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Air Traffic Flow and Capacity ManagementUsing Constraint Programming
Pierre Flener
ASTRA Research Group on CPUppsala University
Sweden
ACP Summer SchoolAussois (France), 6 May 2010
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
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancing
Outline
1 Complexity Resolution in Multi-Sector PlanningObjective & MotivationA CP ModelExperimentsConclusion
2 Dynamic Demand-Capacity BalancingObjective & MotivationA CP ModelExperimentsConclusion
6 May 2010 ACP Summer School 2010 - 3 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
Outline
1 Complexity Resolution in Multi-Sector PlanningObjective & MotivationA CP ModelExperimentsConclusion
2 Dynamic Demand-Capacity BalancingObjective & MotivationA CP ModelExperimentsConclusion
6 May 2010 ACP Summer School 2010 - 4 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
Outline
1 Complexity Resolution in Multi-Sector PlanningObjective & MotivationA CP ModelExperimentsConclusion
2 Dynamic Demand-Capacity BalancingObjective & MotivationA CP ModelExperimentsConclusion
6 May 2010 ACP Summer School 2010 - 5 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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.
6 May 2010 ACP Summer School 2010 - 6 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
Target Scenario
Flight Profiles
Resolution Rules
Resolved Flight Profiles
Complexity Solver
m, m’, ff%, timeOut
Complexity Predictor
high
low
9020 m’
complexity
nowt
m
6 May 2010 ACP Summer School 2010 - 7 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
Contributions
Traffic complexity 6= # flightsComplexity resolution (not just prediction) . . .. . . in multi-sector planningUse of constraint programming (CP) for this purpose
6 May 2010 ACP Summer School 2010 - 8 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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?
6 May 2010 ACP Summer School 2010 - 9 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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)
6 May 2010 ACP Summer School 2010 - 10 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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
6 May 2010 ACP Summer School 2010 - 11 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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.
6 May 2010 ACP Summer School 2010 - 12 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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%
6 May 2010 ACP Summer School 2010 - 13 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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
6 May 2010 ACP Summer School 2010 - 14 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
Example: Temporal Re-Profiling
p5
p4p3
p1p2
p6
x, y of chosen airspace
m+2Lm+Lm
z
t
now
FL 340
FL 245
Resolved profile
6 May 2010 ACP Summer School 2010 - 15 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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?
6 May 2010 ACP Summer School 2010 - 16 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
Example: Vertical Re-Profiling
p2
FL 245
FL 340
now
t
p1
p3 p4
p6
z
x, y of chosen airspace
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
6 May 2010 ACP Summer School 2010 - 17 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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.
6 May 2010 ACP Summer School 2010 - 18 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
Outline
1 Complexity Resolution in Multi-Sector PlanningObjective & MotivationA CP ModelExperimentsConclusion
2 Dynamic Demand-Capacity BalancingObjective & MotivationA CP ModelExperimentsConclusion
6 May 2010 ACP Summer School 2010 - 19 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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
6 May 2010 ACP Summer School 2010 - 20 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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
6 May 2010 ACP Summer School 2010 - 21 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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.
6 May 2010 ACP Summer School 2010 - 22 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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]
6 May 2010 ACP Summer School 2010 - 23 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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.
6 May 2010 ACP Summer School 2010 - 24 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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
6 May 2010 ACP Summer School 2010 - 25 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
Outline
1 Complexity Resolution in Multi-Sector PlanningObjective & MotivationA CP ModelExperimentsConclusion
2 Dynamic Demand-Capacity BalancingObjective & MotivationA CP ModelExperimentsConclusion
6 May 2010 ACP Summer School 2010 - 26 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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
6 May 2010 ACP Summer School 2010 - 27 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
Experimental Setup II
Chosenmulti-sectorairspace,surrounded byan additional34 feedersectors(on thechosen day,the sectorsEBMAKOLand EBMANILwerecollapsed intoEBMAWSL)
6 May 2010 ACP Summer School 2010 - 28 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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.
