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Detailed Mathematical Programming Formulations for the Aircraft Landing Problem on a Single and Multiple Runway Configurations
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Procedia Computer Science 126 (2018) 345–354
22nd International Conference on Knowledge-Based and Intelligent Information & 22nd International ConferenceEngineering on Knowledge-Based Systems and Intelligent Information & Engineering Systems
Detailed Mathematical Programming Formulations for the Aircraft Detailed Mathematical Programming Formulations for the Aircraft Landing Problem on a Single and Multiple Runway Configurations Landing Problem on a Single and Multiple Runway Configurations Meriem Ben Messaoudaa*, Khaled Ghediraaa, Meriam Kefibb Meriem Ben Messaoud *, Khaled Ghedira , Meriam Kefi a The Higher Institute of Management of Tunis, the University of Tunis, Tunis –TUNISIE a College of Computer Information Sciences Saud University, Riyadh, Arabia The Higher Instituteand of Management of Tunis,King the University of Tunis, Tunis Saudi –TUNISIE b College of Computer and Information Sciences King Saud University, Riyadh, Saudi Arabia b
Abstract Abstract We are concerned with supporting the air traffic controller in the management of the inbound traffic. We precisely focus on the We are modeling concernedofwith the air Problem traffic controller in thean management the inbound the careful the supporting Aircraft Landing (ALP) within Air Traffic of Control (ATC)traffic. systemWe for precisely an airportfocus whichonmay careful the Aircraft Landing Air Traffic Control (ATC) system an airportinwhich include modeling a single orofmultiple runways. WeProblem propose (ALP) a new within detailedanMixed Integer Programming (MIP) for formulation whichmay we include a single or multiple runways. We propose three a newsub detailed Mixed Programming (MIP)offormulation in whichand we break down the main problem into simultaneously problems, theInteger scheduling and sequencing aircraft approaches break down main problem sub problems, the scheduling andcontrol sequencing of aircraft approachesisand landings on the TMA resourcesinto (airsimultaneously segment(s) andthree runway(s)), their assignment and the practice. Our achievement the landings on the using TMACPLEX resources (air segment(s) and runway(s)), and of thethe control practice. Our achievement is the model solution and Eclipse. Computational resultstheir showassignment the efficiency proposed approach. model solution using CPLEX and Eclipse. Computational results show the efficiency of the proposed approach. © 2018 The Authors. Published by Elsevier Ltd. © 2018 The Authors. Published by Ltd. © 2018 The Authors. by Elsevier Elsevier Ltd. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an and openpeer-review access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection under responsibility of KES International. Selection and peer-review under responsibility of KES International. Selection and peer-review under responsibility of KES International. Keywords: Terminal Maneuvering Area Operations; Aircraft Landing Problem; Single and Multiple Runway System;Detailed Model Keywords: Terminal Maneuvering Area Operations; Aircraft Landing Problem; Single and Multiple Runway System;Detailed Model
1. Introduction 1. Introduction Over the last decades, the air traffic load increased significantly, and on the basis of forecasts, this trend is Over the last decades, the air Indeed, traffic load increasedknown significantly, and on the basis of forecasts, trend is predicted to persist in the future. the scenario, by EUROCONTROL’s forecast experts this as regulated predicted to persist in the future. Indeed, the scenario, known by EUROCONTROL’s forecast experts as regulated growth, declared that the flight demand in Europe is predicted to be 14.4 million movements in 2035, which is 1.5 growth, declared that the flight demand in Europe is predicted to be 14.4 million movements in 2035, which is 1.5
* Corresponding author. Tel.: +216-98535572
* Corresponding Tel.: +216-98535572 E-mail address:author. [email protected] , [email protected], [email protected] E-mail address: [email protected], [email protected], [email protected] 1877-0509 © 2018 The Authors. Published by Elsevier Ltd. This is an open access under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 1877-0509 © 2018 Thearticle Authors. Published by Elsevier Ltd. Selection under responsibility of KES International. This is an and openpeer-review access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of KES International. 1877-0509 © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of KES International. 10.1016/j.procs.2018.07.268
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times the 2012 volume [1].This continuity of growth in civil aviation project has wide ranging consequences. On the one hand, the air navigation system in the high traffic density areas reached a degree of use close to the limit of capacity (i.e., the operational capacity exceeds the physical one), which will lead on the other hand to delays and a difficulty to quantify air traffic congestion. The first casualties’ areas of congestion and delays have been historically Terminal Maneuvering Area (TMA) surrounding the airport. This part constitutes the critical interface between airspace and airport (surface). Furthermore, these latter dynamic and uncertain regions have been highlighted as the outstanding key areas and remain the main bottleneck for the nation’s Air Traffic Control (ATC) network. Since the TMA has been recognized as one of the bottlenecks in the airport, and due to the fact that their capacity is seen to be a critical component to the extent that it cannot be easily increased; the aircraft operations (landings and take-offs) on the available runway(s) became complex and difficult in real-life, which lead their management to become a key component in air transport systems. Hence, and as a cost-efficient way for improving the capacity of an existing runway system is to improve its take-off and landing schedules; our specific case involves the treatment of the Aircraft Landing Problem (ALP). The ALP has been and still a centre-of interest for many researchers since it is proved to be Nondeterministic Polynomial-time (NP)-hard problem [2]. This is evidenced by the number of works published up to the day [3-4]. The analysis of large number of researches about ALP testifies the fact that there are many types, models, solution methods and applications introduced to deal with the issue. Furthermore, it is possible to distinguish that finding an ALP uniform classification will not be possible. In most cases, the description depends on the researcher’s choice. For that, we’ve submitting in this paper a contribution in which we propose a new set portioning model of our specific problem for a single and multiple runway system. We considered simultaneously three mathematical models for the more general scheduling, sequencing and assignment of aircrafts on the TMA resources (air segment(s), runway(s)) including if necessary the control action. For each of them, we define the objective function and various sophisticated characteristics and real-world TMA constraints that must be satisfied by a problem solution. These three models form a detailed model for the ALP. For a better understanding of what “detailed” means, we resort to this explanation. The ALP models can be classified as basic or detailed. The former includes only the runway(s) in the TMA while the latter schedules aircraft on other relevant TMA resources, for example the air segment(s) [5]. As a modeling technique, we are based on the mature field, the Mixed Integer Programming (MIP) to formulate the detailed ALP. In the rest of the paper, Section 2 provides a description of the aircraft landing operation from a practical standpoint. Next, the existing constrains, objectives and modeling technique related to the ALP are discussed and categorized in Section 3. The detailed model formulation is depicted in Section 4 before devoting the implementation and the experimental results in Section 5. Finally, Section 6 summarizes the work, presents findings and suggests future work. 2. The ALP from a practical standpoint The air traffic controller organizes the inbound flow from the Extended Terminal Maneuvering Area (ETMA) of the airport towards the prescribed Runway Threshold (RT) taking a series of decisions. Typically, as stated by [6], he is in charge of determining approach paths, runway allocation, and landing times of several aircrafts in the radar horizon. The decisions encountered several times by the air traffic controller can be broadly divided into: routing decisions, timing decisions and runway assignment. Routing decisions mean that an origin-destination route for each aircraft has to be chosen regarding air segment(s) and runway(s) under traffic regulation constraints (it is a spatial decision as appointed by [7]). Once a route has been assigned to each aircraft, the ATC problem in the TMA is reduced to the Aircraft Scheduling Problem (ASP) [8], where the aircraft passing timing has to be determined in each air segment, runway and (eventually) holding circle (timing decisions) [9]. At present, all major airports all around the world such as Doha International airport [10], excepting those were ATC advisory tools are not implemented; employ a policy based on First Come First Served (FCFS) to make flight scheduling in the TMA resources. This means, that aircrafts are scheduled according to their estimated time arrivals by simply applying a required minimum separation between them. The separation requirements are among the most sensitive tasks upon
