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Dipartimento di Ingegneria Rolling Horizon Approach For Aircraft Scheduling In The Terminal Control Area Of Busy Airports Andrea DAriano, ROMA TRE University 1 ISTTT, 02/11/2013

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Junior Consulting Dipartimento di Ingegneria Introduction Modeling a Terminal Control Area Solution Framework and Algorithms Computational Experiments Conclusions and Ongoing Research Presentation outline This work was partially supported by the Italian Ministry of Research, project FIRB Advanced tracking system in intermodal freight transportation. 2

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Junior Consulting Dipartimento di Ingegneria Air Traffic Control (ATC) Air traffic control must ensure safe, ordered and rapid transit of aircraft on the ground and in the air segments. [*] Source: EUROCONTROL Short-term forecast 2009 With the increase in air traffic [*], aviation authorities are seeking methods (i) to better use the existing airport infrastructure, and (ii) to better manage aircraft movements in the vicinity of airports during operations. 3

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Junior Consulting Dipartimento di Ingegneria Status of the current ATC practise Airports are becoming a major bottleneck in ATC operations. The optimization of take-off/landing operations is a key factor to improve the performance of the entire ATC system. ATC operations are still mainly performed by human controllers whose computer support is most often limited to a graphical representation of the current aircraft position and speed. Intelligent decision support is under investigation in order to reduce the controller workload (see e.g. recent ATM Seminars). 4

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Junior Consulting Dipartimento di Ingegneria Detailed (e.g. Bianco, DellOlmo, Giordani) Basic (e.g. Bertsimas, Lulli, Odoni ) Literature: Aircraft Scheduling Problem (ASP) Existing Approaches Dynamic (e.g. Beasley, Ernst) Static (e.g. Dear, Hu, Chen) Chris Potts et al

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Junior Consulting Dipartimento di Ingegneria Literature: Research needs & directions Aircraft Scheduling Problem (ASP) in Terminal Control Areas: Most aircraft scheduling models in literature represent the TCA as a single resource, typically the runway. These models are not realistic since the other TCA resources are ignored. 6 We present the alternative graph approach for the accurate modelling of air traffic flows at multiple runways and airways. This approach has already been applied successully to control railway traffic for metro lines and railway networks.

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Junior Consulting Dipartimento di Ingegneria Our approach for TCAs Design, implementation and testing of: a dynamic (rolling horizon) setting a detailed (alternative graph) modeling heuristic and exact (branch & bound) ASP algorithms Research questions: 1.how does the traffic control system react when disturbances arise, 2.when and how is it more convenient to reschedule aircraft in the TCA, 3.which algorithm performs best in terms of delay and travel time minimization, 4.which algorithm is the less sensitive to disturbances. 7

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Junior Consulting Dipartimento di Ingegneria Introduction Modeling a Terminal Control Area Solution Framework and Algorithms Computational Experiments Conclusions and Ongoing Research Presentation outline This work was partially supported by the Italian Ministry of Research, project FIRB Advanced tracking system in intermodal freight transportation. 8

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Junior Consulting Dipartimento di Ingegneria 9 MXP TCA : (MILAN, ITALY) FCO TCA : (ROME, ITALY)

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Junior Consulting Dipartimento di Ingegneria The quality of a schedule is measured in terms of maximum delay minimization (limiting the delay caused by potential conflicts). Fixed constraints in F model feasible timing for each aircraft on its specific route, plus constraints on each resource of its route. Alternative constraints in A represent the aircraft ordering decision at air segments and runways, plus decisions on holding circles. A feasible schedule is an event graph with no positive length cycles. 10 The Alternative Graph (AG) Model Mascis & Pacciarelli 2002

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Junior Consulting Dipartimento di Ingegneria AG Model A1 0 * αAαA Release date α A (α A = expected entry time of aircraft A) Air Segments Common Glide Path Runways Holding Circles SRN 1 TOR MBR RWY 35L RWY 35R 9 A 11

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Junior Consulting Dipartimento di Ingegneria AG Model Entry due date β A ( β A = - α A ) Air Segments Common Glide Path Runways Holding Circles SRN 1 TOR MBR RWY 35L RWY 35R 9 A A1 0 * αAαA βAβA 12

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Junior Consulting Dipartimento di Ingegneria (A4, A1) No holding circle (holding time = 0) (A1, A4) Yes holding circle (holding time = δ) AG Model Air Segments Common Glide Path Runways Holding Circles SRN 1 TOR MBR RWY 35L RWY 35R 9 A A1A4 0 * αAαA βAβA 13 δ 0 -δ-δ 0

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Junior Consulting Dipartimento di Ingegneria AG Model A1A4A10 0 * αAαA βAβA Time window for the travel time in each air segment [min travel time; max travel time] Air Segments Common Glide Path Runways Holding Circles SRN 1 TOR MBR RWY 35L RWY 35R 9 A 14 min - max

