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Deconfliction with Constraint Programming

Nicolas Barnier and Cyril Allignol

barnier@recherche.enac.fr,allignol@tls.cena.fr

ENAC – DTI/R&D

International Workshop on Constraint Technology for Air Traffic Control & Management

INO’08 12/02/2008

(2)

Outline

1 Introduction

2 Context

ATC and ATFM Ground-Holding

3 Deconfliction by Ground-Holding Model

Search and Optimization Results

4 Further Works

5 Conclusion

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

(3)

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 tool

side constraints incrementally added experiment with various search strategies

Feasibility stage : CP able to achieve optimality proof

(4)

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 tool

side constraints incrementally added experiment with various search strategies

Feasibility stage : CP able to achieve optimality proof

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 3 / 23

(5)

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 of routes, sectors and procedures

2 Pre-tactical (a few days to a few hours) : Air Traffic Flow

Management (ATFM), sector openings and capacities, flow regulation by 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)

(6)

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 of routes, sectors and procedures

2 Pre-tactical (a few days to a few hours) : Air Traffic Flow

Management (ATFM), sector openings and capacities, flow regulation by 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

(7)

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 by experts (FMP)

Open sectors capacities : hourly entry rate

Regulation on flows crossing overloaded sectors : Computer Assisted Slot Allocation (CASA) at CFMU

CASA

Greedy algorithm : optimality, consistency

“First-come, first-served” questionable principle Operational setting, real-time updates

(8)

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 by experts (FMP)

Open sectors capacities : hourly entry rate

Regulation on flows crossing overloaded sectors : Computer Assisted Slot 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

(9)

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 by experts (FMP)

Open sectors capacities : hourly entry rate

Regulation on flows crossing overloaded sectors : Computer Assisted Slot Allocation (CASA) at CFMU

CASA

Greedy algorithm : optimality, consistency

“First-come, first-served” questionable principle Operational setting, real-time updates

(10)

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 openings More pertinent metrics w.r.t. real-time merge/split decision [Giannazza, Guittet 06]

Prior Opening Schedule Optimization Optimize upon FMP’s opening schedule

Multiple partitioning problem, possibly with side transition constraints [Barnier 02]

Lower cost for slot allocation

With other workload metrics [Giannazza 07]

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 6 / 23

(11)

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 openings More pertinent metrics w.r.t. real-time merge/split decision [Giannazza, Guittet 06]

Prior Opening Schedule Optimization Optimize upon FMP’s opening schedule

Multiple partitioning problem, possibly with side transition constraints [Barnier 02]

Lower cost for slot allocation

With other workload metrics [Giannazza 07]

(12)

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 openings More pertinent metrics w.r.t. real-time merge/split decision [Giannazza, Guittet 06]

Prior Opening Schedule Optimization Optimize upon FMP’s opening schedule

Multiple partitioning problem, possibly with side transition constraints [Barnier 02]

Lower cost for slot allocation

With other workload metrics [Giannazza 07]

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 6 / 23

(13)

Context Ground-Holding

Results

Standard Model

15 30 35

20 25

10 5 0

0 200 400 600 800 1000 1200 1400

Non régulé 50

45 40

Standard

Entries within the next δ min

Flights in the sector

Marabout

0 0 5 10 15 20 25 30 35 40 45 50

400 600 800 1000 1200

200 1400

Non régulé Tri

30

0 Standard

200 400 600 800 1000 1200 1400

25

20

15

10

5

0 Tri

(14)

Context Ground-Holding

Results

Standard Model

15 30 35

20 25

10 5 0

0 200 400 600 800 1000 1200 1400

Non régulé 50

45 40

Standard

Entries within the next δ min

Flights in the sector

Marabout

0 0 5 10 15 20 25 30 35 40 45 50

400 600 800 1000 1200

200 1400

Non régulé Tri

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

(15)

Context Ground-Holding

Results

Standard Model

15 30 35

20 25

10 5 0

0 200 400 600 800 1000 1200 1400

Non régulé 50

45 40

Standard

Entries within the next δ min

30

0 25

20

15

10

5

0

200 400 600 800 1000 1200 1400

Flights in the sector

Marabout

0 0 5 10 15 20 25 30 35 40 45 50

400 600 800 1000 1200

200 1400

Non régulé Tri

30

0 Standard

200 400 600 800 1000 1200 1400

25

20

15

10

5

0 Tri

(16)

