Air Traffic Flow and Capacity Management Using Constraint …becool.info.ucl.ac.be/summerschool2010/documents/Case... · 2018-06-15 · Air Trafﬁc Flow and Capacity Management Using

Air Traffic Flow and Capacity ManagementUsing Constraint Programming

Pierre Flener

ASTRA Research Group on CPUppsala University

Sweden

ACP Summer SchoolAussois (France), 6 May 2010

http://www.it.uu.se/research/group/astra

ComplexityResolution inMulti-SectorPlanning

DynamicDemand-CapacityBalancing

Air Traffic Management

The objective of air traffic management (ATM) is to ensure asafe, fair, and efficient flow of air traffic, under minimalenvironmental impact, subject to constraints onaircraft separation, airspace capacity, and airport capacity.

This long-term research is financed by theEuropean Organisation for the Safety of Air Navigation,whose mission is to promote the harmonisation of thedifferent national ATM systems in Europe.

6 May 2010 ACP Summer School 2010 - 2 - Pierre Flener

http://www.eurocontrol.int/



Outline

1 Complexity Resolution in Multi-Sector PlanningObjective & MotivationA CP ModelExperimentsConclusion

2 Dynamic Demand-Capacity BalancingObjective & MotivationA CP ModelExperimentsConclusion


ComplexityResolution inMulti-SectorPlanningObjective &Motivation

A CP Model

Experiments

Conclusion


Outline





A CP Model

Experiments

Conclusion


Outline





A CP Model

Experiments

Conclusion


Sector-Based Air Traffic Management

A sector is a3D air volume,whose trafficis monitoredby a pair ofair trafficcontrollers.The air trafficcomplexity forall controllerpairs mustsatisfy someconstraints.



A CP Model

Experiments

Conclusion


Target Scenario

Flight Profiles

Resolution Rules

Resolved Flight Profiles

Complexity Solver

m, m’, ff%, timeOut

Complexity Predictor

high

low

9020 m’

complexity

nowt

m



A CP Model

Experiments

Conclusion


Contributions

Traffic complexity 6= # flightsComplexity resolution (not just prediction) . . .. . . in multi-sector planningUse of constraint programming (CP) for this purpose



A CP Model

Experiments

Conclusion


Air Traffic Complexity Parameters

The complexity of sector s at moment m depends here on:Nsec = # flights in s at moment m (traffic volume)Ncd = # flights in s non-level at m (vertical state)Nnsb = # flights that are

• at most 15 nm horizontally, or at most 40 FL vertically• beyond their entry into s, or before their exit from s

at moment m (proximity to sector boundary)Reminder: 1 nautical mile = 1.852 km = 1.15 miles.

Note: The complexity of sector s at moment m does notdepend here on potentially interacting pairs of aircraft: dotraffic volume & vertical state already capture this effect?



A CP Model

Experiments

Conclusion


Moment Complexity

The moment complexity of sector s at moment m is here:

MC(s,m) = (wsec · Nsec + wcd · Ncd + wnsb · Nnsb) · Snorm

where:wsec , wcd , and wnsb are empirically determined weightsSnorm characterises the structure, equipment used,procedures followed, etc, of s (sector normalisation)



A CP Model

Experiments

Conclusion


Large Variance of Moment Complexity

0

20

40

60

80

100

120

140

1200 1300 1400 1500 1600 1700 1800 1900 2000

planned complexity: k=0planned complexity: k=1, L=420 secondsplanned complexity: k=2, L=210 secondsplanned complexity: k=3, L=140 secondsplanned complexity: k=4, L=130 seconds

Example:Complexityafter 11:10on23/6/2004inEBMALNL



A CP Model

Experiments

Conclusion


Interval Complexity

The interval complexity of sector s over interval [m, . . . ,m′]is the average of its moment complexities at the k + 1sampled moments m, m + L, m + 2L, . . . , m + k · L = m′:

IC(s,m, k ,L) =∑k

i=0 MC(s,m + i · L)k + 1

where:k = smoothing degreeL = time step between the sampled moments

In practice, for complexity resolution: k = 2 & L ≈ 210 sec.