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which the air traffic controller has a great responsibility. Indeed, added to the “radar separation”, which is a longitudinal spacing of 5 nautical miles (nm) (3 nm in congested area) and a vertical spacing of 1000 feet [11], we could mention another most applied notion, the “wake turbulence separation”. It constitutes a minimum separation distances (in nm) required between successive aircrafts based on the preceding aircraft categories. Finally, once the aircrafts are sequencing, an “allocated runway” is assigned to the aircraft. This previous management occurs in the case where the traffic is normal. However, in cases of emergency like air space saturation, small imbalances between demand and capacity during peak times [12]; the aircraft cannot initiate its approaching procedure and it is forced by the air traffic controller to perform some maneuvers (e.g., speed control, path stretching, holding). 3. Previous work 3.1. Operating constraints of ALP The time window and the required separation constraints were handled as an indispensable constraint for the ALP. In connection with this clarification, the Constrained Position Shifting (CPS) concept [13] was also presented as a crucial rule that each aircraft must obey in the sequencing process. The time window constraint means that the Scheduling Landing Time (SLT) for each aircraft to arrive at a certain reference point (e.g., Entry Fix (EF), Final Approach Fix (FAF), or RT), has to be bounded by an earliest time and a latest time. For the minimum separation distance constraint, since the variability of aircraft speed in the TMA has been limited, these separation are dealt with by converting them into separation time using a fixed landing speed depending on the aircraft category [14]. Specific constraints can exist for the ALP by observing at the real. We note what it is called precedence/ priority constraints. For example, [15] have introduced precedence constraints when they have given the priority to the aircraft which arrives in a critical situation of kerosene and to the aircraft which made a maximum delay. Aircraft priorities are taken into account, in the approach proposed by [16], where they have given predominately the priority to the ‘Heavy’ and ‘Large’ aircraft as opposed to ‘Small’ aircraft. In addition, overtake constraint is introduced by several researchers (see e.g., [9]). 3.2. Objective functions The ALP can be classified in the following objectives functions. A goal commonly pursued by the service providers is to maximize the processing capacity of the runway system. This consideration translates into the maximization use of airport capacity (i.e., throughput), which can be viewed as minimizing the completion time or the makespan [17]. On the other hand, since arrival delays are common phenomena in ATC operation, the delay objective attracted many researchers. Knowing that, the delay of an aircraft is partly due to the entrance delay in the TMA if it is delayed at the EF meter and partly due to the additional delay caused by the resolution of potential aircraft conflict. Streams of researchers choose to minimize the first part (minimizing the total of deviation from the target approach times; minimizing the total airborne delay [2]) and the second part (maximum delay minimization [18]). We also note that the contributions to minimize the costs incurred by delays were numerous (see e.g. [19]). We have also observed other objective functions in which the researchers tackled a special aspect of the ALP. We note the work of [20] which opted for balancing the controllers’ workload. We note that, notwithstanding its importance, there is a very limited literature on operational models in aviation that directly consider environmental objective. These few studies include [21] where the authors tried to minimize the total fuel burn. 3.3. Modeling techniques It was normal to envisage the ALP as a particular system of queues. In this context, [22] examined a model for aircraft landing procedure at an airport with up to two runways based on queuing theory concepts. Moreover, based on the hypothesis that the Mixed Integer Linear Program (MILP) presents the advantage of a great flexibility modeling and allows introducing easily the desired extensions (such as the permissible landing time window and the minimum separation time) [23]; most researchers such as [20-24] deal with MILP formulations for the ALP
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modeling. On the other hand, it was being seen that the ALP bears similarities with other optimization problems such as the Traveling Salesman Problem (TSP) [25] and the Vehicle Routing Problem (VRP) [26]. 4. Mathematical formulation 4.1. Problem description Aircrafts usually enter the TMA at entry fixes, and all are merged for approaching the air segment(s) and then landing on a single or multiple runway. The problem is figuring out how a set of approach aircraft (A) is waiting to be instructed by the air traffic controller is; scheduling and sequencing first on a set of air segments (S) at the FAF meter, and then assigning to land at the RT meter of a single or a set of runways (R). Then, for the purpose of model reasonably reflects reality, we will tackle two specific cases in our modeling step. The first one is when the arrival aircraft entering the ETMA could have touched down without control action. The second is when the air traffic controller encounters unforeseeable events such as bad visibility, weather conditions or the occupation of the air segment or runway by the approaching or the landing of another aircraft. Thus, in such a situation, the aircraft cannot initiate its approach and landing procedures and is forced by the air traffic controller to perform a maneuver. To model the first case, we assume that for each aircraft (a = 1,., A) belonging to a class (w = 1,.., W), expected to arrive at the surrounding airspace to enter the ETMA is associated with a minimum entrance time to reach the EF and an earliest ( , target ( and latest ( approach times to reach the meter ( depends on the remaining fuel, a maximal latest time FAF meter of each air segment (s = 1,.., S). Since the is given for each aircraft class. We introduce for this situation, the actual entrance time ( which ( corresponding to the presents the arrival time of the aircraft class at the EF meter. On the basis of the that allows the aircraft to aircraft class, some variable decisions are defined. The first one is the SLT ( is determined, the processing of aircrafts approach efficiently the air segment at the FAF meter. Once the will be in pairs. That means, for a pair of aircrafts ( and ), it will be necessary to determine first (a binary variable that takes 1, if aircraft class keeps approaching the air segment after aircraft class ; 0 otherwise) aircraft class
, then,
(a binary variable which takes 1, if aircraft class
are approaching the same air segment; 0 otherwise)
, and
and (a
binary variable which takes 1, if aircraft class approaches the air segment (s) and aircraft class , . approaches the air segment (s’); 0 otherwise) Once these decisions are made, the separation requirement between aircrafts should be ensured. Knowing that the successive separation method is established, let us assume two parameters, the minimum separation time between successive aircrafts and approaching the same air segment (s), ( and the minimum separation time ( between aircraft class approaching the air segment (s) and . Once the aircraft class and aircraft class approaching the air segment (s’) ) on the corresponding air segment. arrived to the FAF meter, it has to spend a minimum processing time , the assigned landing time ( ) Once the latter time has elapsed, and on the basis of the actual time ( is defined to make the aircraft class land on the corresponding runway r. Consequently, a binary variable is made ( which takes 1 if the aircraft class is assigned to the runway r; 0 otherwise. The process of assigning aircraft to the runway bears some resemblance to the previous one. In fact, at the RT meter, each aircraft class is predicted to arrive at a predicted landing time ( , bounded by the earliest ) and the latest landing time ( ). Then, since the proposed models are intended for a landing time ( single or multiple runway system, it is necessary to determine respectively (a binary variable which takes 1, if aircraft class and aircraft class are scheduled to land on the same runway (r); 0 otherwise) , and (a binary variable which takes 1, if aircraft class is assigned to runway (r)
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and aircraft class is assigned to runway (r’); 0 otherwise) and . In addition, the separation requirement should be respected between each pair of aircrafts landing on the same runway or different represents the minimum separation time between aircraft class and aircraft class runways. In fact, landing on the same runway r such that
, and,
is the minimum separation time
between aircraft class and aircraft class landing on different runways (r and r’) such that and . Then, once the aircraft class crosses the RT meter, it has to spend, on the runway, a defined period of before the landing of another aircraft; knowing that the latter time time known as runway occupancy time is different from an aircraft class to another. The second case that we treat is at its , the aircraft class is forced by the air traffic controller to if aircraft class performed a holding procedure; 0 perform a maneuver (we introduce a binary variable, otherwise). The air traffic controller is limited to the number of holding procedures performed by aircraft class . Then, he decides the number of holding procedure ( that the aircraft class should perform without exceeding the maximum number of holding procedures ( permitted by the ATC. This operation would therefore result in a further delay ( ) undergone by the aircraft class . It is clear that this latter term will be equal to the number of holding ( decided multiplied by the time of maneuver defined for a single holding procedure. Once the aircraft class finished their maneuver, the air traffic controller based on the actual time ( of the corresponding aircraft, will determine the enabling it to approach the air segment (s). Indeed, the figure below demonstrates the two cases explained previously.