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Junior Consulting Dipartimento di Ingegneria Common Glide Path Runways Holding Circles Air Segments SRN 1 TOR MBR RWY 35L RWY 35R 9 A A AG Model A1A4A15A10A13A OUT A16 0 * αAαA βAβA γAγA Exit due date γ A (γ A = - planned landing time) 15

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Junior Consulting Dipartimento di Ingegneria Common Glide Path Runways Holding Circles Air Segments SRN 1 TOR MBR RWY 35L RWY 35R 9 A A B B AG Model A1A4A15A10A13A OUT A16 0 * B3B8B15B12B14B OUT B17 αAαA αBαB βAβA γAγA βBβB γBγB Aircraft ordering problem between A and B on the common glide path (resource 15) : Longitudinal and diagonal distances have to be respected Potential conflict on resource 15 ! 16

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Junior Consulting Dipartimento di Ingegneria Common Glide Path Runways Holding Circles Air Segments SRN 1 TOR MBR RWY 35L RWY 35R 9 A A B B C C AG Model A1A4A15A10A13A OUT A16 0 * B3B8B15B12B14B OUT B17 αAαA αBαB βAβA γAγA βBβB γBγB C OUT C17 γCγC αCαC Aircraft ordering problem between B and C for the runway (resource 17): This is a no-store resource! 17

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Junior Consulting Dipartimento di Ingegneria Introduction Modeling a Terminal Control Area Solution Framework and Algorithms Computational Experiments Conclusions and Ongoing Research Presentation outline This work was partially supported by the Italian Ministry of Research, project FIRB Advanced tracking system in intermodal freight transportation. 18

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Junior Consulting Dipartimento di Ingegneria 19 Developing a decision support tool From a logical point of view, ATC decisions can be divided into: Routing decisions, where a route for each aircraft has to be chosen in order to balance the use of TCA resources. Scheduling decisions, where routes are considered fixed, and feasible aircraft scheduling solutions have to be determined. In practice, the two decisions are taken simultaneously. 19

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Junior Consulting Dipartimento di Ingegneria 20 MILP (Mixed-Integer Linear Programming) model FIXED AIRCRAFT ROUTES

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Junior Consulting Dipartimento di Ingegneria 21 ns: number of routes of aircraft sna: number of aircraft MILP (Mixed-Integer Linear Programming) model FLEXIBLE AIRCRAFT ROUTES

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Junior Consulting Dipartimento di Ingegneria Rolling Horizon (RH) approach time Time horizon T1 Time horizon T2 Time horizon T3 Roll period Length of the overall traffic prediction horizon 22

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Junior Consulting Dipartimento di Ingegneria Common Glide Path Runways Holding Circles Air Segments SRN 1 TOR MBR RWY 35L RWY 35R 9 A A B B RH: Stage 1 A1A4A15A10A13A OUT A16 0 * B3B8B15B12B14B OUT B17 α A = 10 α B = 0 β A = -10 β A = 0 Time horizon T1 [0;15] 23

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Junior Consulting Dipartimento di Ingegneria A1A4A15A10A13A OUT A16 0 * B15B14B OUT B17 αA = 10 α B = 5 β A = -10 β B = -5 C OUT C17 β C = -17 α C = 17 Common Glide Path Runways Holding Circles Air Segments SRN 1 TOR MBR RWY 35L RWY 35R 9 A A B B RH: Stage 2 Roll Period = 5 Time horizon T2 [5;20] Observation: At this stage the release time of A and C can be updated dynamically if updated entry times are known 24 C C

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Junior Consulting Dipartimento di Ingegneria Decision Support System based on the Rolling Horizon Approach Instance Generator Feasible Solution Set new roll period Aircraft not fully processed Single Stage Solver Aircraft entry times (dynamic information) XML file Airport Resources Aircraft Times Aircraft Routes Time Horizon Roll period (if any) 25

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Junior Consulting Dipartimento di Ingegneria Single Stage Solver: AGLIBRARY Aircraft Scheduling Module Stopping Criteria Reached? Aircraft Rerouting Module New Schedule No Yes New Routes Return Best Solution Found Heuristics (e.g. FCFS, AGH, JGH) Branch and Bound (BB) Tabu Search (TS) Airport Resources Aircraft Times Aircraft Routes Time Horizon Roll period 26 DAriano 2008

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Junior Consulting Dipartimento di Ingegneria Scheduling heuristics FCFS (First Come First Served) Gives precedence to the first aircraft requiring the resource. Greedy heuristics (Pranzo et al. 2003): AMCC (Avoid Most Critical Completion time) Chooses the pair containing the alternative arc which would cause the largest increase in consecutive delay. AMSP (Avoid Most Similar Pair) Chooses the pair with the largest sum of consecutive delays. JGH (Job Greedy Heuristic) Selects all the alternative arcs involving a chosen aircraft, so that the sequencing of all the operations of this aircraft are fixed in one step. 27

