Aircraft Ground Traffic Optimization
Jean-Baptiste Gotteland
Nicolas Durand
[email protected] [email protected]
Jean-Marc Alliot Erwan Page
[email protected] [email protected]
Abstract
models of airport operations already exists, such as
SIMMOD1 or TAAM 2 . They can be useful to evaluAir traffic growth and especially hubs development ate qualitatively the relative effects of various airport
cause new significant congestion and ground delays on improvements but do not aim at improving the real-time
major airports.
supervision and giving advices to ground controllers, as
Accurate models of airport traffic prediction can pro- conflict detection and resolution is not developed. The
vide new tools to assist ground controllers in choosing DP3 project ([IDA+98]) focuses on improving the perthe best taxiways and the most adapted holding points formance of departure operations, without taking into
for aircraft. Such tools could also be used by airport account the taxi problem. Finally, a component of the
designers to evaluate possible improvements on airport TARMAC4 project focuses on the ATC-related traffic
configurations and airport structure.
planning systems for airport movements, but does not
In this paper, a ground traffic simulation tool is pro- provide any optimization method for taxiing aircraft.
posed and applied to Roissy Charles De Gaulle and Orly
In this paper, a ground traffic simulation tool is introairports. A global optimization method using genetic duced and tested on a one day traffic sample on Roissy
algorithms is compared to a 1-to-n strategy to minimize Charles De Gaulle and Orly airports. Different optitime spent between gate and runway, while respecting mization strategies are used to find the best trajectory
aircraft separation and runway capacity.
and the most adapted holding points for taxiing aircraft.
In order to compare the efficiency of the different The goal is to minimize the time spent from gate to takeoptimization methods, simulations are carried out on a off or from landing to gate, respecting the separation
one day traffic sample, and ground delay due to holding with other aircraft and the runway capacity. During the
points or taxiway lengthening is correlated to the traffic optimization process, existing one way taxiways, operdensity on the airport.
ational airport configurations and speed uncertainty can
be considered.
1 Introduction
2 Problem modeling
Traffic delay due to airport congestion and ground operations becomes more and more penalizing in the total
gate-to-gate flight cycle. This phenomenon can be in
a large part attributed to recent hubs development, as
all departures and arrivals are tending to be scheduled
at the same time. Moreover, many ATC problems and
environmental inefficiencies can appear as a result of
taxi queueing and take-off time uncertainty. As airport
designers are in charge to build new taxiways to reduce
congestion and improve ground operations, ground simulation tools become essential to validate their choices
before realization.
Even if most research projects are concentrated on
decision making tools for airspace controllers and do
not consider ground operations utilities, highly detailed
The problem is to find for each aircraft an optimal path
from its gate to a given runway take-off position or
from its runway exit to its parking position, respecting
a given separation between aircraft.
An optimal path can have different definitions as for
example the length of the path or the total taxiing time.
Holding on a taxiway can be more or less penalizing
than increasing the length of the path. It can be cheaper
to hold at the parking position than on a taxiway. At
1 SIMulation
MODel (FAA)
Airspace and Airport Modeler (Preston Group)
3 Departure Planer
4 Taxi and Ramp Management And Control (DLR)
2 Total
1
Speed limitation (m/s)
taxiways themselves, parking positions, and landing or
take-off points. The cost from a taxiway node to its
connected nodes is the time spent to proceed via this
taxiway, taking into account speed limitations due to
this taxiway. The cost from other nodes (parking and
runway positions) to their connected nodes is null.
Figure 2 represents the graphs of Roissy and Orly
airports. These graphs are obviously connected. Classic graph algorithms can be used to compute alternative
paths for aircraft:
10
0
Turning rate (°)
0
10
20
30
40
50
60
70
80
90
Figure 1: Speed limitation as a function of turning rate
the same topic, it can be better to lengthen slightly the
routes of two aircraft than to make one aircraft wait a
long time.