Fig. A layout of the two cases that could occur for the arrival aircraft class w (a)
4.2. MIP formulations Arrival Aircraft Scheduling Sequencing Objective and Constraints. We formulate the real time scheduling aircraft classes on the air segment(s) using the notation introduced in the previous subsection. In this model, we consider a relevant objective which consists in delay minimization. Specifically, the minimization of the maximum consecutive delay over all aircrafts at the two meter fixes, the EF of the TMA and the FAF meter of the air segment (Equation1).
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(1)
The first constraint (Equation 2) explains the fact that the for the aircraft class has to be as close as . The constraint (3) accounts that the must belong to a time window, bounded by the possible to its and with the delay imposed ( ) to arrival aircraft class if it performs a maneuver. In most cases of approach aircrafts, their actual times are almost impossible to be the same as their target approaching
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times; which is demonstrated in (4) for an aircraft class . Equation (5) is to restrain the delay time of the ; it should not be larger than the parameter maximum approach delay time ( approach aircraft class for the aircraft class The constraint given by (6) indicates that an aircraft class approaches the air segment (s) before other aircraft in the case that its SLT at the FAF meter is earlier than the others. In other words, overtakes are not allowed. Equation (7) indicates the safety interval that the aircrafts and need to meet if there are two successive aircrafts approaching the same air segment (s) (suppose that aircraft class is the former and the aircraft class is the latter). Indeed, equation (8) indicates the safety interval that the aircrafts and need to meet if there are two successive aircrafts approaching different air segments (s and s’). Equations (9) indicates that, for two approach flights and , either is the leading and is the trailing or the contrary, is the trailing and is the leading. Equation (10) indicates that any approach aircraft class has only one leading/trailing aircraft. The constraints given by (11), (12), (13) and (14) establish the longitudinal separation between each pair of aircrafts approaching the same or different air segments and for any approaching sequence. If aircraft class approaches the air segment (s) before aircraft class , expression (11) is naturally satisfied since M is a sufficiently large constant used to ensure that the equation is and expression (12) ensures the redundant in the case when approaches before separation between and . The expressions (13) and (14) have the same goal than the two latter equations when they ensure the separation between a leading and trailing aircraft ( and ) approaching in this case of each aircraft class varies different air segments (s and s’). Constraint (15) explains that the between a pre-defined time windows, due to a limited possibility of aircraft speed changes. Finally, we must specify the non negativity constraint (constraint 16). Arrival Aircraft Runway Assignment Objective and Constraints. Even in the context of delay, for the objective formulation in this step, we want to minimize the maximum consecutive delay at the RT meter (Equation 17).
Equation (18) explains the pigeonhole principle where the runway is a blocking resource as the presence of an aircraft on the runway imposes that no other aircraft can use it. Therefore, since the runway can be occupied by only one aircraft at a time, a safety check must be ensured between any pair of aircraft classes ( and ). In this
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respect, we have two cases, that one if the pair of aircrafts class lands on the same runway (r) and on different runways (r and r’). The first case is presented by (19); and (20) presents the case of different runways. Constraint of the aircraft class must belong to a time window; bounded by the and (21) explains that the . The equation (22) explains the fact that the trailing aircraft class of any pair (suppose that aircraft class the is the former and the aircraft class is the latter) cannot touchdown the runway (r) before the leading aircraft class is clear of the runway after passing the . The equation (23) ensures that when both aircraft class and aircraft class are allocated to the same runway (r); the runway must be identical. Finally, constraint (24) forces variables to be binary variables. Arrival Aircraft / Control Action Objectives and Constraints. The objective function (25) represents the minimization of the maneuver time that the aircraft class performs.
The constraint given by (27) imposes a maximum number of holding procedures that can be performed by each aircraft class . The last constraint (28) corresponds to the non negativity constraint. 5. Computational results and discussion In order to ascertain whether the objectives have been met, we are using Eclipse and CPLEX as tools. Indeed, the 64-bit version of Eclipse is setting up for the Java API of IBM ILOG CPLEX Optimization Studio 12.6.3 version, on a computer with an Intel Core2 Duo 3.00 GHZ processor. After that step, each of the three MIP formulations is written, respectively in three java class files. Then, after entering all the input data in the first class, the experiment is focused on exploring the properly ordered set of aircrafts classes with indicating for each aircraft the if it performs a maneuver ( and the for the aircraft class that does not ). The Arrival Aircraft Scheduling Sequencing Class takes as input the latter ordered perform a maneuver ( . Finally, the Arrival sequence which of its share finds an ordered sequence indicating for each aircraft the Aircraft Runway Assignment Class will extend the latter ordered sequence and establish an ordered sequence looking to the case of a single runway. In the case of multiple runways, the results are an ordered sequence of a set of aircrafts on each runway: a sequence for each runway. The overall framework returns the sequence that minimizes the maximum delay of a plurality of aircrafts classes from the EF meter to the RT meter of the runway(s). 5.1. Data generation Since there is no benchmark instance sets in the literature for the Aircraft Control Scheduling Sequencing Assignment (ACSSA) problems, randomly generated instance sets were adopted in this research for the evaluation of the proposed approach. We generate several families of problem instances. For each family, we fix the number and type of the aircrafts to be proceeding. Regarding the classification of aircrafts selected, it is based on the International Council Aviation Organization (ICAO) classification. Hence, we have scattered 12 aircrafts (A = 12) following the ratio of 2 Super, 4 Heavy, 4 Medium and 2 Light (W = 4) that are anticipated to arrive at airport for an hour of traffic. We assume for each data set under study that we known at the start time all the aircraft class , , , , , , and ). The separation information’s ( distances between aircrafts class ( and ) whether before achieving the FAF meter of the air segment or
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the RT meter of the corresponding runway are based on real data. We use the separation distances issued from the , , , and Federal Aviation Administration (FAA). Whereas, for the data related to , we applied a nominal data since they are not available in the literature. Note that all the initial data mentioned above act as parameters, i.e. they get initial values that do not change during the run. However, the set of air segment (S) and the set of runway (R) will change from run to another as described in Table1. Table1. Data Sets Instance
Set of Aircraft (A)
Set of air Segment (S)
Set of Runways (R)
i=1
12
1
1
i=2
12
2
1
i=3
12
1
2
i=4
12
2
2
5.2. Results and discussion Looking at the computational results summarized in Table 2, the main conclusion is that the proposed approach can obtain optimal results with less computational effort with regards to one hour flight traffic planning horizon. These results have been achieved thanks to Eclipse that supports the declarative modeling of iterations required by mathematical programming problems by providing the declarative loops on the one hand. On the other hand, the CPLEX disposes of a Mixed Integer Optimizer that is called by default for each MIP formulation. In addition, the optimizer invoked by CPLEX for the MIP models was the Branch & Cut algorithm. Table 2. Experimental Results Instances
The problem solution time in (s)
i=1
15 s
i=2
25 s
i=3
45s
i=4
60 s
6. Conclusions To present and in view of the above literature investigation features, the aircraft landing operation are still a relevant issue for the ATC. Moreover its importance, it is not an easy task for several reasons. On the one hand, it requires depth knowledge of several components which are affected by high uncertainty. On the other hand, it returns to the air transportation system complexity and the differences between airports and different stakeholder aims. Taking account of all these distinctions, this work provides not only the first overview of the various constraints and objectives related to the ALP. Moreover, we were investigating mathematical models that dissect the timing, sequencing of aircraft and their assignment to the runway (s) taking into account the control aspect which was usually leaving aside for the majority of models proposed in the literature. In forthcoming works, we plan to treat the dynamic case of the ALP since it is resolved in a static fashion in this paper. We are also interested to suggest solution that scale large number of aircrafts flying trough TMA. Acknowledgements This work was supported by the Research Center of College of Computer and Information Sciences, King Saud University. The authors are grateful for this support.
