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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

Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol [email protected],[email protected]

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Page 1: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

Deconfliction with Constraint Programming

Nicolas Barnier and Cyril [email protected],[email protected]

ENAC – DTI/R&D

International Workshop on Constraint Technologyfor Air Traffic Control & Management

INO’0812/02/2008

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 1 / 23

Page 2: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

Outline

1 Introduction

2 ContextATC and ATFMGround-Holding

3 Deconfliction by Ground-HoldingModelSearch and OptimizationResults

4 Further Works

5 Conclusion

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 2 / 23

Page 3: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

Introduction

Introduction

Congested European Sky

Traffic still growing by a yearly 5%

Increasing regulation delays due to en-route sector capacities

Structural limits of the ATM system reached

Optimization of airspace structure and ATFM regulations

EC Single European Sky (SESAR) / Episode 3 - WP3

Pre-tactical Deconfliction with Constraint Programming

Deconfliction by ground-holding

Highly combinatorial/disjunctive large scale problem

Constraint Programming (CP) technology :

versatile modelling toolside constraints incrementally addedexperiment with various search strategies

Feasibility stage : CP able to achieve optimality proofN. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 3 / 23

Page 4: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

Introduction

Introduction

Congested European Sky

Traffic still growing by a yearly 5%

Increasing regulation delays due to en-route sector capacities

Structural limits of the ATM system reached

Optimization of airspace structure and ATFM regulations

EC Single European Sky (SESAR) / Episode 3 - WP3

Pre-tactical Deconfliction with Constraint Programming

Deconfliction by ground-holding

Highly combinatorial/disjunctive large scale problem

Constraint Programming (CP) technology :

versatile modelling toolside constraints incrementally addedexperiment with various search strategies

Feasibility stage : CP able to achieve optimality proofN. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 3 / 23

Page 5: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

Context ATC and ATFM

ATC and ATFM

Objectives

1 Safety : maintaining aircraft separated

2 Efficiency : expedite the flow of traffic

Layered Filters with Decreasing Time Horizon

1 Strategic (several months) : AirSpace Management (ASM), design ofroutes, sectors and procedures

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

4 Emergency (< 5 min) : safety nets, ground-based (STCA, MSAW)and airborne (TCAS, GPWS)

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 4 / 23

Page 6: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

Context ATC and ATFM

ATC and ATFM

Objectives

1 Safety : maintaining aircraft separated

2 Efficiency : expedite the flow of traffic

Layered Filters with Decreasing Time Horizon

1 Strategic (several months) : AirSpace Management (ASM), design ofroutes, sectors and procedures

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

4 Emergency (< 5 min) : safety nets, ground-based (STCA, MSAW)and airborne (TCAS, GPWS)

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 4 / 23

Page 7: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 8: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 9: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 10: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 11: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 12: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 13: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 14: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 15: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 16: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 17: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 18: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 19: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 20: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 21: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 22: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 23: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 24: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 25: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 26: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 27: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 28: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 29: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 30: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

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

Page 31: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

ijd

0

i

j

−2w 2w415370

t4i = 1045, [t3

j = 630− t6j = 675], dij 6∈ [370, 415] ⊆ [370, 415]

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 12 / 23

Page 32: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

ijd

0

i

j

−2w 2w430370

t5i = 1060, [t3

j = 630− t7j = 690], dij 6∈ [370, 430] ⊆ [370, 430]

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 12 / 23

Page 33: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

ijd

0

i

j

−2w 2w430370

t6i = 1075, [t4

j = 645− t8j = 705], dij 6∈ [370, 430] ⊆ [370, 430]

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 12 / 23

Page 34: Deconfliction with Constraint Programming - Uppsala University · Decon iction with Constraint Programming Nicolas Barnier and Cyril Allignol barnier@recherche.enac.fr,allignol@tls.cena.fr

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

ijd

0

i

j

−2w 2w445370 385

t7i = 1090, [t4

j = 645− t8j = 705], dij 6∈ [385, 445] ⊆ [370, 445]

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 12 / 23

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Deconfliction by Ground-Holding Model

4D-Conflict Constraints

ijd

0

i

j

−2w 2w370 385 445

t8i = 1105, [t5

j = 660− t9j = 720], dij 6∈ [385, 445] ⊆ [370, 445]

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Deconfliction by Ground-Holding Model

4D-Conflict Constraints

ijd

0

i

j

−2w 2w370 385 460

t9i = 1120, [t5

j = 660− t10j = 735], dij 6∈ [385, 460] ⊆ [370, 460]

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Deconfliction by Ground-Holding Model

4D-Conflict Constraints

ijd

0

i

j

−2w 2w370 400 460

t10i = 1135, [t6

j = 675− t10j = 735], dij 6∈ [400, 460] ⊆ [370, 460]

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 12 / 23

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Deconfliction by Ground-Holding Model

4D-Conflict Constraints

ijd

0

i

j

−2w 2w370 415 460

t i11 = 1150, [t7

j = 690− t10j = 735], dij 6∈ [415, 460] ⊆ [370, 460]

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 12 / 23

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Deconfliction by Ground-Holding Model

4D-Conflict Constraints

ijd

0

i

j

−2w 2w370 415 460430

t i12 = 1165, [t9

j = 720− t10j = 735], dij 6∈ [415, 430] ⊆ [370, 460]

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 12 / 23

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Deconfliction by Ground-Holding Model

4D-Conflict Constraints

ijd

0

i

j

−2w 2w370 460

dij = δj − δi 6∈ [370, 460]