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Junior Consulting Dipartimento di Ingegneria Branch and bound (BB) algorithm Lower bound: Blocking extension of the Jackson pre-emptive schedule [Carlier & Pinson 1989] on air segments and runways. Constraint propagation: Speed up based on network topology and graph proprieties developed in [DAriano et al. 2007]. Experimental setup: Branching rule: Choose the most critical unselected alternative pair with criteria AMSP and branch on this pair. Hybrid search strategy: Alternate four repetitions of the depth- first visit with the choice of the open node of the search tree with the smallest lower bound among the last five generated nodes. 28

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Junior Consulting Dipartimento di Ingegneria ASP with flexible routes: Move & neighbour We start from the solution obtained for the ASP problem with fixed routes. The search for better aircraft routes is as follows: A move is to change one aircraft route and its evaluation is to solve the associated ASP problem with fixed routes; At each iteration the best (local) move is taken from a set of neighbours of a current ASP solution; Neighbourhood: It is well known that a job shop scheduling solution can be improved by changing the critical path C(S) related to the current graph selection (solution) S only [Balas OR 69]; We use ramified critical paths [DAriano et al. 2008]. 29

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Junior Consulting Dipartimento di Ingegneria ASP with flexible routes: Ramified Critical Path CRITICAL PATH: 0, C1, C4, C7, C10, B10, B11, B13, Bout WAITING OPERATION: B10 RAMIFIED CRITICAL PATH: 0, C1, C4, C7, C10, B10, B11, B13, Bout + B1, B4, B7 (BACKWARD) C11, C13, Cout (FORWARD) 30

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Junior Consulting Dipartimento di Ingegneria ASP with flexible routes: Tabu Search (TS) A tabu search algorithm is proposed to escape from local minima by taking a non-improving move and then forbidding the inverse move for a given number of iterations. Another technique to escape from local minima is to perform moves based on restart technique. The ramified critical paths are well focused on reducing the maximum consecutive delay but, in general, are not opt-connected [Corman et al. 2010]. Example: Critical path on aircraft B only but rerouting aircraft A or C may reduce the critical path 31

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Junior Consulting Dipartimento di Ingegneria Introduction Modeling a Terminal Maneuvering Area Solution Framework and Algorithms Computational Experiments Conclusions and Ongoing Research Presentation outline This work was partially supported by the Italian Ministry of Research, project FIRB Advanced tracking system in intermodal freight transportation. 32 Processor Intel i7 (2.84 GHz), 8 GB Ram

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Junior Consulting Dipartimento di Ingegneria 33 3-hour horizon Centralized vs Rolling Horizon [20 instances]

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Junior Consulting Dipartimento di Ingegneria Static/Dynamic Case: BB vs FCFS 34 1-hour horizon [20 instances]

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Junior Consulting Dipartimento di Ingegneria Introduction Modeling a Terminal Control Area Solution Framework and Algorithms Computational Experiments Conclusions and Ongoing Research Presentation outline This work was partially supported by the Italian Ministry of Research, project FIRB Advanced tracking system in intermodal freight transportation. 35

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Junior Consulting Dipartimento di Ingegneria Achievements Detailed ASP models have been investigated for MXP and FCO; The computational experiments proved the effectiveness of our rolling horizon approach compared to a centralized approach; Optimization algorithms outperforms simple rules, both for static and dynamic cases, in terms of delay and travel time minimization; The BB-based rolling horizon approach solves the one-hour instances quickly.

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Junior Consulting Dipartimento di Ingegneria Further research directions Development of detailed models for the coordination & real-time optimization of en-route, approach and TCA traffic management Transformative: Practical realization of integrated (closed-loop) intelligent decision support systems at traffic control centers Study of multiple criteria for aircraft traffic control at busy TCAs (e.g. delay, priority, fairness, environmental and other cost factors) 37 Evaluation of aircraft rescheduling and rerouting approaches for optimal decision making in case of various traffic disturbances

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Junior Consulting Dipartimento di Ingegneria Malpensa Airport: Results from DAriano et al AlgorithmTime Horizon Max Cons Delay (s) Avg Cons Delay (s) Max Tot Delay (s) Avg Tot Delay (s) Delayed Aircraft Total DTTS (s) BB TS (C) TS (A) TS (R) BB TS (C) TS (A) TS (R) RESULTS ON THE AIRCRAFT REROUTING MODULE: The Tabu Search (TS) algorithm is applied to perform three kinds of optimal rerouting strategies: Combined (C), Air (A) and Runway (R). BEST DSS CONFIG: Compared to the BB for aircraft scheduling, TS (C) achieves an improvement on the max cons delay minimization by 34% for 30-min instances and by 46% for 45-min instances.

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