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References [1] European Organization for the safety of Air Navigation. (2013) “Challenge of growth 2013: Summary Report. Task 4: European Air Traffic in 2035.” http://www.eurocontrol.int/articles/challengesgrowth. [2] ZHAN Zhi-Hui, ZHANG Jun, LI Yun, LIU Ou, KWOK S K, LP W H, and KAYNAK Okyay. (2010) “An efficient ant colony system based on receding horizon control for the aircraft arrival sequencing and scheduling problem.” IEEE Transactions on Intelligent Transportation Systems 11 (2): 399-412. [3] HONG Youkyung, CHOI Bynghun, LEE Somang, LEE Keumjin, and KIM Youndan. (2017) “Optimal and practical aircraft sequencing and scheduling for point merge system.” In: IFAC-PapersOnLine 50 (1) pp. 14644-14649. [4] LIANG Man, DELAHAYE Daniel, and MARECHAL Pierre. (2017) “Integrated sequencing and merging aircraft to parallel runways with automated conflict resolution and advanced avionics capabilities.”Transportation Research Part C 85:268-291. [5] SABAR Nasser R, and Kendall Graham. (2015) “An iterated local search with multiple perturbation operators and time varying perturbation strength for the aircraft landing problem.” OMEGA 56: 88-98. [6] Diallo Coumba, NDIAYE B.abacar Mbaya, and SECK Diaraf. (2012) “Scheduling Aircraft Landing at LSS Airport.” American Journal of Operations Research 2 (2): 235-241. [7] KJENSTAD Dag, MANNINO Carlo, NORDLANDER Tomas Eric, SCHITTEKAT Patrick, and SMEDSRUD Morten. (2013) “Optimizing AMAN-SMAN-DMAN at Hamburg and Arlanda airport.” In: Proceedings of third Sesar Innovation Days (SIDs), Stockholm. [8] SAMA Marcella, D’ARIANO Andrea, TOLI Alessandro, PACCIARELLI Dario, and CORMAN Francesco. (2015) “A variable neighborhood search for optimal scheduling and routing of take-off and landing aircraft.” In: Proceedings on Models and Technologies for Intelligent Transportation System (MT- ITS), pp.491-498, Budapest, Hungary. [9] D’ARIANO Andrea, PISTELLI Mario, and PACCIARELLI Dario. (2011) “Aircraft Retiming and rerouting in vicinity of airports.” In: 2nd International Conference on Models and Technologies for Intelligent Transportation Systems, Leuven, Belgium. [10] GHONIEM Ahmed, SHERALI Hanif D, BALK Hojong. (2014) “Enhanced models for a mixed arrival-departure aircraft sequencing problem.” INFORMS Journal on Computing 26 (3): 514-530. [11] FURINI Fabio, PERSIANI Carlo Alfredo, and TOTH Paolo. (2012) “Aircraft sequencing problems via a rolling horizon algorithm.” In: International Symposium on Combinatorial Optimization (ISCO), Athens, Greece, pp. 273-284. [12] International Civil Aviation Organization. (2007) “Procedures for air navigation services (Air Traffic Management).” Doc 4444, the fifteenth edition, Council, Montréal. [13] DEAR Roger G. (1976) “The dynamic scheduling of aircraft in the near terminal area.” (Ph. D. thesis). Flight Transportation Laboratory, MIT, USA, 1-325. [14] BEASLEY John E, SONANDER J, and HAVELOCK P. (2001) “Scheduling aircraft Landings at London Heathrow using a population heuristics.” Journal of the Operational Research Society 52 (5): 483-493. [15] ANDREUSSI Alberto, BIANCO Lucio, and RICCIARDELLI Salvatore. (1981) “A simulation model for aircraft sequencing in the near terminal area.” European Journal of Operational Research 8 (4): 345-354. [16] GHONIEM Ahmed, FARHADI Farbod, and REIHANECH Mohammed. (2015) “An accelerated branch-and price algorithm for multiplerunway aircraft sequencing problems.” European Journal of Operational Research 246 (5): 34-43. [17] BIANCO Lucio, DELL’OLMO Paolo, and GIORDANI Stefano. (1999) “Coordination of traffic flow in the TMA.” In: L. Bianco, P. Dell’Olmo, A. R. Odoni, (Eds.), New Concepts and Methods in Air Traffic Management, pp. 95-124. [18] HANBONG Lee, and BALAKRISHNAN Hamsa. (2008) “A Study of Tradeoffs in Scheduling Terminal-Area Operations.” Proceedings of the IEEE 96, 2081–2095. [19] BENCHEIKH Ghizlane, BOUKACHOUR Jaouad, ALAOUI Ahmed Elhilali, and ELKHOUKHI Fatima. (2009) “Hybrid method for aircraft landing scheduling based on a job shop formulation.” International Journal of Computer Science and Network Security 9 (8): 78-88. [20] BEASLEY John E, KRISHNAMOORTHY M, SHARAIHA Y. M, and ABRAMSON D. (2000) “Scheduling Aircrafts Landings- the static case. “Transportation Science 34 (2), 180-197. [21] ANDREAVA-MORI Adriana, SUZUKI Shinji, and LTOH Eri. (2013) “Rule derivation for arrival aircraft sequencing.” Aerospace Science Technology 30 (1):200-209. [22] BAUERLE N, ENGELHARDT-FUNKE O, and KOLONKO M. (2007) “On the waiting time of arriving aircrafts and the capacity of airports with one or two runways. “European Journal of Operational Research 177 (2):1180-1196. [23] JI Xiao-Peng, CAO Xiao-Bin, and TANG Ke. (2015) “Sequence Searching and evaluations: a unified approach for aircraft arrival sequencing and scheduling problems.” Memetic Computing 8 (2):109-123. [24] SAMA Marcella, D’ARIANO Andrea, D’ARIANO Paolo, and PACCIARELLI Dario. (2017) “Scheduling models for optimal aircraft traffic control at busy airports: Tardiness, priorities, equity and violations considerations.” OMEGA 67: 81-98. [25] BERTSIMAS Dimitris, and FRANKOVISH Micheal. (2015) “Unified optimization of traffic flows through airports.”Transportation Science 50 (1): 77-93. [26] BRISKORN Dirk, and STOLLETZ Raik. (2014) “Aircraft landing problems with aircraft classes.” Journal of Scheduling 17 (1) 31-45.