A CP Model

Experiments

Conclusion


Allowed Forms of Complexity Resolution I

Temporal Re-Profiling:Change the entry time of a flight into the chosen airspace:

Waiting: Change the take-off time of a not yet airborneflight by an integer amount of minutes in [−5, . . . ,+10]Airborne: Change the remaining approach time into thechosen airspace of an already airborne flight by aninteger amount of minutes, but only within the twolayers of feeder sectors around the chosen airspace:

• at a speed-up rate of maximum 5%• at a slow-down rate of maximum 10%



A CP Model

Experiments

Conclusion


Example: Temporal Re-Profiling

x, y of chosen airspace

p5

m+2Lm+Lm

z

p6

p4p3

p1

t

now

FL 340

FL 245

p2

Planned profile



A CP Model

Experiments

Conclusion


Example: Temporal Re-Profiling

p5

p4p3

p1p2

p6


m+2Lm+Lm

z

t

now

FL 340

FL 245

Resolved profile



A CP Model

Experiments

Conclusion


Allowed Forms of Complexity Resolution II

Vertical Re-Profiling:Change the altitude of passage over a way-point in thechosen airspace by an integer amount of flight levels(FL) within [−30, . . . ,+10], so that the flight

• climbs at most 10 FL / min• descends at most 30 FL / min if it is a jet• descends at most 10 FL / min if it is a turbo-prop

Reminder: 1 flight level = 30.48 m = 100 feet.

2D Re-Profiling:Future work?



A CP Model

Experiments

Conclusion


Example: Vertical Re-Profiling

p2

FL 245

FL 340

now

t

p1

p3 p4

p6

z


m m+L m+2L

p5

Planned profile, and resolved profile that minimises thenumber of climbing segments for the considered flight atthe sampled moments m, m+L, and m+2L



A CP Model

Experiments

Conclusion


Assumptions

Proximity to a sector boundary is approximatableby being at most hvnsb = 120 sec of flight beyond theentry to, or before the exit from, the considered sector.This approximation only holds for en-route airspace.Times can be controlled with an accuracy of 1 minute:the profiles are just shifted in time.Flight time along a segment does not change if werestrict the flight level changes over its endpoints to be“small”. Otherwise, many more time variables will beneeded, leading to combinatorial explosion.



A CP Model

Experiments

Conclusion


Outline





A CP Model

Experiments

Conclusion


Some Parameters

now is the time at which a resolved scenario is wantedwith a forecast of lookahead minuteslookahead is typically a multiple of 10 in [20, . . . ,90]m = now + lookahead is the start moment of the timeinterval [m, . . . ,m + k · L] for complexity resolutionff = minimum fraction of flights planned to be in chosenairspace that must stay there at the sampled momentstimeOut = amount of CPU seconds after which thecurrently best feasible solution is to be returned



A CP Model

Experiments

Conclusion


Some Decision Variables

δT [f ] = entry-time change in [−5, . . . ,+10] of flight fδH[p] = level change in [−30, . . . ,+10] of flight-point pNsec[i , s] = # flights in sector s at sampled moment iNcd [i , s] = # flights on a non-level segment in s at iNnsb[i , s] = # flights near the boundary of s at i



A CP Model

Experiments

Conclusion


Some Constraints

All flights planned to take off until now have taken offexactly according to their profile, but their approachtimes (within the feeder sectors) can be modified.All other flights take off after now .Points flown over until now cannot get changed FLs.Changed FLs stay within the bounds of the sector, as(yet) no re-routing through a lower or higher sector.No climbing > maxUpJet = 10 FL / min,No climbing > maxUpTurbo = 10 FL / min,No descending > maxDownJet = 30 FL / min,No descending > maxDownTurbo = 10 FL / min.Minimum fraction ff of the number of flights planned tobe in the chosen airspace at the sampled moments imust remain then in that chosen airspace.



A CP Model

Experiments

Conclusion


The Objective Function

Multi-objective optimisation problem:minimise the vector 〈IC[s1], . . . , IC[sn]〉of the interval complexities of n sectors si .A vector of values is Pareto minimal if no element canbe reduced without increasing some other element.Standard technique: Combine the multiple objectivesinto a single objective using a weighted sum∑n

j=1 αj · IC[sj ] for some weights αj > 0.In practice, and as often done, we take αj = 1 for all j :

minimise∑

s∈OurSectors

IC[s]



A CP Model

Experiments

Conclusion


The Search Procedure and Heuristics

1 Assign the Nsec[i , s], Ncd [i , s], and Nnsb[i , s] variables:Try placing a flight within s at sampled moment i , but– neither on a non-level segment,– nor near the boundary of s.Begin with the sectors planned to be the busiest.

