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**Andrea D’Ariano, ROMA TRE University**

Rolling Horizon Approach For Aircraft Scheduling In The Terminal Control Area Of Busy Airports Andrea D’Ariano, ROMA TRE University ISTTT, 22/03/2017 1

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**Modeling a Terminal Control Area Solution Framework and Algorithms **

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

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**Air Traffic Control (ATC)**

Air traffic control must ensure safe, ordered and rapid transit of aircraft on the ground and in the air segments. 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. Indicating Standard Itinerary (IFR) = num passengers SFT: Short-Term Forecast (September 2009) Tween towers, usa economy crisis [*] Source: EUROCONTROL Short-term forecast 2009

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**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).

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**Literature: Aircraft Scheduling Problem (ASP)**

Chris Potts et al. 2011 Detailed (e.g. Bianco, Dell’Olmo, Giordani) Basic (e.g. Bertsimas, Lulli, Odoni ) Dynamic (e.g. Beasley, Ernst) Static (e.g. Dear, Hu, Chen) Existing Approaches

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**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. 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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**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: how does the traffic control system react when disturbances arise, when and how is it more convenient to reschedule aircraft in the TCA, which algorithm performs best in terms of delay and travel time minimization, which algorithm is the less sensitive to disturbances.

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**Modeling a Terminal Control Area Solution Framework and Algorithms **

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

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MXP TCA : (MILAN, ITALY) FCO TCA : (ROME, ITALY)

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**The Alternative Graph (AG) Model**

Mascis & Pacciarelli 2002 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. Conflict-free schedule = no positive length cycles and all potential conflicts are solved (alternative arcs are selected)

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**AG Model Release date αA (αA = expected entry time of aircraft A) A1**

Segments AG Model Holding Circles Common Glide Path Runways A 1 TOR 4 10 13 16 5 9 RWY 35L MBR 2 6 11 15 7 14 3 SRN 17 8 12 RWY 35R A1 * αA Devi dire che per avere un approccio microscopico proponiamo un modello basato sull’alternative graph, Si tratta di un modello più dettagliato di quello di Bianco ma cmq basato sul job shop scheduling Release date αA (αA = expected entry time of aircraft A)

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**AG Model Entry due date βA ( βA = - αA ) A1 Holding Circles Air**

Segments Common Glide Path Runways A 1 TOR 4 10 13 16 5 9 RWY 35L MBR 2 6 11 15 7 14 3 SRN 17 8 12 RWY 35R A1 * αA βA Entry due date βA ( βA = - αA )

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**AG Model (A4, A1) No holding circle (holding time = 0) (A1, A4)**

Holding Circles Air Segments Common Glide Path Runways A 1 TOR 4 10 13 16 5 9 RWY 35L MBR 2 6 11 15 7 14 3 SRN 17 8 12 A1 A4 * αA βA δ RWY 35R -δ (A4, A1) No holding circle (holding time = 0) (A1, A4) Yes holding circle (holding time = δ)

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**AG Model Time window for the travel time in each air segment**

Holding Circles Air Segments Common Glide Path Runways A 1 TOR 4 10 13 16 5 9 RWY 35L MBR 2 6 11 15 7 14 3 SRN 17 8 12 RWY 35R min A1 A4 A10 - max αA βA * Time window for the travel time in each air segment [min travel time; max travel time]

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**AG Model Exit due date γA (γA = - planned landing time) A1 A4 A10 A13**

Common Glide Path Holding Circles Air Segments Runways A A 1 TOR 4 10 13 16 5 9 RWY 35L MBR 2 6 11 15 7 14 3 SRN 17 8 12 RWY 35R A1 A4 A10 A13 A15 A16 AOUT αA γA βA * Exit due date γA (γA = - planned landing time)

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**AG Model Potential conflict on resource 15 !**

Holding Circles Air Segments Common Glide Path Runways A A 1 TOR 4 10 13 16 5 9 Potential conflict on resource 15 ! RWY 35L MBR 2 6 11 15 7 14 17 B 3 SRN 8 12 B RWY 35R A1 A4 A15 A10 A13 AOUT A16 * B3 B8 B15 B12 B14 BOUT B17 αA αB βA γA βB γB Aircraft ordering problem between A and B on the common glide path (resource 15) : Longitudinal and diagonal distances have to be respected

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AG Model Holding Circles Air Segments Common Glide Path Runways A A 1 TOR Aircraft ordering problem between B and C for the runway (resource 17): This is a no-store resource! 4 10 13 16 5 9 RWY 35L MBR 2 6 11 15 C 7 14 17 B 3 SRN C 8 12 B RWY 35R A1 A4 A15 A10 A13 AOUT A16 * B3 B8 B15 B12 B14 BOUT B17 αA αB βA γA βB γB COUT C17 γC αC