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Procedia Computer Science 126 (2018) 345–354
22nd International Conference on Knowledge-Based and Intelligent Information & 22nd International ConferenceEngineering on Knowledge-Based Systems and Intelligent Information & Engineering Systems
Detailed Mathematical Programming Formulations for the Aircraft Detailed Mathematical Programming Formulations for the Aircraft Landing Problem on a Single and Multiple Runway Configurations Landing Problem on a Single and Multiple Runway Configurations Meriem Ben Messaoudaa*, Khaled Ghediraaa, Meriam Kefibb Meriem Ben Messaoud *, Khaled Ghedira , Meriam Kefi a The Higher Institute of Management of Tunis, the University of Tunis, Tunis –TUNISIE a College of Computer Information Sciences Saud University, Riyadh, Arabia The Higher Instituteand of Management of Tunis,King the University of Tunis, Tunis Saudi –TUNISIE b College of Computer and Information Sciences King Saud University, Riyadh, Saudi Arabia b
Abstract Abstract We are concerned with supporting the air traffic controller in the management of the inbound traffic. We precisely focus on the We are modeling concernedofwith the air Problem traffic controller in thean management the inbound the careful the supporting Aircraft Landing (ALP) within Air Traffic of Control (ATC)traffic. systemWe for precisely an airportfocus whichonmay careful the Aircraft Landing Air Traffic Control (ATC) system an airportinwhich include modeling a single orofmultiple runways. WeProblem propose (ALP) a new within detailedanMixed Integer Programming (MIP) for formulation whichmay we include a single or multiple runways. We propose three a newsub detailed Mixed Programming (MIP)offormulation in whichand we break down the main problem into simultaneously problems, theInteger scheduling and sequencing aircraft approaches break down main problem sub problems, the scheduling andcontrol sequencing of aircraft approachesisand landings on the TMA resourcesinto (airsimultaneously segment(s) andthree runway(s)), their assignment and the practice. Our achievement the landings on the using TMACPLEX resources (air segment(s) and runway(s)), and of thethe control practice. Our achievement is the model solution and Eclipse. Computational resultstheir showassignment the efficiency proposed approach. model solution using CPLEX and Eclipse. Computational results show the efficiency of the proposed approach. © 2018 The Authors. Published by Elsevier Ltd. © 2018 The Authors. Published by Ltd. © 2018 The Authors. by Elsevier Elsevier Ltd. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an and openpeer-review access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection under responsibility of KES International. Selection and peer-review under responsibility of KES International. Selection and peer-review under responsibility of KES International. Keywords: Terminal Maneuvering Area Operations; Aircraft Landing Problem; Single and Multiple Runway System;Detailed Model Keywords: Terminal Maneuvering Area Operations; Aircraft Landing Problem; Single and Multiple Runway System;Detailed Model
1. Introduction 1. Introduction Over the last decades, the air traffic load increased significantly, and on the basis of forecasts, this trend is Over the last decades, the air Indeed, traffic load increasedknown significantly, and on the basis of forecasts, trend is predicted to persist in the future. the scenario, by EUROCONTROL’s forecast experts this as regulated predicted to persist in the future. Indeed, the scenario, known by EUROCONTROL’s forecast experts as regulated growth, declared that the flight demand in Europe is predicted to be 14.4 million movements in 2035, which is 1.5 growth, declared that the flight demand in Europe is predicted to be 14.4 million movements in 2035, which is 1.5
* Corresponding author. Tel.: +216-98535572
* Corresponding Tel.: +216-98535572 E-mail address:author. [email protected] , [email protected], [email protected] E-mail address: [email protected], [email protected], [email protected] 1877-0509 © 2018 The Authors. Published by Elsevier Ltd. This is an open access under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 1877-0509 © 2018 Thearticle Authors. Published by Elsevier Ltd. Selection under responsibility of KES International. This is an and openpeer-review access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of KES International. 1877-0509 © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of KES International. 10.1016/j.procs.2018.07.268
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times the 2012 volume [1].This continuity of growth in civil aviation project has wide ranging consequences. On the one hand, the air navigation system in the high traffic density areas reached a degree of use close to the limit of capacity (i.e., the operational capacity exceeds the physical one), which will lead on the other hand to delays and a difficulty to quantify air traffic congestion. The first casualties’ areas of congestion and delays have been historically Terminal Maneuvering Area (TMA) surrounding the airport. This part constitutes the critical interface between airspace and airport (surface). Furthermore, these latter dynamic and uncertain regions have been highlighted as the outstanding key areas and remain the main bottleneck for the nation’s Air Traffic Control (ATC) network. Since the TMA has been recognized as one of the bottlenecks in the airport, and due to the fact that their capacity is seen to be a critical component to the extent that it cannot be easily increased; the aircraft operations (landings and take-offs) on the available runway(s) became complex and difficult in real-life, which lead their management to become a key component in air transport systems. Hence, and as a cost-efficient way for improving the capacity of an existing runway system is to improve its take-off and landing schedules; our specific case involves the treatment of the Aircraft Landing Problem (ALP). The ALP has been and still a centre-of interest for many researchers since it is proved to be Nondeterministic Polynomial-time (NP)-hard problem [2]. This is evidenced by the number of works published up to the day [3-4]. The analysis of large number of researches about ALP testifies the fact that there are many types, models, solution methods and applications introduced to deal with the issue. Furthermore, it is possible to distinguish that finding an ALP uniform classification will not be possible. In most cases, the description depends on the researcher’s choice. For that, we’ve submitting in this paper a contribution in which we propose a new set portioning model of our specific problem for a single and multiple runway system. We considered simultaneously three mathematical models for the more general scheduling, sequencing and assignment of aircrafts on the TMA resources (air segment(s), runway(s)) including if necessary the control action. For each of them, we define the objective function and various sophisticated characteristics and real-world TMA constraints that must be satisfied by a problem solution. These three models form a detailed model for the ALP. For a better understanding of what “detailed” means, we resort to this explanation. The ALP models can be classified as basic or detailed. The former includes only the runway(s) in the TMA while the latter schedules aircraft on other relevant TMA resources, for example the air segment(s) [5]. As a modeling technique, we are based on the mature field, the Mixed Integer Programming (MIP) to formulate the detailed ALP. In the rest of the paper, Section 2 provides a description of the aircraft landing operation from a practical standpoint. Next, the existing constrains, objectives and modeling technique related to the ALP are discussed and categorized in Section 3. The detailed model formulation is depicted in Section 4 before devoting the implementation and the experimental results in Section 5. Finally, Section 6 summarizes the work, presents findings and suggests future work. 2. The ALP from a practical standpoint The air traffic controller organizes the inbound flow from the Extended Terminal Maneuvering Area (ETMA) of the airport towards the prescribed Runway Threshold (RT) taking a series of decisions. Typically, as stated by [6], he is in charge of determining approach paths, runway allocation, and landing times of several aircrafts in the radar horizon. The decisions encountered several times by the air traffic controller can be broadly divided into: routing decisions, timing decisions and runway assignment. Routing decisions mean that an origin-destination route for each aircraft has to be chosen regarding air segment(s) and runway(s) under traffic regulation constraints (it is a spatial decision as appointed by [7]). Once a route has been assigned to each aircraft, the ATC problem in the TMA is reduced to the Aircraft Scheduling Problem (ASP) [8], where the aircraft passing timing has to be determined in each air segment, runway and (eventually) holding circle (timing decisions) [9]. At present, all major airports all around the world such as Doha International airport [10], excepting those were ATC advisory tools are not implemented; employ a policy based on First Come First Served (FCFS) to make flight scheduling in the TMA resources. This means, that aircrafts are scheduled according to their estimated time arrivals by simply applying a required minimum separation between them. The separation requirements are among the most sensitive tasks upon