2 Assign the δT [f ] variables.Try by increasing absolute values in [−10, . . . ,+5].

3 Assign the δH[p] variables.Try by increasing absolute values in [−30, . . . ,+10].

The given orderings guarantee resolved flight profiles thatdeviate as little as possible from the planned ones.



A CP Model

Experiments

Conclusion


Implementation

The constraints were implemented in the OptimizationProgramming Language (OPL), marketed by ILOG. Theresulting model has non-linear and higher-order constraints,hence constraint propagation takes place at runtime.

Prejudice:

The contribution of the article should be the reductionof an engineering problem to a known optimization format.

[. . . ] showcases pseudo code [. . . ] submit thiswork to a journal interested in code semantics [. . . ].— Reviewer of this work at a prestigious OR journal



A CP Model

Experiments

Conclusion


Outline





A CP Model

Experiments

Conclusion


Experimental Setup I

ATC centre = Maastricht, in the NetherlandsMulti-sector airspace =five high-density, en-route, upper-airspace sectors:

sectorId bottomFL topFL wsec wcd wnsb Snorm

EBMALNL 245 340 7.74 15.20 5.69 1.35EBMALXL 245 340 5.78 5.71 15.84 1.50EBMAWSL 245 340 6.00 7.91 10.88 1.33EDYRHLO 245 340 12.07 6.43 9.69 1.00EHDELMD 245 340 4.42 10.59 14.72 1.11

Time = peak traffic hours, from 7 to 22, on 23/6/2004Flights = turbo-props and jets, on standard routes

Central Flow Management Unit (CFMU): 1,798 flights



A CP Model

Experiments

Conclusion


Experimental Setup II

Chosenmulti-sectorairspace,surrounded byan additional34 feedersectors(on thechosen day,the sectorsEBMAKOLand EBMANILwerecollapsed intoEBMAWSL)



A CP Model

Experiments

Conclusion


Results

Significant complexity reductions and re-balancing,obtained quickly (though with long proofs of optimality):

lookahead k L Average planned Average resolved20 2 210 87.92 47.6920 3 180 86.55 50.1745 2 210 87.20 45.2745 3 180 85.67 47.8190 2 210 87.29 44.6790 3 180 85.64 47.13

Average planned and resolved complexities in the chosenairspace, with at least ff = 90% of the flights kept there, andtimeOut = 120 seconds on an Intel Pentium 4 CPU with2.53GHz, a 512 KB cache, and a 1 GB memory.



A CP Model

Experiments

Conclusion


Outline





A CP Model

Experiments

Conclusion


Summary

Reduction: Complexity can be reduced by combination of:Reprofiling flights into less complex sectorsReprofiling flights away from sector boundariesReprofiling flights onto level segments

Non-Zero Sum:Take-off and speed resolutions do not just transfercomplexity to adjacent multi-sectors, because aparameter controls the percentage of flights that mustbe kept within the considered multi-sector.Level and speed resolutions can reduce the complexityof a sector without increasing it elsewhere.

Rebalancing: Current flight profiles often yield hugecomplexity discrepancies among sectors, but complexityresolution also addresses this.



A CP Model

Experiments

Conclusion


Contributions

Traffic complexity 6= # flightsComplexity resolution (not just prediction) . . .. . . in multi-sector planningUse of constraint programming (CP) for this purpose



A CP Model

Experiments

Conclusion


Future Work

Strategic use of the model, rather than deployment:new definitions of complexity can readily be tried, andconstraints can readily be changed or added.In practice, complexity resolution is not an optimisationproblem, but a satisfaction problem:need constraints on interval for resolved complexities.Constraints on fast executability of resolved profiles.Example: Keep # affected flights under threshold.Horizontal re-profiling: among static / dynamic route listCost minimisation: of ground / air holding, . . .Airline equity: towards a collaborative decision makingprocess between EUROCONTROL and the airlines.



A CP Model

Experiments

Conclusion


Acknowledgements

This research project was funded by EUROCONTROL

grant C/1.246/HQ/JC/04 + amendments 1/04 and 2/05.Many thanks to Carlos Garcia-Avello, Mete Çeliktin,and Søren Dissing at EUROCONTROL Headquarters(Brussels, Belgium) for the definition of the problemand the feedback on our progress.Many thanks to Bernard Delmée, Jacques Lemaître,and Patrick Tasker at EUROCONTROL DAP/DIA(Brussels, Belgium), for pre-processing the CFMU rawdata into the extended data we needed.



