Chapter 5. Airport Traffic Management
5.3. Runway scheduling
different possible encoding to solve the problem with a genetic algorithm, and they found out that a binary encoding, combined with a uniform crossover, makes the genetic algorithm more efficient.
Hybridization between different metaheuristics is also often used in the literature to improve the efficiency of the algorithms. In [CHE 12], on the same instances of the gate assignment problem at Incheon International Airport, a hybridization between a simulated annealing algorithm and a tabu search yielded better results than those obtained with the two metaheuristics alone.
When there are not enough gates for all the scheduled flights, the gate assignment problem is said to be over-constrained: in this case, a new objective is to minimize the number of flights that cannot be assigned a gate. In [DIN 05], the authors solved this problem with a new hybridization between a simulated annealing algorithm and a tabu search. They used the same kind of neighborhood operators as those described in [XU 01] to facilitate the use of heuristics and improve their results.
When a departure metering strategy is used at an airport (with a DMAN system), some departing aircraft are held at gate, which can create gate conflicts with some arriving aircraft. The initial gate assignment can try to minimize the probability of these conflicts, by maximizing the time gap between two consecutive flights at the same gate: in [KIM 14], using some actual flight data of New York-LaGuardia Airport, the authors used a tabu search with two neighborhood operators, in order to build a robust gate assignment, and measured a significant diminution of gate conflicts in their simulations.
5.3. Runway scheduling
Aircraft sorted by their minimal runway access times
First come first served scheduling
Optimal scheduling
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Figure 5.3.Runway scheduling
Additional separations can be considered by the airport controllers, in order to ensure a minimal distance between the aircraft in the approach sectors, before landing or after takeoff. In this case, the necessary separation depends on the speeds of the aircraft and on the standard terminal arrival route or standard instrument departure procedure used. These distance separations can be converted into times (considering the speeds of the aircraft) and mixed to the wake vortex separations (by keeping the most penalizing separation time between each pair of aircraft).
Some airports can also have crossing or parallel dependent runways, in which case some separations (that can still be expressed in time) have to be ensured between the operations of the different runways.
Depending on the airport configuration, a runway can be used either in mixed mode (used for takeoff and landing) or in segregated mode (with only one type of operation). In the literature, the runway scheduling problem is sometimes reduced to the airport landing problem or the airport takeoff problem, considering a runway used in the segregated mode.
In Europe, some specific constraints have to be added for the departure scheduling because the European Network Manager Operations Center can assign some calculated takeoff times (CTOT) to some flights that go through overloaded airspace. These constrained departures can only take off 5 min before or 10 min after their CTOT.
Respecting these different constraints, the main objective of the runway scheduling problem is to ensure a good level of performance for the airport operations:
– minimizing arrival and departure delay (which can be formulated as maximizing the runways throughput);
– maximizing the traffic predictability (which can be formulated as minimizing the deviations to an initial runway schedule and to the requested CTOT);
– maximizing the fairness among the different flights, to avoid the solutions where some particular flights are highly penalized compared to others.
5.3.2. An example of problem formulation
Considering a given set of dependent runways used either in segregated mode or in mixed mode, on whichNaircraft are scheduled in a given time period (for takeoff or landing) and assuming that each aircraft is assigned a fixed runway by the airport controllers (as this is most often the case at big airports, due to approach constraints), the variables of the problem can be the takeoff and landing times that have to be scheduled for each aircraft:
(ti)1 i N
A lower boundLi, a targeted valueTiand an optional upper boundUioftican be defined for each aircrafti(1 i N):
– for a departure constrained by a CTOT,Tiis the CTOT andLiandUiare given by the feasible takeoff slot around the CTOT, given the current position of the aircraft and its scheduled departure time for an aircraft at the gate;
– for other aircraft, Li can be computed by considering the current position of the aircraft (in the air for an arrival or on the ground for a departure),Ui can be set to+1or toLi added to a maximal delay andTi set toLi or to the last scheduled takeoff or landing time. In a real case application, these values could be provided by the AMAN and DMAN systems, and the gap betweenLiandUiwould be reduced to a few minutes for a landing aircraft, as far as the airport control is concerned.
As explained earlier, the separation rules can be modeled as a fixed minimal time sij between each pair of aircraft(i; j)whenti < tj(even if the two aircraft are not scheduled on the same runway). With an additional fairness coefficient 1, the problem can be formulated as follows:
Minimize:PN
i=1jti Tij
Subject to: Li ti Ui (1 i N)
ti+sij tjortj+sji ti (1 i6=j N)
5.3.3. Resolution methods
As described in a detailed survey [BEN 11], many runway scheduling problems can be formulated and solved with exact methods using dynamic programming or branch and bound algorithms. For more flexibility (or more realism) in the formulation of the constraints and the objectives of the problem, or to quickly obtain various good solutions on large instances, metaheuristics are also largely applied to the runway optimization problems.
