Large-Scale Network Slot Allocation with Dynamic Time Horizons
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1 page 1 > Large-Scale Network Slot Allocation with Dynamic Time Horizons (Lau, Berling et al.) Large-Scale Network Slot Allocation with Dynamic Time Horizons Alexander Lau 1, Jan Berling 1, Florian Linke 1, Volker Gollnick 1 and Karl Nachtigall 2 11 th USA/EUROPE Air Traffic Management R&D Seminar June 2015, Lisbon, Portugal Network and Strategic Flow Optimization, 24 th June DLR Air Transportation Systems 2 Dresden University of Technology
2 page 2 > Large-Scale Network Slot Allocation with Dynamic Time Horizons (Lau, Berling et al.) Motivation Network Management in Europe Centralized function to balance air traffic demand with system capacity 9.5 Mio. flight movements per year, up to flight movements per day Dynamic Network Impact (Weather) Ceiling/visibility, wind, winter weather, icing, etc. (airport) Convection, turbulence (en-route) Consistent weather picture throughout NM and ATC units Late regulation initiation / updating Dynamic optimization architecture Slot allocation with updated convective nowcasts Rolling-horizon architecture (repetitive optimization runs) NMOC Eurocontrol
3 page 3 > Large-Scale Network Slot Allocation with Dynamic Time Horizons (Lau, Berling et al.) Agenda The Network Flow Environment (NFE) Overview State-of-the-art slot allocation General Optimization Approach Large-Scale Problem Solving Mathematical Model Experimental Example Rolling Time Horizon Concept Operational Constraints Process Chain Results & Next Steps
4 page 4 > Large-Scale Network Slot Allocation with Dynamic Time Horizons (Lau, Berling et al.) Network Flow Environment (NFE) Network represention Allocation of ATFCM departure slots and preflight routings Airspace representation with approximately 640 ATC sectors ATFM mathematical problem Heuristic slot allocation according to CASA Binary Integer Programing (BIP) Application of Problem Decomposition Quantification of network performance ATFCM delay quantification Atmospheric impact, e.g. convection
5 page 5 > Large-Scale Network Slot Allocation with Dynamic Time Horizons (Lau, Berling et al.) FPFS (First-Planned-First-Served) slot allocation F1 ETO 12:02z Regulation 12:00-01:00 1 flight / 5 min F4 ETO 12:07z departure slots F1 F2 F2 F3 ETO 12:04z F2 ETO 12:03z F3 F4 F3 F4 Estimated Calculated
6 page 6 > Large-Scale Network Slot Allocation with Dynamic Time Horizons (Lau, Berling et al.) General ATFM Model Formation Objective function: ZZ(xx) = mmmmmmmmmmmmmmmm ωω ff,dd xx ff,dd. ff εε FF dd εε DD(ff) Decision variable: 1, if flight ff obtains departure slot dd, xx ff,dd = 0, ooooheeeeeeeeeeee. Departure constraint: xx ff,dd = 1 ff. dd εε DD(ff) Capacity constraint: aa (ss,tt),(ff,dd) xx ff,dd CC ss,tt ss, tt. ff εε FF dd εε DD(ff) Flight time transformation: 1, iiii CCCCCC ss (ff, dd) = tt, aa (ss,tt),(ff,dd) = 0, ooooheeeeeeeeeeee. Departure time restriction: dd 0 dd εε DD(ff). adapted from Bertsimas, Stock: The Air Traffic Management Problem with Enroute Capacities, 1998
7 Seite 7 > Large-Scale Network Slot Allocation with Dynamic Time Horizons (Lau, Berling et al.) Problem Decomposition Column Generation Devides Master Problem into a subset of Restricted Master Problems Solution close to global optimum Variable Pricing Iterative generation of RMPs Add negative reduced cost -variables, which improve cost formulation Dual Problem Equivalent of the Primal Problem Transposition of the rows and columns Reversed inequalities Correlating Dual Variables NFE-CASA initial solution Restricted Master Problem (RMP) Solver RMP* New variables Pricer Dual variables ( shadow prices )