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which the air traffic controller has a great responsibility. Indeed, added to the “radar separation”, which is a longitudinal spacing of 5 nautical miles (nm) (3 nm in congested area) and a vertical spacing of 1000 feet [11], we could mention another most applied notion, the “wake turbulence separation”. It constitutes a minimum separation distances (in nm) required between successive aircrafts based on the preceding aircraft categories. Finally, once the aircrafts are sequencing, an “allocated runway” is assigned to the aircraft. This previous management occurs in the case where the traffic is normal. However, in cases of emergency like air space saturation, small imbalances between demand and capacity during peak times [12]; the aircraft cannot initiate its approaching procedure and it is forced by the air traffic controller to perform some maneuvers (e.g., speed control, path stretching, holding). 3. Previous work 3.1. Operating constraints of ALP The time window and the required separation constraints were handled as an indispensable constraint for the ALP. In connection with this clarification, the Constrained Position Shifting (CPS) concept [13] was also presented as a crucial rule that each aircraft must obey in the sequencing process. The time window constraint means that the Scheduling Landing Time (SLT) for each aircraft to arrive at a certain reference point (e.g., Entry Fix (EF), Final Approach Fix (FAF), or RT), has to be bounded by an earliest time and a latest time. For the minimum separation distance constraint, since the variability of aircraft speed in the TMA has been limited, these separation are dealt with by converting them into separation time using a fixed landing speed depending on the aircraft category [14]. Specific constraints can exist for the ALP by observing at the real. We note what it is called precedence/ priority constraints. For example, [15] have introduced precedence constraints when they have given the priority to the aircraft which arrives in a critical situation of kerosene and to the aircraft which made a maximum delay. Aircraft priorities are taken into account, in the approach proposed by [16], where they have given predominately the priority to the ‘Heavy’ and ‘Large’ aircraft as opposed to ‘Small’ aircraft. In addition, overtake constraint is introduced by several researchers (see e.g., [9]). 3.2. Objective functions The ALP can be classified in the following objectives functions. A goal commonly pursued by the service providers is to maximize the processing capacity of the runway system. This consideration translates into the maximization use of airport capacity (i.e., throughput), which can be viewed as minimizing the completion time or the makespan [17]. On the other hand, since arrival delays are common phenomena in ATC operation, the delay objective attracted many researchers. Knowing that, the delay of an aircraft is partly due to the entrance delay in the TMA if it is delayed at the EF meter and partly due to the additional delay caused by the resolution of potential aircraft conflict. Streams of researchers choose to minimize the first part (minimizing the total of deviation from the target approach times; minimizing the total airborne delay [2]) and the second part (maximum delay minimization [18]). We also note that the contributions to minimize the costs incurred by delays were numerous (see e.g. [19]). We have also observed other objective functions in which the researchers tackled a special aspect of the ALP. We note the work of [20] which opted for balancing the controllers’ workload. We note that, notwithstanding its importance, there is a very limited literature on operational models in aviation that directly consider environmental objective. These few studies include [21] where the authors tried to minimize the total fuel burn. 3.3. Modeling techniques It was normal to envisage the ALP as a particular system of queues. In this context, [22] examined a model for aircraft landing procedure at an airport with up to two runways based on queuing theory concepts. Moreover, based on the hypothesis that the Mixed Integer Linear Program (MILP) presents the advantage of a great flexibility modeling and allows introducing easily the desired extensions (such as the permissible landing time window and the minimum separation time) [23]; most researchers such as [20-24] deal with MILP formulations for the ALP
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modeling. On the other hand, it was being seen that the ALP bears similarities with other optimization problems such as the Traveling Salesman Problem (TSP) [25] and the Vehicle Routing Problem (VRP) [26]. 4. Mathematical formulation 4.1. Problem description Aircrafts usually enter the TMA at entry fixes, and all are merged for approaching the air segment(s) and then landing on a single or multiple runway. The problem is figuring out how a set of approach aircraft (A) is waiting to be instructed by the air traffic controller is; scheduling and sequencing first on a set of air segments (S) at the FAF meter, and then assigning to land at the RT meter of a single or a set of runways (R). Then, for the purpose of model reasonably reflects reality, we will tackle two specific cases in our modeling step. The first one is when the arrival aircraft entering the ETMA could have touched down without control action. The second is when the air traffic controller encounters unforeseeable events such as bad visibility, weather conditions or the occupation of the air segment or runway by the approaching or the landing of another aircraft. Thus, in such a situation, the aircraft cannot initiate its approach and landing procedures and is forced by the air traffic controller to perform a maneuver. To model the first case, we assume that for each aircraft (a = 1,., A) belonging to a class (w = 1,.., W), expected to arrive at the surrounding airspace to enter the ETMA is associated with a minimum entrance time to reach the EF and an earliest ( , target ( and latest ( approach times to reach the meter ( depends on the remaining fuel, a maximal latest time FAF meter of each air segment (s = 1,.., S). Since the is given for each aircraft class. We introduce for this situation, the actual entrance time ( which ( corresponding to the presents the arrival time of the aircraft class at the EF meter. On the basis of the that allows the aircraft to aircraft class, some variable decisions are defined. The first one is the SLT ( is determined, the processing of aircrafts approach efficiently the air segment at the FAF meter. Once the will be in pairs. That means, for a pair of aircrafts ( and ), it will be necessary to determine first (a binary variable that takes 1, if aircraft class keeps approaching the air segment after aircraft class ; 0 otherwise) aircraft class
, then,
(a binary variable which takes 1, if aircraft class
are approaching the same air segment; 0 otherwise)
, and
and (a
binary variable which takes 1, if aircraft class approaches the air segment (s) and aircraft class , . approaches the air segment (s’); 0 otherwise) Once these decisions are made, the separation requirement between aircrafts should be ensured. Knowing that the successive separation method is established, let us assume two parameters, the minimum separation time between successive aircrafts and approaching the same air segment (s), ( and the minimum separation time ( between aircraft class approaching the air segment (s) and . Once the aircraft class and aircraft class approaching the air segment (s’) ) on the corresponding air segment. arrived to the FAF meter, it has to spend a minimum processing time , the assigned landing time ( ) Once the latter time has elapsed, and on the basis of the actual time ( is defined to make the aircraft class land on the corresponding runway r. Consequently, a binary variable is made ( which takes 1 if the aircraft class is assigned to the runway r; 0 otherwise. The process of assigning aircraft to the runway bears some resemblance to the previous one. In fact, at the RT meter, each aircraft class is predicted to arrive at a predicted landing time ( , bounded by the earliest ) and the latest landing time ( ). Then, since the proposed models are intended for a landing time ( single or multiple runway system, it is necessary to determine respectively (a binary variable which takes 1, if aircraft class and aircraft class are scheduled to land on the same runway (r); 0 otherwise) , and (a binary variable which takes 1, if aircraft class is assigned to runway (r)
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and aircraft class is assigned to runway (r’); 0 otherwise) and . In addition, the separation requirement should be respected between each pair of aircrafts landing on the same runway or different represents the minimum separation time between aircraft class and aircraft class runways. In fact, landing on the same runway r such that
, and,
is the minimum separation time
between aircraft class and aircraft class landing on different runways (r and r’) such that and . Then, once the aircraft class crosses the RT meter, it has to spend, on the runway, a defined period of before the landing of another aircraft; knowing that the latter time time known as runway occupancy time is different from an aircraft class to another. The second case that we treat is at its , the aircraft class is forced by the air traffic controller to if aircraft class performed a holding procedure; 0 perform a maneuver (we introduce a binary variable, otherwise). The air traffic controller is limited to the number of holding procedures performed by aircraft class . Then, he decides the number of holding procedure ( that the aircraft class should perform without exceeding the maximum number of holding procedures ( permitted by the ATC. This operation would therefore result in a further delay ( ) undergone by the aircraft class . It is clear that this latter term will be equal to the number of holding ( decided multiplied by the time of maneuver defined for a single holding procedure. Once the aircraft class finished their maneuver, the air traffic controller based on the actual time ( of the corresponding aircraft, will determine the enabling it to approach the air segment (s). Indeed, the figure below demonstrates the two cases explained previously.