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**Modeling a Terminal Control Area Solution Framework and Algorithms **

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

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**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. However, the main objective of real-time routing decisions is typically to balance the use of alternative runways and airways while that of real-time scheduling is the delay minimization. 19

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**MILP (Mixed-Integer Linear Programming) model**

FIXED AIRCRAFT ROUTES 20

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**MILP (Mixed-Integer Linear Programming) model FLEXIBLE AIRCRAFT ROUTES**

ns: number of routes of aircraft s na: number of aircraft 21

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**Rolling Horizon (RH) approach**

Time horizon T1 Roll period Time horizon T2 Roll period Time horizon T3 time Length of the overall traffic prediction horizon

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**RH: Stage 1 A1 A4 A10 A13 A15 A16 AOUT B3 B8 B12 B14 B15 B17 BOUT**

Common Glide Path Runways Holding Circles Air Segments 8 16 17 3 SRN 1 TOR MBR 2 6 4 10 11 12 15 7 5 13 14 RWY 35L RWY 35R 9 A B Time horizon T1 [0;15] A1 A4 A10 A13 A15 A16 AOUT αA = 10 βA = -10 * βA = 0 αB = 0 B3 B8 B12 B14 B15 B17 BOUT

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**RH: Stage 2 A1 A4 A10 A13 A15 A16 AOUT B14 B15 B17 BOUT C17 COUT**

Air Segments Holding Circles Common Glide Path Runways A A 1 TOR 4 10 13 16 5 9 RWY 35L MBR 2 6 11 15 C Roll Period = 5 Time horizon T2 [5;20] 7 14 C 17 B 3 SRN 8 12 B RWY 35R A1 A4 A10 A13 A15 A16 AOUT αA = 10 βA = -10 αB = 5 * B14 B15 B17 BOUT Non so se mettere la observation. Sono indeciso perché: Da un lato spiega come rendiamo il modello dinamico Dall’altro non è poi messa negli esperimenti (per motivi di tempo mi pare abbiamo deciso di escluderlo) αC = 17 βB = -5 C17 COUT Observation: At this stage the release time of A and C can be updated dynamically if updated entry times are known βC = -17

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**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) L’approccio mi permette di: 1) scomporre il problema in sottoproblemi (multi stage approach) 2) tener conto di nuove informazioni/misure del tempo stimato di ingresso nella TCA

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**Single Stage Solver: AGLIBRARY**

D’Ariano 2008 Heuristics (e.g. FCFS, AGH, JGH) Branch and Bound (BB) Aircraft Scheduling Module Stopping Criteria Reached? Rerouting New Schedule No Yes Routes Return Best Solution Found Airport Resources Aircraft Times Aircraft Routes Time Horizon Roll period Tabu Search (TS)

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**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.

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**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 [D’Ariano 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. Settaggio sperimentale + proprietà delle implicazioni statiche e dinamiche

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**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 [D’Ariano et al. 2008].

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**ASP with flexible routes: Ramified Critical Path**

0, C1, C4, C7, C10, B10, B11, B13, Bout WAITING OPERATION: B10 RAMIFIED CRITICAL PATH: + B1, B4, B7 (BACKWARD) C11, C13, Cout (FORWARD)

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**ASP with flexible routes: Tabu Search (TS)**

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 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.

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**Processor Intel i7 (2.84 GHz), 8 GB Ram**

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

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**Centralized vs Rolling Horizon**

3-hour horizon [20 instances]

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**Static/Dynamic Case: BB vs FCFS**

1-hour horizon [20 instances]

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**Modeling a Terminal Control Area Solution Framework and Algorithms **

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

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**Achievements a.dariano@dia.uniroma3.it**

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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**Further research directions**

Evaluation of aircraft rescheduling and rerouting approaches for optimal decision making in case of various traffic disturbances Study of multiple criteria for aircraft traffic control at busy TCAs (e.g. delay, priority, fairness, environmental and other cost factors) 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

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**Malpensa Airport: Results from D’Ariano et al. 2012**

Algorithm Time Horizon Max Cons Delay (s) Avg Cons Max Tot Avg Tot Delayed Aircraft Total DTTS (s) BB 30 139.1 24.1 659 120.1 5.8 1832 TS (C) 91.6 12.6 622 107.3 6.5 1587 TS (A) 127.8 22.1 655 115.2 7.4 1868 TS (R) 94.9 14.1 635 108.8 6.8 1672 45 305.9 61.6 1227 253.4 13.2 3646 166 35.9 1087 200.6 13.5 2988 234.9 57.9 1125 229.8 14.9 170.7 31.6 1104 200.0 2901 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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