Therefore a global optimum criteria will have to be
defined in the following. However, the purpose of this
article is not to discuss the choice of such criteria, which
can be refined without modifying the algorithm itself,
considering many different factors related to the airport
geometry, the traffic, or airlines preferences...
By the way, it is quite difficult to predict with a good
accuracy the future positions of aircraft on taxiways.
First of all, the exact departure time is generally known
only a few minutes in advance (many factors can cause
delays), and the exact landing time depends on the runway sequencing. Hence, the proposed model should
take into account speed uncertainty and must be regularly updated with real aircraft positions.
A Recursive Enumeration algorithm [MJ96] using
the Dijkstra’s result can then compute the k best
paths from a given node to another.
A simple Branch and Bound algorithm [HT95] can
computes all alternate paths lengthening the trajectory less than a given distance.
In order to minimize the total delay and to ensure separations, the path of an aircraft can be modified and
aircraft can hold position at the parking, on taxiway or
queue at the holding point before take off.
Aircraft separation criteria is defined as follows:
An airport is described by its gates, taxiways and runways. Different kind of taxiways can be differenced:
A Dijkstra algorithm [AMO93] can compute best
paths and corresponding minimal time spent from
a given node to every other node.
2.2 Aircraft possible maneuvers
2.1 Airport structure
An A algorithm [Pea84] can compute the best
path and the corresponding minimal time spent between two given nodes (parking and runway exit
for example).
Parking specific access (entries, forward exits and
push-backs), characterized by a very low speed;
Runways access (entries and exits), containing the
existing holding points before take-off and exit
points after landing with specific speed limitations;
Taxiways intersecting runways;
Simple taxiways, where speed limitations is modeled as a function of the turning rate (figure 1).
Connections between taxiways are restricted (it is not
always possible to proceed from a taxiway to another,
even if they are intersecting). The airport description
specify usable taxiways connections.
Thus, the airport is defined by a graph: links represent connections between taxiways whereas nodes are
2
The distance between two taxiing aircraft must
never be lower than 60 meters.
No more than one aircraft can occupy a given runway at a time. An aircraft is considered on the
runway from the defined holding point for takeoff and until the defined exit point for landing. A
time separation of 1 or 2 minutes (depending on
the aircraft category) is necessary after a landing
or a take-off to clear next movement from wake
turbulence. Of course, an aircraft proceeding via
a taxiway which intersect a runway also occupies
the runway.
0
1000
Figure 2: Roissy airport graph - Example of shortest and alternate paths
0
1000
Figure 3: Orly airport graph - Example of shortest and alternate paths
3
Tw
Holding position
∆
path
possible positions
Prediction
End holding
Simulation steps
Figure 5: Time window
is defined.
Consequently a time window Tw >
Only aircraft taxiing in the time window will be considered. The time window will be shifted every minutes,
the problem reconsidered and a new optimization performed (see figure 5).
time
2.5 Conflict resolution
Figure 4: Uncertainty reduction on holding points
At each simulation step (every minutes), traffic prediction
is performed for the next Tw minutes and pairs
In order to perform acceptable maneuvers, only one
of
conflicting
aircraft positions are extracted. A transiholding order should be given to the pilot at a time (hold
tive
closure
is
applied on these pairs and gives the difat position p0 until time t1 ), and proposed alternative
ferent
clusters
of
conflicting aircraft [DAN96].
paths should not lead an aircraft to use the same taxiway
In
order
to
lower
the complexity of the problem as
twice.
often as possible, these different clusters will be solved
independently at first. If the resolution of two clusters
creates new conflicting positions between them, the two
2.3 Speed uncertainty
clusters are unified and the resultant cluster is solved.
Speed uncertainty is modeled as a fixed percentage of
the initial defined speed (which is function of procedures and turning rate). Therefore, an aircraft is consid- 2.6 Global optimum criteria
ered to have multiple possible positions at a given time.