Fig. A layout of the two cases that could occur for the arrival aircraft class w (a)
4.2. MIP formulations Arrival Aircraft Scheduling Sequencing Objective and Constraints. We formulate the real time scheduling aircraft classes on the air segment(s) using the notation introduced in the previous subsection. In this model, we consider a relevant objective which consists in delay minimization. Specifically, the minimization of the maximum consecutive delay over all aircrafts at the two meter fixes, the EF of the TMA and the FAF meter of the air segment (Equation1).
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(1)
The first constraint (Equation 2) explains the fact that the for the aircraft class has to be as close as . The constraint (3) accounts that the must belong to a time window, bounded by the possible to its and with the delay imposed ( ) to arrival aircraft class if it performs a maneuver. In most cases of approach aircrafts, their actual times are almost impossible to be the same as their target approaching
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times; which is demonstrated in (4) for an aircraft class . Equation (5) is to restrain the delay time of the ; it should not be larger than the parameter maximum approach delay time ( approach aircraft class for the aircraft class The constraint given by (6) indicates that an aircraft class approaches the air segment (s) before other aircraft in the case that its SLT at the FAF meter is earlier than the others. In other words, overtakes are not allowed. Equation (7) indicates the safety interval that the aircrafts and need to meet if there are two successive aircrafts approaching the same air segment (s) (suppose that aircraft class is the former and the aircraft class is the latter). Indeed, equation (8) indicates the safety interval that the aircrafts and need to meet if there are two successive aircrafts approaching different air segments (s and s’). Equations (9) indicates that, for two approach flights and , either is the leading and is the trailing or the contrary, is the trailing and is the leading. Equation (10) indicates that any approach aircraft class has only one leading/trailing aircraft. The constraints given by (11), (12), (13) and (14) establish the longitudinal separation between each pair of aircrafts approaching the same or different air segments and for any approaching sequence. If aircraft class approaches the air segment (s) before aircraft class , expression (11) is naturally satisfied since M is a sufficiently large constant used to ensure that the equation is and expression (12) ensures the redundant in the case when approaches before separation between and . The expressions (13) and (14) have the same goal than the two latter equations when they ensure the separation between a leading and trailing aircraft ( and ) approaching in this case of each aircraft class varies different air segments (s and s’). Constraint (15) explains that the between a pre-defined time windows, due to a limited possibility of aircraft speed changes. Finally, we must specify the non negativity constraint (constraint 16). Arrival Aircraft Runway Assignment Objective and Constraints. Even in the context of delay, for the objective formulation in this step, we want to minimize the maximum consecutive delay at the RT meter (Equation 17).
Equation (18) explains the pigeonhole principle where the runway is a blocking resource as the presence of an aircraft on the runway imposes that no other aircraft can use it. Therefore, since the runway can be occupied by only one aircraft at a time, a safety check must be ensured between any pair of aircraft classes ( and ). In this
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respect, we have two cases, that one if the pair of aircrafts class lands on the same runway (r) and on different runways (r and r’). The first case is presented by (19); and (20) presents the case of different runways. Constraint of the aircraft class must belong to a time window; bounded by the and (21) explains that the . The equation (22) explains the fact that the trailing aircraft class of any pair (suppose that aircraft class the is the former and the aircraft class is the latter) cannot touchdown the runway (r) before the leading aircraft class is clear of the runway after passing the . The equation (23) ensures that when both aircraft class and aircraft class are allocated to the same runway (r); the runway must be identical. Finally, constraint (24) forces variables to be binary variables. Arrival Aircraft / Control Action Objectives and Constraints. The objective function (25) represents the minimization of the maneuver time that the aircraft class performs.
The constraint given by (27) imposes a maximum number of holding procedures that can be performed by each aircraft class . The last constraint (28) corresponds to the non negativity constraint. 5. Computational results and discussion In order to ascertain whether the objectives have been met, we are using Eclipse and CPLEX as tools. Indeed, the 64-bit version of Eclipse is setting up for the Java API of IBM ILOG CPLEX Optimization Studio 12.6.3 version, on a computer with an Intel Core2 Duo 3.00 GHZ processor. After that step, each of the three MIP formulations is written, respectively in three java class files. Then, after entering all the input data in the first class, the experiment is focused on exploring the properly ordered set of aircrafts classes with indicating for each aircraft the if it performs a maneuver ( and the for the aircraft class that does not ). The Arrival Aircraft Scheduling Sequencing Class takes as input the latter ordered perform a maneuver ( . Finally, the Arrival sequence which of its share finds an ordered sequence indicating for each aircraft the Aircraft Runway Assignment Class will extend the latter ordered sequence and establish an ordered sequence looking to the case of a single runway. In the case of multiple runways, the results are an ordered sequence of a set of aircrafts on each runway: a sequence for each runway. The overall framework returns the sequence that minimizes the maximum delay of a plurality of aircrafts classes from the EF meter to the RT meter of the runway(s). 5.1. Data generation Since there is no benchmark instance sets in the literature for the Aircraft Control Scheduling Sequencing Assignment (ACSSA) problems, randomly generated instance sets were adopted in this research for the evaluation of the proposed approach. We generate several families of problem instances. For each family, we fix the number and type of the aircrafts to be proceeding. Regarding the classification of aircrafts selected, it is based on the International Council Aviation Organization (ICAO) classification. Hence, we have scattered 12 aircrafts (A = 12) following the ratio of 2 Super, 4 Heavy, 4 Medium and 2 Light (W = 4) that are anticipated to arrive at airport for an hour of traffic. We assume for each data set under study that we known at the start time all the aircraft class , , , , , , and ). The separation information’s ( distances between aircrafts class ( and ) whether before achieving the FAF meter of the air segment or
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the RT meter of the corresponding runway are based on real data. We use the separation distances issued from the , , , and Federal Aviation Administration (FAA). Whereas, for the data related to , we applied a nominal data since they are not available in the literature. Note that all the initial data mentioned above act as parameters, i.e. they get initial values that do not change during the run. However, the set of air segment (S) and the set of runway (R) will change from run to another as described in Table1. Table1. Data Sets Instance
Set of Aircraft (A)
Set of air Segment (S)
Set of Runways (R)
i=1
12
1
1
i=2
12
2
1
i=3
12
1
2
i=4
12
2
2
5.2. Results and discussion Looking at the computational results summarized in Table 2, the main conclusion is that the proposed approach can obtain optimal results with less computational effort with regards to one hour flight traffic planning horizon. These results have been achieved thanks to Eclipse that supports the declarative modeling of iterations required by mathematical programming problems by providing the declarative loops on the one hand. On the other hand, the CPLEX disposes of a Mixed Integer Optimizer that is called by default for each MIP formulation. In addition, the optimizer invoked by CPLEX for the MIP models was the Branch & Cut algorithm. Table 2. Experimental Results Instances
The problem solution time in (s)
i=1
15 s
i=2
25 s
i=3
45s
i=4
60 s
6. Conclusions To present and in view of the above literature investigation features, the aircraft landing operation are still a relevant issue for the ATC. Moreover its importance, it is not an easy task for several reasons. On the one hand, it requires depth knowledge of several components which are affected by high uncertainty. On the other hand, it returns to the air transportation system complexity and the differences between airports and different stakeholder aims. Taking account of all these distinctions, this work provides not only the first overview of the various constraints and objectives related to the ALP. Moreover, we were investigating mathematical models that dissect the timing, sequencing of aircraft and their assignment to the runway (s) taking into account the control aspect which was usually leaving aside for the majority of models proposed in the literature. In forthcoming works, we plan to treat the dynamic case of the ALP since it is resolved in a static fashion in this paper. We are also interested to suggest solution that scale large number of aircrafts flying trough TMA. Acknowledgements This work was supported by the Research Center of College of Computer and Information Sciences, King Saud University. The authors are grateful for this support.