A CP Model

Experiments

Conclusion


Bibliography

P. Flener, J. Pearson, M. Ågren, C. Garcia Avello,M. Çeliktin, and S. Dissing.Air-traffic complexity resolution in multi-sector planning.J. of Air Transport Management, 13(6):323–328, 2007.Also in: Ch. Pusch and S. Saunders-Hodge (editors),Proceedings of ATM’07, the 7th USA / Europe R&DSeminar on Air Traffic Management. July 2007.Full version: Technical Report 2007-003.


http://dx.doi.org/10.1016/j.jairtraman.2007.05.001

http://www.it.uu.se/research/reports/2007-003/


DynamicDemand-CapacityBalancingObjective &Motivation

A CP Model

Experiments

Conclusion

Outline






A CP Model

Experiments

Conclusion

Outline






A CP Model

Experiments

Conclusion

Objective & Motivation

Tactical planning, in quasi-real-time,for the entire European airspace,necessary for future flight volumes:minimise the total ground-holding(e.g., by maximum 120 minutes per flight),such that all the capacity constraints are satisfied,within a rolling horizon (of, e.g., one hour)that starts, e.g., three hours from now:

now s e 1h 3h

Planning horizon

Ideally: also balance demands on portions of airspace.




A CP Model

Experiments

Conclusion

European ATM at Present

Flight planning is done globally,at the strategic and tactical levels:

• at the Central Flow Management Unit (CFMU),• but without achieving optimal global flow, and

under almost certainly incorrect data estimates.

Flight control is done locally,at the operational level:

• at regional air-traffic control centres (ATCCs),• but without a global view when re-planning flights,

even though much more precise data are available.




A CP Model

Experiments

Conclusion

European ATM in the Future?

Year 2030: 50,000 flights/day (now: 30,000 flights/day)The airspace might be partitioned into a 3D-gridof same-sized box-shaped cells(as building blocks for a new sectorisation),e.g., 75 nm × 75 nm × 12500 ft:

• 4 layers• 4,600 cells• 700,000 cell entries per day

75 nm

75 nm

12500 ft

Reminder: 1 nm = 1.852 km = 1.15 miles; 1000 ft = 304.8 m6 May 2010 ACP Summer School 2010 - 40 - Pierre Flener



A CP Model

Experiments

Conclusion

3D Cells over Europe

Europeanairspacedivided intocells




A CP Model

Experiments

Conclusion

Outline






A CP Model

Experiments

Conclusion

Sliding Windows

Capacity = max number of entering flights per hour.Constraints: at any given moment,no capacity is exceeded within the last hour.In practice, we sample every t minutes, e.g., t = 12:

S1S2

S3S4

S5S6

now +1h +2h s e

df af

t=12min

+3h +4h s‐w

e‐s = 60min




A CP Model

Experiments

Conclusion

Variables, Constraints, and Objective

Decision variables:for each non-airborne flight:a ground-holding delay within 0 . . . 120 minutes.Constraints:for each cell and each sliding window:# airborne flights + # re-planned flights ≤ cell capacity.Objective function, to be minimised:α · sum(all delays) + β · violations(all constraints)

where α and β are weights.




A CP Model

Experiments

Conclusion

Typical Problem Instance

Horizon 9 to 10 pm, for a projected data-set of year 2030:Decision variables: 4,295 (= # non-airborne flights)Relevant cells: 2,294Cell entries: 51,879Constraints: 1,936




A CP Model

Experiments

Conclusion

Three-State Heuristic

State 1, initially:• Select a delay based on a probability function.• Select a flight (that achieves the largest decrease in

violations) for the selected delay.State 2, when violations drop below a threshold:

• Select the most violating flight.• Select a delay (that achieves the largest decrease in

violations) for the selected flight.State 3, when violations drop below a lower threshold(very close to satisfaction):

• Select a (flight, delay) pair (that achieves the largestdecrease in violations).




A CP Model

Experiments

Conclusion

State 1 of Heuristic

Select a delay based on a probability function:

0 2 4 6 8 10 12

0.05

0.10

0.15

0.20

f 1.3,KyC12 , f 1.3, floor KyC12

0 0 0 0 0 0

Longer delays are less likely than shorter delays.




