Air Traffic Flow and Capacity Management Using Constraint Programming

Transcription

1 Air Traffic Flow and Management Using Constraint Programming Pierre Flener ASTRA Research Group on CP Uppsala University Sweden ACP Summer School Aussois (France), 6 May 2010

2 Air Traffic Management The objective of air traffic management (ATM) is to ensure a safe, fair, and efficient flow of air traffic, under minimal environmental impact, subject to constraints on aircraft separation, airspace capacity, and airport capacity. This long-term research is financed by the European Organisation for the Safety of Air Navigation, whose mission is to promote the harmonisation of the different national ATM systems in Europe. 6 May 2010 ACP Summer School Pierre Flener

3 Outline May 2010 ACP Summer School Pierre Flener

4 Outline May 2010 ACP Summer School Pierre Flener

5 Outline May 2010 ACP Summer School Pierre Flener

6 Sector-Based Air Traffic Management A sector is a 3D air volume, whose traffic is monitored by a pair of air traffic controllers. The air traffic complexity for all controller pairs must satisfy some constraints. 6 May 2010 ACP Summer School Pierre Flener

7 Target Scenario m, m, ff%, timeout Resolution Rules complexity Predictor Flight Profiles Solver high Resolved Flight Profiles low now 20 m m 90 t 6 May 2010 ACP Summer School Pierre Flener

8 Contributions Traffic complexity # flights resolution (not just prediction) in multi-sector planning Use of constraint programming (CP) for this purpose 6 May 2010 ACP Summer School Pierre Flener

9 Air Traffic Parameters The complexity of sector s at moment m depends here on: N sec = # flights in s at moment m (traffic volume) N cd = # flights in s non-level at m (vertical state) N nsb = # 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 = km = 1.15 miles. Note: The complexity of sector s at moment m does not depend here on potentially interacting pairs of aircraft: do traffic volume & vertical state already capture this effect? 6 May 2010 ACP Summer School Pierre Flener

10 Moment The moment complexity of sector s at moment m is here: MC(s, m) = (w sec N sec + w cd N cd + w nsb N nsb ) S norm where: w sec, w cd, and w nsb are empirically determined weights S norm characterises the structure, equipment used, procedures followed, etc, of s (sector normalisation) 6 May 2010 ACP Summer School Pierre Flener

11 Large Variance of Moment planned complexity: k=0 planned complexity: k=1, L=420 seconds planned complexity: k=2, L=210 seconds planned complexity: k=3, L=140 seconds planned complexity: k=4, L=130 seconds Example: after 11:10 on 23/6/2004 in EBMALNL May 2010 ACP Summer School Pierre Flener

12 Interval The interval complexity of sector s over interval [m,..., m ] is the average of its moment complexities at the k + 1 sampled moments m, m + L, m + 2L,..., m + k L = m : where: IC(s, m, k, L) = k = smoothing degree k i=0 MC(s, m + i L) k + 1 L = time step between the sampled moments In practice, for complexity resolution: k = 2 & L 210 sec. 6 May 2010 ACP Summer School Pierre Flener

13 Allowed Forms of 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 airborne flight by an integer amount of minutes in [ 5,..., +10] Airborne: Change the remaining approach time into the chosen airspace of an already airborne flight by an integer amount of minutes, but only within the two layers 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 Pierre Flener

14 Example: Temporal Re-Profiling FL 340 z p6 p5 FL 245 p1 p2 p3 p4 now m m+l m+2l t x, y of chosen airspace Planned profile 6 May 2010 ACP Summer School Pierre Flener

15 Example: Temporal Re-Profiling FL 340 z p6 p5 FL 245 p1 p2 p3 p4 now m m+l m+2l t x, y of chosen airspace Resolved profile 6 May 2010 ACP Summer School Pierre Flener

16 Allowed Forms of Resolution II Vertical Re-Profiling: Change the altitude of passage over a way-point in the chosen 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 = m = 100 feet. 2D Re-Profiling: Future work? 6 May 2010 ACP Summer School Pierre Flener

17 Example: Vertical Re-Profiling z FL 340 p6 p5 FL 245 now p1 p2 p3 p4 m m+l m+2l t x, y of chosen airspace Planned profile, and resolved profile that minimises the number of climbing segments for the considered flight at the sampled moments m, m+l, and m+2l 6 May 2010 ACP Summer School Pierre Flener

18 Assumptions Proximity to a sector boundary is approximatable by being at most hv nsb = 120 sec of flight beyond the entry 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 we restrict the flight level changes over its endpoints to be small. Otherwise, many more time variables will be needed, leading to combinatorial explosion. 6 May 2010 ACP Summer School Pierre Flener