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References [1] European Organization for the safety of Air Navigation. (2013) “Challenge of growth 2013: Summary Report. Task 4: European Air Traffic in 2035.” http://www.eurocontrol.int/articles/challengesgrowth. [2] ZHAN Zhi-Hui, ZHANG Jun, LI Yun, LIU Ou, KWOK S K, LP W H, and KAYNAK Okyay. (2010) “An efficient ant colony system based on receding horizon control for the aircraft arrival sequencing and scheduling problem.” IEEE Transactions on Intelligent Transportation Systems 11 (2): 399-412. [3] HONG Youkyung, CHOI Bynghun, LEE Somang, LEE Keumjin, and KIM Youndan. (2017) “Optimal and practical aircraft sequencing and scheduling for point merge system.” In: IFAC-PapersOnLine 50 (1) pp. 14644-14649. [4] LIANG Man, DELAHAYE Daniel, and MARECHAL Pierre. (2017) “Integrated sequencing and merging aircraft to parallel runways with automated conflict resolution and advanced avionics capabilities.”Transportation Research Part C 85:268-291. [5] SABAR Nasser R, and Kendall Graham. (2015) “An iterated local search with multiple perturbation operators and time varying perturbation strength for the aircraft landing problem.” OMEGA 56: 88-98. [6] Diallo Coumba, NDIAYE B.abacar Mbaya, and SECK Diaraf. (2012) “Scheduling Aircraft Landing at LSS Airport.” American Journal of Operations Research 2 (2): 235-241. [7] KJENSTAD Dag, MANNINO Carlo, NORDLANDER Tomas Eric, SCHITTEKAT Patrick, and SMEDSRUD Morten. (2013) “Optimizing AMAN-SMAN-DMAN at Hamburg and Arlanda airport.” In: Proceedings of third Sesar Innovation Days (SIDs), Stockholm. [8] SAMA Marcella, D’ARIANO Andrea, TOLI Alessandro, PACCIARELLI Dario, and CORMAN Francesco. (2015) “A variable neighborhood search for optimal scheduling and routing of take-off and landing aircraft.” In: Proceedings on Models and Technologies for Intelligent Transportation System (MT- ITS), pp.491-498, Budapest, Hungary. [9] D’ARIANO Andrea, PISTELLI Mario, and PACCIARELLI Dario. (2011) “Aircraft Retiming and rerouting in vicinity of airports.” In: 2nd International Conference on Models and Technologies for Intelligent Transportation Systems, Leuven, Belgium. [10] GHONIEM Ahmed, SHERALI Hanif D, BALK Hojong. (2014) “Enhanced models for a mixed arrival-departure aircraft sequencing problem.” INFORMS Journal on Computing 26 (3): 514-530. [11] FURINI Fabio, PERSIANI Carlo Alfredo, and TOTH Paolo. (2012) “Aircraft sequencing problems via a rolling horizon algorithm.” In: International Symposium on Combinatorial Optimization (ISCO), Athens, Greece, pp. 273-284. [12] International Civil Aviation Organization. (2007) “Procedures for air navigation services (Air Traffic Management).” Doc 4444, the fifteenth edition, Council, Montréal. [13] DEAR Roger G. (1976) “The dynamic scheduling of aircraft in the near terminal area.” (Ph. D. thesis). Flight Transportation Laboratory, MIT, USA, 1-325. [14] BEASLEY John E, SONANDER J, and HAVELOCK P. (2001) “Scheduling aircraft Landings at London Heathrow using a population heuristics.” Journal of the Operational Research Society 52 (5): 483-493. [15] ANDREUSSI Alberto, BIANCO Lucio, and RICCIARDELLI Salvatore. (1981) “A simulation model for aircraft sequencing in the near terminal area.” European Journal of Operational Research 8 (4): 345-354. [16] GHONIEM Ahmed, FARHADI Farbod, and REIHANECH Mohammed. (2015) “An accelerated branch-and price algorithm for multiplerunway aircraft sequencing problems.” European Journal of Operational Research 246 (5): 34-43. [17] BIANCO Lucio, DELL’OLMO Paolo, and GIORDANI Stefano. (1999) “Coordination of traffic flow in the TMA.” In: L. Bianco, P. Dell’Olmo, A. R. Odoni, (Eds.), New Concepts and Methods in Air Traffic Management, pp. 95-124. [18] HANBONG Lee, and BALAKRISHNAN Hamsa. (2008) “A Study of Tradeoffs in Scheduling Terminal-Area Operations.” Proceedings of the IEEE 96, 2081–2095. [19] BENCHEIKH Ghizlane, BOUKACHOUR Jaouad, ALAOUI Ahmed Elhilali, and ELKHOUKHI Fatima. (2009) “Hybrid method for aircraft landing scheduling based on a job shop formulation.” International Journal of Computer Science and Network Security 9 (8): 78-88. [20] BEASLEY John E, KRISHNAMOORTHY M, SHARAIHA Y. M, and ABRAMSON D. (2000) “Scheduling Aircrafts Landings- the static case. “Transportation Science 34 (2), 180-197. [21] ANDREAVA-MORI Adriana, SUZUKI Shinji, and LTOH Eri. (2013) “Rule derivation for arrival aircraft sequencing.” Aerospace Science Technology 30 (1):200-209. [22] BAUERLE N, ENGELHARDT-FUNKE O, and KOLONKO M. (2007) “On the waiting time of arriving aircrafts and the capacity of airports with one or two runways. “European Journal of Operational Research 177 (2):1180-1196. [23] JI Xiao-Peng, CAO Xiao-Bin, and TANG Ke. (2015) “Sequence Searching and evaluations: a unified approach for aircraft arrival sequencing and scheduling problems.” Memetic Computing 8 (2):109-123. [24] SAMA Marcella, D’ARIANO Andrea, D’ARIANO Paolo, and PACCIARELLI Dario. (2017) “Scheduling models for optimal aircraft traffic control at busy airports: Tardiness, priorities, equity and violations considerations.” OMEGA 67: 81-98. [25] BERTSIMAS Dimitris, and FRANKOVISH Micheal. (2015) “Unified optimization of traffic flows through airports.”Transportation Science 50 (1): 77-93. [26] BRISKORN Dirk, and STOLLETZ Raik. (2014) “Aircraft landing problems with aircraft classes.” Journal of Scheduling 17 (1) 31-45.