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 12 / 23

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Deconfliction by Ground-Holding Model

Mutliply-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∈ [lb1ij ..ub1

ij ] ∪ · · · ∪ [lbkij ..ubk

ij ]

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 13 / 23

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Deconfliction by Ground-Holding Model

Flight Conflicting with Many Other

Constraint Graph of High Degree

Maximally delayed flight potentially conflicting with 130 other

Highest degree > 300

Large cliques > 60

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

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Deconfliction by Ground-Holding Model

Further Instance Conditioning

Simulator Data

Date of the day of traffic

Standard or direct routes

Trajectories sampled every 15s

Instance Filtering

TMA : trajectories cut around airports (10 NM) for takeoff/landing

Maximal delay : problem size grows as more conflicts may occur

Minimal flight level (usually upper airspace ≥ FL290)

Minimal gap between two disjoint conflicting intervals of the samepair, otherwise merged

Time unit (1 min) : scaled with strict enclosure of conflicting intervals

Flights without conflict are withdrawn

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 15 / 23

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Deconfliction by Ground-Holding Model

Further Instance Conditioning

Simulator Data

Date of the day of traffic

Standard or direct routes

Trajectories sampled every 15s

Instance Filtering

TMA : trajectories cut around airports (10 NM) for takeoff/landing

Maximal delay : problem size grows as more conflicts may occur

Minimal flight level (usually upper airspace ≥ FL290)

Minimal gap between two disjoint conflicting intervals of the samepair, otherwise merged

Time unit (1 min) : scaled with strict enclosure of conflicting intervals

Flights without conflict are withdrawn

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 15 / 23

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Deconfliction by Ground-Holding Search and Optimization

Search and Optimization

Search Strategy

Directly labelling the delay decision variables is inefficient

High-order decision scheme by analogy with disjunctive tasks inscheduling problems

Order conflicting flights by branching within the disjoint intervalsof their dij domain

Dynamic variable ordering : choose dij with highest sparsity first

Choose smaller interval first to maximize propagation

Then label the delays δi by increasing values

Optimization

Cost = maximum delay : equity, easiest for optimality proof

Sum/Mean : exponentially harder

Leximin ? might be too propagation-costly

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 16 / 23

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Deconfliction by Ground-Holding Search and Optimization

Search and Optimization

Search Strategy

Directly labelling the delay decision variables is inefficient

High-order decision scheme by analogy with disjunctive tasks inscheduling problems

Order conflicting flights by branching within the disjoint intervalsof their dij domain

Dynamic variable ordering : choose dij with highest sparsity first

Choose smaller interval first to maximize propagation

Then label the delays δi by increasing values

Optimization

Cost = maximum delay : equity, easiest for optimality proof

Sum/Mean : exponentially harder

Leximin ? might be too propagation-costly

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 16 / 23

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Deconfliction by Ground-Holding Results

Results

Instance Size

Traffic from 2006/2007

Up to 8000 flights

Up to 300 000 conflicting pairs

Best solvable volume of airspace down to FL0 (except TMA) for theeasiest day

Disjoint conflicts for the same pair : up to 26 with raw data, 4 afterprocessing

Difference domains with up to 97% sparsity

Limitations

Instance size limited by memory usage (4 GB)

Running times < 30 min (Core 2 Duo @ 2.4 GHz)

No optimization of the mean/sum

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 17 / 23

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Deconfliction by Ground-Holding Results

Results

Instance Size

Traffic from 2006/2007

Up to 8000 flights

Up to 300 000 conflicting pairs

Best solvable volume of airspace down to FL0 (except TMA) for theeasiest day

Disjoint conflicts for the same pair : up to 26 with raw data, 4 afterprocessing

Difference domains with up to 97% sparsity

Limitations

Instance size limited by memory usage (4 GB)

Running times < 30 min (Core 2 Duo @ 2.4 GHz)

No optimization of the mean/sum

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 17 / 23

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Deconfliction by Ground-Holding Results

Minimal Flight Level vs Number of Flights

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

100 150 200 250 300 350 400

060709s060709d

070123070622060425

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 18 / 23

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Deconfliction by Ground-Holding Results

Number of Flights vs Number of Conflicts

0

50000

100000

150000

200000

250000

300000

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

060709s060709d

070123070622060425

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Deconfliction by Ground-Holding Results

Number of Flights vs Computation Time (Proof)

0

200

400

600

800

1000

1200

1400

1600

1800

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

060709s060709d

070123070622060425

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 20 / 23

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Deconfliction by Ground-Holding Results

Minimal flight level vs optimal cost

0

20

40

60

80

100

120

140

160

180

260 280 300 320 340 360 380 400

060709s060709d

070123070622060425

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 21 / 23

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Further Works

Further Works

Validation and Robustness

Validation of the solutions with the CATS simulator (undergoing)

Robustness of solutions w.r.t. uncertainty : vertical and groundspeed, takeoff time

Perspectives

Rotation constraints : easy to implement but not provided by airlines

Prior flight level allocation : pre-deconfliction, lower delay costs[CP-AI-OR’02]

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

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Further Works

Further Works

Validation and Robustness

Validation of the solutions with the CATS simulator (undergoing)

Robustness of solutions w.r.t. uncertainty : vertical and groundspeed, takeoff time

Perspectives

Rotation constraints : easy to implement but not provided by airlines

Prior flight level allocation : pre-deconfliction, lower delay costs[CP-AI-OR’02]

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

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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

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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