A CP Model

Experiments

Conclusion

Outline






A CP Model

Experiments

Conclusion

Platform

Constraint solver: local-search back-end of Comet.Operating system: Linux Ubuntu 9.04 (32-bit).CPU: Intel Core 2 Duo T7300 2GHz, 2MB cache.Memory: 4GB (only 2GB available to Comet).




A CP Model

Experiments

Conclusion

Planned Cell Demands (Layer 3)

Before optimisation, for the 9–10 pm horizon, in layer 3:Mean Std Dev Max

before 15.7 24.6 166

For instance (when all cells have capacity 40):

0

10

20

30

40

50

60

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Num

ber o

f Flig

hts

Cells Flown by Flight 210




A CP Model

Experiments

Conclusion

Optimised Cell Demands (Layer 3)

After optimisation, for the 9–10 pm horizon, in layer 3:Mean Std Dev Max

before 15.7 24.6 166after 11.0 12.0 40


0

10

20

30

40

50

60

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Num

ber o

f Flig

hts

Cells Flown by Flight 210




A CP Model

Experiments

Conclusion

Planned Cell Demands (All Layers)

Before optimisation, for the 9–10 pm horizon, all layers:Mean Std Dev Max

before 12.4 22.4 235


0

20

40

60

80

100

120

140

1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654

Num

ber o

f Flig

hts

Cells




A CP Model

Experiments

Conclusion

Optimised Cell Demands (All Layers)

After optimisation, for the 9–10 pm horizon, all layers:Mean Std Dev Max

before 12.4 22.4 235after 8.4 10.4 40


0

20

40

60

80

100

120

140

1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654

Num

ber o

f Flig

hts

Cells




A CP Model

Experiments

Conclusion

Distribution of Delays




A CP Model

Experiments

Conclusion

More Results

All the capacity constraints can be satisfied.By-product:standard deviation of cell demands shrinks significantly.Quasi-real-time performance.

Horizon Run-time # Waiting # Airborne9 – 10 pm 140 sec 4,295 4635 – 6 pm 620 sec 8,806 811

Horizon Total Delay Avg Delay Demand Dev9 – 10 pm 65,457 min 13.76 min −35%5 – 6 pm 246,267 min 25.61 min −43%




A CP Model

Experiments

Conclusion

Outline






A CP Model

Experiments

Conclusion

Summary and Future Work

Constraint programming can be used to model andsolve large ATM problem instances efficiently.Future Work?

• Increase realism by adding extra constraints.• Enforce a notion of first-scheduled-first-served.• Enforce load constraints (→ less total delay)

(load = max number of flights simultaneously present).• Vertical re-routing of flights along the planned 2D route.• Systematic search: constraint-based scheduling,

mixed integer linear programming

Need for a tight integration of planning and control!(Witness huge capacity violations in CFMU plans, andwitness our unacceptably high average delays.)Need for a dynamic adjustment of capacity to demand,rather than of demand to capacity?!




A CP Model

Experiments

Conclusion

Acknowledgements

This research project was financed by EUROCONTROL

under its Care INO III programme grant 08-121447-C.Many thanks to Franck Ballerini, Marc Bisiaux, MarcDalichampt, Hamid Kadour, Serge Manchon, and LeïlaZerrouki at the EUROCONTROL Experimental Centre(Brétigny, France) for the definition of the problem, thedata-set used, and the feedback on our progress.




A CP Model

Experiments

Conclusion

Bibliography

F. Hassani Bijarbooneh, P. Flener, and J. Pearson.Dynamic demand-capacity balancing for air trafficmanagement using constraint-based local search: Firstresults.In: Y. Deville and Ch. Solnon (editors), Proceedings ofLSCS’09, the 6th International Workshop on LocalSearch Techniques in Constraint Satisfaction.Electronic Proceedings in Theoretical ComputerScience 5:27–40, 2009.Also in: D. Schaefer (editor), Proceedings of INO’09,the 8th EUROCONTROL Innovative Research Workshop& Exhibition, Brétigny (France), December 2009.


http://dx.doi.org/10.4204/EPTCS.5.3



Documents

Air Traffic Flow and Capacity Management Using Constraint …becool.info.ucl.ac.be/summerschool2010/documents/Case... · 2018-06-15 · Air Trafﬁc Flow and Capacity Management Using