Context Ground-Holding

Results

Standard Model

15 30 35

20 25

10 5 0

0 200 400 600 800 1000 1200 1400

Non régulé 50

45 40

Standard

Entries within the next δ min

30

0 25

20

15

10

5

0

200 400 600 800 1000 1200 1400

Flights in the sector

Marabout

0 0 5 10 15 20 25 30 35 40 45 50

400 600 800 1000 1200

200 1400

Non régulé Tri

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

(17)

Context Ground-Holding

Results

Standard Model

15 30 35

20 25

10 5 0

0 200 400 600 800 1000 1200 1400

Non régulé 50

45 40

Standard

Entries within the next δ min

30

0 25

20

15

10

5

0

200 400 600 800 1000 1200 1400

Flights in the sector

Marabout

0 0 5 10 15 20 25 30 35 40 45 50

400 600 800 1000 1200

200 1400

Non régulé Tri

30

0 Standard

200 400 600 800 1000 1200 1400

25

20

15

10

5

0 Tri

(18)

Context Ground-Holding

Results

Standard Model

15 30 35

20 25

10 5 0

0 200 400 600 800 1000 1200 1400

Non régulé 50

45 40

Standard

Entries within the next δ min

30

0 25

20

15

10

5

0

200 400 600 800 1000 1200 1400

Flights in the sector

Marabout

0 0 5 10 15 20 25 30 35 40 45 50

400 600 800 1000 1200

200 1400

Non régulé Tri

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

(19)

Context Ground-Holding

Conflict-Free 4D Tubes

4D Trajectory Planning

European Commission Episode 3 project (WP3)

4D trajectory planning to reduce conflicts number and controller workload

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...

(20)

Context Ground-Holding

Conflict-Free 4D Tubes

4D Trajectory Planning

European Commission Episode 3 project (WP3)

4D trajectory planning to reduce conflicts number and controller workload

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

(21)

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) over French controlled airspace

Notation : flight i at point pik at time tik if not delayed

Variables and Constraints

Decision variables : delay δi for each flight i Auxilliary variables : θki = tik + δi dij = δj − δi

Constraints : two flights cannot be at two conflicting points of their trajectories at the same time

(22)

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) over French controlled airspace

Notation : flight i at point pik at time tik if not delayed

Variables and Constraints

Decision variables : delay δi for each flight i Auxilliary variables : θki = tik + δi dij = δj − δi

Constraints : two flights cannot be at two conflicting points of their trajectories at the same time

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 9 / 23

(23)

Deconfliction by Ground-Holding Model

Constraints

Conflict Constraints

∀i 6= j, ∀k, l, such that dh(pik, pil) < 5 NM ∧ dv(pki, pil) < 1000 ft : θki 6= θjl

tik+ δi 6= tjl+ δj dij 6= tik− tjl Note : bandwidth coloring as a particular case

Non European Flight

Flights originating outside the ECAC zone cannot be delayed by Eurocontrol instances (≈ 10%)

Delay fixed to 0

Remaining conflicts discarded (a few dozens)

(24)

Deconfliction by Ground-Holding Model

Constraints

Conflict Constraints

∀i 6= j, ∀k, l, such that dh(pik, pil) < 5 NM ∧ dv(pki, pil) < 1000 ft : θki 6= θjl

tik+ δi 6= tjl+ δj dij 6= tik− tjl Note : bandwidth coloring as a particular case

Non European Flight

Flights originating outside the ECAC zone cannot be delayed by Eurocontrol 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

(25)

Deconfliction by Ground-Holding Model

Conflict Detection

Conflicting Points Detection

0000 1111 00 00 0 11 11

1 000000000000 11111111 11115 NM 1000 ft

pik

pjl

i j

d < 5 Nm  &  d < 1000 fth v

Na¨ıve 3D Conflicting Segments

3D transitive closure of segments of conflicting points

Forbidden time interval corresponds to extremities of segments Same route : whole trajectory conflicting !

(26)

Deconfliction by Ground-Holding Model

Conflict Detection

Conflicting Points Detection

0000 1111 00 00 0 11 11

1 000000000000 11111111 11115 NM 1000 ft

pik

pjl

i j

d < 5 Nm  &  d < 1000 fth v

Na¨ıve 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

(27)

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

dij

0 i

j

−2w 2w

tik ∈ [1000, 1180], tjl ∈ [600, 750]

(28)

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

dij

0 i

j

−2w 2w

ti1= 1000

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

(29)

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

dij

0 i

j

−2w 2w

ti2= 1015

(30)

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

dij

0 i

j

−2w 370 400 2w

ti3 = 1030, [tj3 = 630, tj5 = 660], dij 6∈ [370,400]

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

(31)

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

dij

0 i

j

−2w 370 415 2w

ti4 = 1045, [tj3 = 630 − tj6= 675], dij 6∈ [370, 415] ⊆ [370,415]