In the current version, the global criteria to minimize is
Separation is ensured if all of the possible aircraft podefined by the time spent from the departure time to the
sitions are separated from others, as defined before.
take off time, or from the landing time to the gate, added
Speed uncertainty reduces the validity period of pre- to the time spent in lengthened trajectory: with this defdictions. Thus, simulations with speed uncertainty will inition, lengthened trajectories appears to be twice more
be carried out with a lower time window (see 2.4). penalizing than holding positions.
However, the holding model (hold at position p0 until
time t1 ) allows to reduce uncertainties while referencing a precise holding position and a precise end holding 3 A*: 1-to-n strategy
time (see figure 4).
In this strategy, taxiing aircraft are sorted and considered one after the other. The A algorithm finds the best
2.4 Simulation model
path and/or the best holding point for an aircraft, taking
As the aircraft future positions and movements are not into account the other aircraft already considered. In
known with a good accuracy, it is necessary to regularly this point of view, first considered aircraft have a higher
update the situation, every minutes for example. By priority than last considered aircraft.
A simple way to assign priority levels to aircraft is to
the same time, looking a long period ahead is not possort them by their flight-plan transmission time to the
sible as predictions are not good enough.
4
ground controllers. This option seams the most realistic
as ground controllers can hardly take into account an
aircraft without its flight-plan. In the simulation context, this is equivalent to sort aircraft by departure or
arrival time.
However, it can be really appropriated to sort already
taxiing aircraft in a different way, as the last considered
aircraft is obviously extremely penalized. As there exists a large number of ways to sort aircraft, the choice
of such a filing can be done with genetic algorithms.
(1)
(2)
...
(j)
...
(i)
...
...
(n)
(1)
...
...
(j)
...
(i)
...
...
(n)
80
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
25
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4 Genetic Algorithms
Table 1: Fitness matrix
In this paper, classical Genetic Algorithms and Evolutionary Computation principles such as described in the
literature [Gol89, Mic92] are used. The algorithm is
minutes on the problem defined in secused every
tion 2.4.
Else :
F
= 2 + P 1 Mf (i; j )
i<j
4.3 Crossover operator
4.1 Data structure
The conflict resolution problem is partially separable as
defined in [DA98, DAN96]. In order to increase the
probability of producing children with a better fitness
than their parents, principles applied in [DA98] were
applied. For each aircraft i of a population element, a
local fitness Fi value is defined as the sum of the ith line
(or column) of the fitness matrix (except the diagonal
element).
During each optimization process, each aircraft trajectory is described by numbers (n, p0 , t1 ). n is the
number of the path: as detailed in section 2.2, all the alternate path lengthening the aircraft trajectory less than
some distance can be initially computed and sorted. The
aircraft may hold position p0 and resume taxi at t1 (if
p0 is reached after t1 , the aircraft does not stop). When
N aircraft are simultaneously taxiing, the problem is
defined by N variables.
3
Fi =
3
Pj=i Mf i; j
6
The crossover operator is presented on the figure 6.
First two population elements are randomly chosen. For
each parent A and B , fitness Ai and Bi of aircraft i are
The fitness function must ensure that a solution without
compared. If Ai < Bi ), the children will take aircraft i
any conflict is always better than a solution with a conof parent A. If Bi < Ai , the children will take aircraft
flict. Consequently it was decided that the fitness of a
i of parent B . If Ai Bi children randomly choose
1
solution without conflict should be less than 2 and the
aircraft Ai or Bi or even a combination of Ai and Bi .
1
fitness of a solution with a conflict more than 2 . The
different conflicts between each pair of aircraft can be
initially computed in a n n matrix (see table 1). A 4.4 Mutation operator
conflict during time steps between aircraft i and j sets
For each candidate to mutation, parameters of an airelements i; j and j; i to . Element i; i is filled
craft having one of the worst local fitness are modified
with the trajectory lengthening due to the path chosen
(n; p0 ; t1 ). If every conflict is solved, an aircraft is ranand holding time t1 t p0 .
domly chosen and its parameters changed.