8 Seite 8 > Large-Scale Network Slot Allocation with Dynamic Time Horizons (Lau, Berling et al.) Dual Problem (RMP) and Dual Restriction Primal Constraints Departure Capacity aa (ss,tt),(ff,dd) xx ff,dd CC ss,tt ff εε FF dd εε DD(ff) xx ff,dd = 1 dd εε DD(ff) GGGG = ee (ξξ) Є N FF AAxx cc (µ) Є N SS,DD ξ: dual prices departure μ: dual prices infratructure ω: primal cost coefficient G,A: coefficient matrices Dual Cost Function: Dual Restriction: mmmmmm ξξ + cc T µ GG TT ξξ + AA TT µ ωω ξξ ff + AA TT ff,dd µ ωω ff,dd Violated Reduced Dual Costs: Restriction: rr ff,dd = ωω ff,dd ξξ ff + ξξaa ffff,dd µ AA> ff,dd ωω ff,dd TT TT µ
9 Seite 9 > Large-Scale Network Slot Allocation with Dynamic Time Horizons (Lau, Berling et al.) Rolling Horizon
10 page 10 > Large-Scale Network Slot Allocation with Dynamic Time Horizons (Lau, Berling et al.) Rolling Horizon Process Chain
11 Seite 11 > Large-Scale Network Slot Allocation with Dynamic Time Horizons (Lau, Berling et al.) Exemplary Scenario # ATC sectors # airports Network Data # ATC sectors (model) # airports (model) Regulation Data concerned traffic volumes regulation causes # total # airspace #airport #CNL # CAP #WX
12 page 12 > Large-Scale Network Slot Allocation with Dynamic Time Horizons (Lau, Berling et al.) Hot Spot Identification Latitude Latitude
13 page 13 > Large-Scale Network Slot Allocation with Dynamic Time Horizons (Lau, Berling et al.) Scenario Output Traffic Data from # IOBT to # flights (total) # flights (model) 00:00z 23:59z Time Horizon Output flights iterations Delay Cancelations Delay [# flights] [# flights] total [min] Calculation time [ø min] ATFM departure delay:
14 page 14 > Large-Scale Network Slot Allocation with Dynamic Time Horizons (Lau, Berling et al.) Variables and Delay Decision Variables Average: 4 considered departure slots per flight Infrequent instabilities during N+1 th solution initiation Validation with static SoPlex solutions resulted in correct total system cost Horizon Delay Shares Main en-route WX-impact between 18:00z and 22:00z (main regulation timeframe) ATFM-delay arouse around 3 hours before impact
15 page 15 > Large-Scale Network Slot Allocation with Dynamic Time Horizons (Lau, Berling et al.) Conclusion Framework to improve departure slot allocation by integrating (short-term) network impact information. Rolling Horizon concept to regularily update CTOTs according to actual network states. Therefore, devide large instances of the ATFM slot allocation problem into sub-problems by column generation and structured variable pricing. Whole-day restricted European traffic scenario was solved within low computation times, ATFM departure delay considerably low.
16 page 16 > Large-Scale Network Slot Allocation with Dynamic Time Horizons (Lau, Berling et al.) Next Steps Integration of Regulation Data Initiation times Cancellation times Trajectory-based constraint integration Trajectory-related penalty cost instead of capacity regulations Cost formulations Pre-tactical reduction of conflict-potential Update trajectory forecast to reduce uncertainty Conflict cost
17 Seite 17 > Large-Scale Network Slot Allocation with Dynamic Time Horizons (Lau, Berling et al.) 11 th USA/EUROPE Air Traffic Management R&D Seminar Thank you for your attention! We greatly appreciate the excellent support of Eurocontrol, DFS Deutsche Flugsicherung GmbH and WxFusion GmbH.
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