19 Outline May 2010 ACP Summer School Pierre Flener

20 Some Parameters now is the time at which a resolved scenario is wanted with a forecast of lookahead minutes lookahead is typically a multiple of 10 in [20,..., 90] m = now + lookahead is the start moment of the time interval [m,..., m + k L] for complexity resolution ff = minimum fraction of flights planned to be in chosen airspace that must stay there at the sampled moments timeout = amount of CPU seconds after which the currently best feasible solution is to be returned 6 May 2010 ACP Summer School Pierre Flener

21 Some Decision Variables δt [f ] = entry-time change in [ 5,..., +10] of flight f δh[p] = level change in [ 30,..., +10] of flight-point p N sec [i, s] = # flights in sector s at sampled moment i N cd [i, s] = # flights on a non-level segment in s at i N nsb [i, s] = # flights near the boundary of s at i 6 May 2010 ACP Summer School Pierre Flener

22 Some Constraints All flights planned to take off until now have taken off exactly according to their profile, but their approach times (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 to be in the chosen airspace at the sampled moments i must remain then in that chosen airspace. 6 May 2010 ACP Summer School Pierre Flener

23 The Objective Function Multi-objective optimisation problem: minimise the vector IC[s 1 ],..., IC[s n ] of the interval complexities of n sectors s i. A vector of values is Pareto minimal if no element can be reduced without increasing some other element. Standard technique: Combine the multiple objectives into a single objective using a weighted sum n j=1 α j IC[s j ] for some weights α j > 0. In practice, and as often done, we take α j = 1 for all j: minimise IC[s] s OurSectors 6 May 2010 ACP Summer School Pierre Flener

24 The Search Procedure and Heuristics 1 Assign the N sec [i, s], N cd [i, s], and N nsb [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 that deviate as little as possible from the planned ones. 6 May 2010 ACP Summer School Pierre Flener

25 Implementation The constraints were implemented in the Optimization Programming Language (OPL), marketed by ILOG. The resulting model has non-linear and higher-order constraints, hence constraint propagation takes place at runtime. Prejudice: The contribution of the article should be the reduction of an engineering problem to a known optimization format. [... ] showcases pseudo code [... ] submit this work to a journal interested in code semantics [... ]. Reviewer of this work at a prestigious OR journal 6 May 2010 ACP Summer School Pierre Flener

26 Outline May 2010 ACP Summer School Pierre Flener

27 Experimental Setup I ATC centre = Maastricht, in the Netherlands Multi-sector airspace = five high-density, en-route, upper-airspace sectors: sector I d bottomfl topfl w sec w cd w nsb S norm EBMALNL EBMALXL EBMAWSL EDYRHLO EHDELMD Time = peak traffic hours, from 7 to 22, on 23/6/2004 Flights = turbo-props and jets, on standard routes Central Flow Management Unit (CFMU): 1,798 flights 6 May 2010 ACP Summer School Pierre Flener

28 Experimental Setup II Chosen multi-sector airspace, surrounded by an additional 34 feeder sectors (on the chosen day, the sectors EBMAKOL and EBMANIL were collapsed into EBMAWSL) 6 May 2010 ACP Summer School Pierre Flener

29 Results Significant complexity reductions and re-balancing, obtained quickly (though with long proofs of optimality): lookahead k L Average planned Average resolved Average planned and resolved complexities in the chosen airspace, with at least ff = 90% of the flights kept there, and timeout = 120 seconds on an Intel Pentium 4 CPU with 2.53GHz, a 512 KB cache, and a 1 GB memory. 6 May 2010 ACP Summer School Pierre Flener

30 Outline May 2010 ACP Summer School Pierre Flener

31 Summary Reduction: can be reduced by combination of: Reprofiling flights into less complex sectors Reprofiling flights away from sector boundaries Reprofiling flights onto level segments Non-Zero Sum: Take-off and speed resolutions do not just transfer complexity to adjacent multi-sectors, because a parameter controls the percentage of flights that must be kept within the considered multi-sector. Level and speed resolutions can reduce the complexity of a sector without increasing it elsewhere. Rebalancing: Current flight profiles often yield huge complexity discrepancies among sectors, but complexity resolution also addresses this. 6 May 2010 ACP Summer School Pierre Flener

32 Contributions Traffic complexity # flights resolution (not just prediction) in multi-sector planning Use of constraint programming (CP) for this purpose 6 May 2010 ACP Summer School Pierre Flener

33 Future Work Strategic use of the model, rather than deployment: new definitions of complexity can readily be tried, and constraints can readily be changed or added. In practice, complexity resolution is not an optimisation problem, 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 list Cost minimisation: of ground / air holding,... Airline equity: towards a collaborative decision making process between EUROCONTROL and the airlines. 6 May 2010 ACP Summer School Pierre Flener