The multiple runways aircraft landing problem consists of both assigning a runway to each aircraft and scheduling each aircraft on its runway. In [BEN 09], this problem was formulated as a job shop scheduling problem. The authors solved it with a hybrid method, in which ant colony optimization was used to generate the initial population of a genetic algorithm. They tested the efficiency of this hybridization on a collection of test data sets, involving up to 50 aircraft that have to be scheduled on 4 runways.
In [HU 09b], the authors also solved a multiple runways aircraft landing problem, with a genetic algorithm. They confirmed the efficiency of a specific encoding, based on a binary matrix, that specified the Boolean priority relationships between each pair of aircraft: this encoding can be associated with a uniform crossover (that makes each child inherit a specific part of the priority relationships of his parents) and provides better results than a more intuitive integer encoding, especially by avoiding some premature convergence toward local optima. Indeed, this kind of encoding can maintain some promising subsequences across several generations, while still favoring a good exploration of all the possible sequences. In [HU 09a], the authors again improved their results with a newripple spreadinggenetic algorithm: in this model, each chromosome encodes an epicenter point in a two-dimensional artificial space, and a method to project each aircraft in this space (depending on its wake vortex category and its soonest landing time). The ripple spreading process is a simple algorithm that assigns a runway to each aircraft and defines the sequence on each runway, from the set of points in the artificial space (by sorting these points by increasing distance to the epicenter). Thus, each chromosome is reduced to five numbers (x; y; 1; 2; 3), where (x; y) are the coordinates of the epicenter and ( 1; 2; 3)are the coefficients defining the projection in the artificial space. A big advantage of this method is that the size of the chromosomes no longer depends on the number of aircraft but only on the number of parameters used to characterize them.
The aircraft takeoff scheduling problem can appear more complex as it involves the whole departure process (with the need of predicting accurate start-up and taxi times). In [ALI 08] and [LEI 08], the authors considered the problem of the departure flow that have to be scheduled on a runway and that can use different routes to access this runway: each departure route is seen as a first-in-first-out queue (aircraft using the same route cannot change their order). The problem is to find the gate departure
times and the takeoff times that minimize the time spent to offload the whole traffic (while maintaining the separation constraints between taxiing aircraft). The authors improved the convergence of a particle swarm optimization algorithm with an evolution function based on an oscillating equation of the second order (inherited from the control theory) [LEI 08] or by controlling the evolution with a simulated annealing method [ALI 08].
In [ATK 07], using an actual traffic sample at London Heathrow Airport, and with a quite realistic departure model (including the reordering possibilities offered by the runway access layouts), the authors combined a tabu search with different search methodologies and heuristics to minimize the departure delay and the deviations to the CTOT. In further work [ATK 08], the authors described how these techniques could provide decision support tools that would help the airport controllers in their real-time tasks.
In his PhD thesis [DEA 10], the author provided a formulation for the aircraft scheduling problem on a runway that can be used either in the segregated or in the mixed mode, and where some of the departures are constrained by a specific CTOT.
This formulation is similar to that described in section 5.3.2, except that it is reduced to one independent runway with a neutral fairness coefficient = 1: the variables are the takeoff and landing times, and the minimization criterion is a balance between the deviations to the CTOT (of the constrained departures) and the delay (of the other flights). With this formulation, the author took advantage of some particular properties of the problem (symmetries, aircraft equivalences, and detection of sub-optimal scheduling as illustrated in Figure 5.4) and defined a branch and bound algorithm that finds and proves an optimal solution in a few seconds, for a large
Aircraft sorted by their minimal runway access times
Feasible scheduling
Sub-optimal scheduling
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Figure 5.4.Detection of suboptimal runway scheduling
sample of problems involving more than 50 aircraft, extracted from actual data at Roissy-CDG Airport.
Complete simulation Runway FCFS Runway OPT 0
10 20 30 40 50 60 70 80 90
Mean delay (seconds per aircraft)
Figure 5.5.Runway scheduling at Roissy-CDG Airport
By applying this scheduling algorithm on shifting periods of a whole day of traffic at Roissy-CDG Airport [DEA 09], the authors found a feasible scheduling for all the operations on all the runways. As illustrated in Figure 5.5, the generated delay appears to be 20 s lower (in average per aircraft) than with a first-come-first-served (FCFS) runway scheduling and half less than that measured by a full simulation (including taxi conflict resolution) of the same traffic. These results show that the runways are not the only source of delay for big airports such as Roissy-CDG and that the traffic also needs optimization during taxiing.
5.4. Surface routing