6 May 2010 ACP Summer School 2010 - 29 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
Outline
1 Complexity Resolution in Multi-Sector PlanningObjective & MotivationA CP ModelExperimentsConclusion
2 Dynamic Demand-Capacity BalancingObjective & MotivationA CP ModelExperimentsConclusion
6 May 2010 ACP Summer School 2010 - 30 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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.
6 May 2010 ACP Summer School 2010 - 31 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
Contributions
Traffic complexity 6= # flightsComplexity resolution (not just prediction) . . .. . . in multi-sector planningUse of constraint programming (CP) for this purpose
6 May 2010 ACP Summer School 2010 - 32 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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.
6 May 2010 ACP Summer School 2010 - 33 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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.
6 May 2010 ACP Summer School 2010 - 34 - Pierre Flener
ComplexityResolution inMulti-SectorPlanningObjective &Motivation
A CP Model
Experiments
Conclusion
DynamicDemand-CapacityBalancing
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.
6 May 2010 ACP Summer School 2010 - 35 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
A CP Model
Experiments
Conclusion
Outline
1 Complexity Resolution in Multi-Sector PlanningObjective & MotivationA CP ModelExperimentsConclusion
2 Dynamic Demand-Capacity BalancingObjective & MotivationA CP ModelExperimentsConclusion
6 May 2010 ACP Summer School 2010 - 36 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
A CP Model
Experiments
Conclusion
Outline
1 Complexity Resolution in Multi-Sector PlanningObjective & MotivationA CP ModelExperimentsConclusion
2 Dynamic Demand-Capacity BalancingObjective & MotivationA CP ModelExperimentsConclusion
6 May 2010 ACP Summer School 2010 - 37 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
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.
6 May 2010 ACP Summer School 2010 - 38 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
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.
6 May 2010 ACP Summer School 2010 - 39 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
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
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
A CP Model
Experiments
Conclusion
3D Cells over Europe
Europeanairspacedivided intocells
6 May 2010 ACP Summer School 2010 - 41 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
A CP Model
Experiments
Conclusion
Outline
1 Complexity Resolution in Multi-Sector PlanningObjective & MotivationA CP ModelExperimentsConclusion
2 Dynamic Demand-Capacity BalancingObjective & MotivationA CP ModelExperimentsConclusion
6 May 2010 ACP Summer School 2010 - 42 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
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
6 May 2010 ACP Summer School 2010 - 43 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
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.
6 May 2010 ACP Summer School 2010 - 44 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
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
6 May 2010 ACP Summer School 2010 - 45 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
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).
6 May 2010 ACP Summer School 2010 - 46 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
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.
6 May 2010 ACP Summer School 2010 - 47 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
A CP Model
Experiments
Conclusion
Outline
1 Complexity Resolution in Multi-Sector PlanningObjective & MotivationA CP ModelExperimentsConclusion
2 Dynamic Demand-Capacity BalancingObjective & MotivationA CP ModelExperimentsConclusion
6 May 2010 ACP Summer School 2010 - 48 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
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).
6 May 2010 ACP Summer School 2010 - 49 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
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
6 May 2010 ACP Summer School 2010 - 50 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
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
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
6 May 2010 ACP Summer School 2010 - 51 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
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
For instance (when all cells have capacity 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
6 May 2010 ACP Summer School 2010 - 52 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
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
For instance (when all cells have capacity 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
6 May 2010 ACP Summer School 2010 - 53 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
A CP Model
Experiments
Conclusion
Distribution of Delays
6 May 2010 ACP Summer School 2010 - 54 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
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%
6 May 2010 ACP Summer School 2010 - 55 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
A CP Model
Experiments
Conclusion
Outline
1 Complexity Resolution in Multi-Sector PlanningObjective & MotivationA CP ModelExperimentsConclusion
2 Dynamic Demand-Capacity BalancingObjective & MotivationA CP ModelExperimentsConclusion
6 May 2010 ACP Summer School 2010 - 56 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
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?!
6 May 2010 ACP Summer School 2010 - 57 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
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.
6 May 2010 ACP Summer School 2010 - 58 - Pierre Flener
ComplexityResolution inMulti-SectorPlanning
DynamicDemand-CapacityBalancingObjective &Motivation
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.
6 May 2010 ACP Summer School 2010 - 59 - Pierre Flener