(32)

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

dij

0 i

j

−2w 370 430 2w

ti5 = 1060, [tj3 = 630 − tj7= 690], dij 6∈ [370, 430] ⊆ [370,430]

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

(33)

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

dij

0 i

j

−2w 370 430 2w

ti6 = 1075, [tj4 = 645 − tj8= 705], dij 6∈ [370, 430] ⊆ [370, 430]

(34)

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

dij

0 i

j

−2w 370 385 445 2w

ti7 = 1090, [tj4 = 645 − tj8= 705], dij 6∈ [385, 445] ⊆ [370,445]

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

(35)

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

dij

0 i

j

−2w 370 385 445 2w

ti8 = 1105, [tj5 = 660 − tj9= 720], dij 6∈ [385, 445] ⊆ [370, 445]

(36)

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

dij

0 i

j

−2w 370 385 460 2w

ti9 = 1120, [tj5= 660 − tj10= 735], dij 6∈ [385, 460] ⊆ [370,460]

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

(37)

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

dij

0 i

j

−2w 370 400 460 2w

ti10= 1135, [tj6 = 675 − tj10= 735], dij 6∈ [400, 460] ⊆ [370, 460]

(38)

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

dij

0 i

j

−2w 370 415 460 2w

t11i = 1150, [tj7 = 690 − tj10= 735], dij 6∈ [415, 460] ⊆ [370, 460]

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

(39)

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

dij

0 i

j

−2w 370 415 430 460 2w

t12i = 1165, [tj9 = 720 − tj10= 735], dij 6∈ [415, 430] ⊆ [370, 460]

(40)

Deconfliction by Ground-Holding Model

4D-Conflict Constraints

dij

0 i

j

−2w 370 460 2w

dij = δj − δi 6∈ [370, 460]

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

(41)

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

4503 4589

900 910 920 930 940 950 960 970

dij = δj − δi 6∈ [lb1ij..ub1ij] ∪ · · · ∪ [lbkij..ubkij]

(42)

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 0 100 50 150 200 250 300 350 400 450

500 550 600 650 700 750 800 850 900

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 14 / 23

(43)

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 same pair, otherwise merged

Time unit (1 min) : scaled with strict enclosure of conflicting intervals Flights without conflict are withdrawn

(44)

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 same pair, 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

(45)

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 in scheduling problems

Order conflicting flights by branching within the disjoint intervals of 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

(46)

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 in scheduling problems

Order conflicting flights by branching within the disjoint intervals of 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

(47)

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 the easiest day

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

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

(48)

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 the easiest day

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

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

(49)

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

060709s 060709d 070123 070622 060425

(50)

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

060709s 060709d 070123 070622 060425

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 19 / 23

(51)

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

060709s 060709d 070123 070622 060425

(52)

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

060709s 060709d 070123 070622 060425

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

(53)

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 ground speed, 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 other

optimization paradigms : local search (LS), meta-heuristics, combined with CP (LNS)

Post-optimization of the sum/mean with LS or CP once the maximum delay is bounded

(54)

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 ground speed, 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 other

optimization paradigms : local search (LS), meta-heuristics, combined with CP (LNS)

Post-optimization of the sum/mean with LS or CP once the maximum delay is bounded

N. Barnier & C. Allignol (ENAC – DTI) Deconfliction with Constraint Programming ATM-CT 12/02/08 22 / 23

(55)

Conclusion

Conclusion

ATM

Ground-Holding for deconfliction vs macroscopic regulation Large problem but optimality proof obtained (w.r.t. max) with CP Some instances with solution compatible with CFMU figures, too costly for some others

Better results with direct routes

Has to be combined with other strategies, like flight level allocation, to lower the delay cost

Uncertainties : have to be taken into account in the operational setting, until accurate 4D-FMS are designed

CP

CP technology scalable to such LSCOP

Still scalable to European instances 20 000-30 000 flights/day ? Combined with other search paradigms : LS to solve CSP, CP to speed up LS...

(56)

Conclusion

Conclusion

ATM

Ground-Holding for deconfliction vs macroscopic regulation Large problem but optimality proof obtained (w.r.t. max) with CP Some instances with solution compatible with CFMU figures, too costly for some others

Better results with direct routes

Has to be combined with other strategies, like flight level allocation, to lower the delay cost

Uncertainties : have to be taken into account in the operational setting, until accurate 4D-FMS are designed

CP

CP technology scalable to such LSCOP

Still scalable to European instances 20 000-30 000 flights/day ? Combined with other search paradigms : LS to solve CSP, CP to speed up LS...

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

References

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