34 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 problem and 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 raw data into the extended data we needed. 6 May 2010 ACP Summer School Pierre Flener

35 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): , Also in: Ch. Pusch and S. Saunders-Hodge (editors), Proceedings of ATM 07, the 7th USA / Europe R&D Seminar on Air Traffic Management. July Full version: Technical Report May 2010 ACP Summer School Pierre Flener

36 Outline May 2010 ACP Summer School Pierre Flener

37 Outline May 2010 ACP Summer School Pierre Flener

38 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: horizon now s e 3h 1h Ideally: also balance demands on portions of airspace. 6 May 2010 ACP Summer School Pierre Flener

39 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 Pierre Flener

40 European ATM in the Future? Year 2030: 50,000 flights/day (now: 30,000 flights/day) The airspace might be partitioned into a 3D-grid of same-sized box-shaped cells (as building blocks for a new sectorisation), e.g., 75 nm 75 nm ft: 4 layers 4,600 cells 700,000 cell entries per day ft 75 nm 75 nm Reminder: 1 nm = km = 1.15 miles; 1000 ft = m 6 May 2010 ACP Summer School Pierre Flener

41 3D Cells over Europe European airspace divided into cells 6 May 2010 ACP Summer School Pierre Flener

42 Outline May 2010 ACP Summer School Pierre Flener

43 Sliding Windows = 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: S 2 S 1 now +1h +2h s w a f t=12min S 3 S 4 S 5 S 6 d f e s = 60min +3h +4h s e 6 May 2010 ACP Summer School Pierre Flener

44 Variables, Constraints, and Objective Decision variables: for each non-airborne flight: a ground-holding delay within 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 Pierre Flener

45 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: 2,294 Cell entries: 51,879 Constraints: 1,936 6 May 2010 ACP Summer School Pierre Flener

46 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 largest decrease in violations). 6 May 2010 ACP Summer School Pierre Flener

47 State 1 of Heuristic Select a delay based on a probability function: f 1.3,KyC12, f 1.3, floor KyC Longer delays are less likely than shorter delays. 6 May 2010 ACP Summer School Pierre Flener

48 Outline May 2010 ACP Summer School Pierre Flener

49 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 Pierre Flener

50 Planned Cell Demands (Layer 3) Before optimisation, for the 9 10 pm horizon, in layer 3: Mean Std Dev Max before For instance (when all cells have capacity 40): Number of Flights Cells Flown by Flight May 2010 ACP Summer School Pierre Flener

51 Optimised Cell Demands (Layer 3) After optimisation, for the 9 10 pm horizon, in layer 3: Mean Std Dev Max before after For instance (when all cells have capacity 40): Number of Flights Cells Flown by Flight May 2010 ACP Summer School Pierre Flener

52 Planned Cell Demands (All Layers) Before optimisation, for the 9 10 pm horizon, all layers: Mean Std Dev Max before For instance (when all cells have capacity 40): Number of Flights Cells 6 May 2010 ACP Summer School Pierre Flener

53 Optimised Cell Demands (All Layers) After optimisation, for the 9 10 pm horizon, all layers: Mean Std Dev Max before after For instance (when all cells have capacity 40): Number of Flights Cells 6 May 2010 ACP Summer School Pierre Flener

54 Distribution of Delays 6 May 2010 ACP Summer School Pierre Flener

55 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 # Airborne 9 10 pm 140 sec 4, pm 620 sec 8, Horizon Total Delay Avg Delay Demand Dev 9 10 pm 65,457 min min 35% 5 6 pm 246,267 min min 43% 6 May 2010 ACP Summer School Pierre Flener

56 Outline May 2010 ACP Summer School Pierre Flener

57 Summary and Future Work Constraint programming can be used to model and solve 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, and witness 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 Pierre Flener

58 Acknowledgements This research project was financed by EUROCONTROL under its Care INO III programme grant C. Many thanks to Franck Ballerini, Marc Bisiaux, Marc Dalichampt, Hamid Kadour, Serge Manchon, and Leïla Zerrouki at the EUROCONTROL Experimental Centre (Brétigny, France) for the definition of the problem, the data-set used, and the feedback on our progress. 6 May 2010 ACP Summer School Pierre Flener

59 Bibliography F. Hassani Bijarbooneh, P. Flener, and J. Pearson. demand-capacity balancing for air traffic management using constraint-based local search: First results. In: Y. Deville and Ch. Solnon (editors), Proceedings of LSCS 09, the 6th International Workshop on Local Search Techniques in Constraint Satisfaction. Electronic Proceedings in Theoretical Computer Science 5:27 40, Also in: D. Schaefer (editor), Proceedings of INO 09, the 8th EUROCONTROL Innovative Research Workshop & Exhibition, Brétigny (France), December May 2010 ACP Summer School Pierre Flener