring as a particular case
Non European Flight
Flights originating outside the ECAC zone cannot be delayed byEurocontrol instances (≈ 10%)
Delay fixed to 0
Remaining conflicts discarded (a few dozens)
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 10 / 23
Deconfliction by Ground-Holding Model
Constraints
Conflict Constraints
∀i 6= j ,∀k, l , such that dh(pki , p
li ) < 5 NM ∧ dv (pk
i , pli ) < 1000 ft :
θki 6= θl
j
tki + δi 6= t l
j + δj
dij 6= tki − t l
j
Note : bandwidth coloring as a particular case
Non European Flight
Flights originating outside the ECAC zone cannot be delayed byEurocontrol instances (≈ 10%)
Delay fixed to 0
Remaining conflicts discarded (a few dozens)
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 10 / 23
Deconfliction by Ground-Holding Model
Conflict Detection
Conflicting Points Detection
��������
�����
�����
������������
������������5 NM
1000 ft
pik
pjl
i
j
d < 5 Nm & d < 1000 fth v
Naıve 3D Conflicting Segments
3D transitive closure of segments of conflicting points
Forbidden time interval corresponds to extremities of segments
Same route : whole trajectory conflicting !
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 11 / 23
Deconfliction by Ground-Holding Model
Conflict Detection
Conflicting Points Detection
��������
�����
�����
������������
������������5 NM
1000 ft
pik
pjl
i
j
d < 5 Nm & d < 1000 fth v
Naıve 3D Conflicting Segments
3D transitive closure of segments of conflicting points
Forbidden time interval corresponds to extremities of segments
Same route : whole trajectory conflicting !
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 11 / 23
Deconfliction by Ground-Holding Model
4D-Conflict Constraints
ijd
0
i
j
−2w 2w
tki ∈ [1000, 1180], t l
j ∈ [600, 750]
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 12 / 23
Deconfliction by Ground-Holding Model
4D-Conflict Constraints
ijd
0
i
j
−2w 2w
t1i = 1000
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 12 / 23
Deconfliction by Ground-Holding Model
4D-Conflict Constraints
ijd
0
i
j
−2w 2w
t2i = 1015
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 12 / 23
Deconfliction by Ground-Holding Model
4D-Conflict Constraints
ijd
0
i
j
−2w 2w370 400
t3i = 1030, [t3
j = 630, t5j = 660], dij 6∈ [370, 400]
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 12 / 23
Larger (European) instances with soft constraints and otheroptimization paradigms : local search (LS), meta-heuristics, combinedwith CP (LNS)
Post-optimization of the sum/mean with LS or CP once themaximum delay is bounded
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 22 / 23
Conclusion
Conclusion
ATM
Ground-Holding for deconfliction vs macroscopic regulationLarge problem but optimality proof obtained (w.r.t. max) with CPSome instances with solution compatible with CFMU figures, toocostly for some othersBetter results with direct routesHas to be combined with other strategies, like flight levelallocation, to lower the delay costUncertainties : have to be taken into account in the operationalsetting, until accurate 4D-FMS are designed
CP
CP technology scalable to such LSCOPStill scalable to European instances 20 000-30 000 flights/day ?Combined with other search paradigms : LS to solve CSP, CP tospeed up LS...
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 23 / 23
Conclusion
Conclusion
ATM
Ground-Holding for deconfliction vs macroscopic regulationLarge problem but optimality proof obtained (w.r.t. max) with CPSome instances with solution compatible with CFMU figures, toocostly for some othersBetter results with direct routesHas to be combined with other strategies, like flight levelallocation, to lower the delay costUncertainties : have to be taken into account in the operationalsetting, until accurate 4D-FMS are designed
CP
CP technology scalable to such LSCOPStill scalable to European instances 20 000-30 000 flights/day ?Combined with other search paradigms : LS to solve CSP, CP tospeed up LS...
N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 23 / 23