Using the fitness matrix Mf , it is possible to compute
The crossover and mutation operators are quite deterthe fitness value as follows:
ministic at the beginning because there are many conIf the matrix is diagonal :
flicts to solve. They focus on making feasible solutions.
When the solutions without conflict appear in the popF
n M i; i
ulation, they become less deterministic.
f
4.2 Fitness function
=
( )
( ) ( ) 3
( ( ))
3
= 12 + 1 + P 1
i=0
( )
( )
5
parent B
parent A
aircraft 1 A1 << B1
A1
aircraft 2
A2
aircraft 3
A3
aircraft 4
A4
aircraft 5 A5 # B5
A5
aircraft 6
A6
child 1
Roissy Charles De Gaulle. It will of course be updated
with new simulations including Orly in the final version
of this paper.
The simulations where carried out with real flight
plans on a complete day at Roissy Airport (May nd
1999). Aircraft are assigned to terminals according to
the airline they belong to (for example an Air France
flight is assigned to Roissy 2).
When taking off or landing, aircraft are randomly assigned one of the two runways. They are sequenced on
runways every minute using the first in first out principle.
Three hypotheses are done:
B1
child 2
B2
B3 B3 << A3
A
A
B
B
B4
B5
1−d
C
d
d
C
B5 # A5
22
B6
1−d
Figure 6: Crossover operator
4.4.1 Sharing
in the “random hypothesis”, taking off and landing aircraft are randomly allocated both runways.
The problem is very combinatorial and may have many
local optima. In order to prevent the algorithm from a
in the “deterministic hypothesis”, taking off and
premature convergence, the sharing process introduced
landing aircraft are allocated the runway that minby Yin and Germay [YG93] is used. The complexity
imizes the distance to the allocated parking.
of this sharing process has the great advantage to be in
n n (instead of n2 for classical sharing) if n is the
in an “middle hypothesis”, taking off aircraft are
size of the population.
randomly allocated both runways and landing airA distance between two chromosomes must be decraft are allocated the runway that minimizes the
fined to implement a sharing process. Defining a disdistance to the parking.
tance between two sets of N trajectories is not very simple. In the experiments, the following distance is used The three hypotheses are tested with the genetic algointroduced:
rithm. The last hypothesis is tested with a 1-to-n stratN jl ln j
egy that uses an A algorithm: aircraft are sorted acB
A
i
i
i
=0
D A; B
cording to their time of departure or arrival, each airN
craft trajectory is then optimized considering previous
th
lAi (resp lBi ) is the i aircraft path length of chromo- aircraft trajectory as a constraint.
some A (resp B ). As the paths are sorted according to
their length, the distance increases with the difference
5.1 Parameters
of lengths.
log( )
(
) =
P
Tw = 12mn
4.5 Ending criteria
= = 3mn
As time to solve a problem is limited, the number of
generations is limited, as follows: as long as no available solution is found, the number of generation is limited to 100. The algorithm is stopped generations after the first acceptable solution (with no remaining conflict) is found.
20
Population size: 300
Max number of generations: 100
60%
Mutation rate: 15%
5 Experimental results
The experimental results presented in this extended abstract come from old simulations and only concern
6
Crossover rate:
Selection principle: stochastic reminder without
replacement
900
90
middle assumption - 1 to n method (A*)
deterministic assumption - global method (AG)
middle assumption - global method (AG)
random assumption - global method (AG)
80
700
70
600
60
number of generations
total delay (seconds)
800
500
400
300
50
40
30
200
20
100
10
0
0
0
10
20
30
40
number of aircraft on taxiways
50
60
0
Figure 7: Total delay as a function of the number of
aircraft on taxiways.
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
time
Figure 8: Number of generations (random strategy) as
a function of time
90
mean delay
255
198
195
271
max nb of acft
55
48
46
45
80
70
number of generations
Hypothesis
random (GA)
determ (GA)
medium (GA)
medium (A )
Table 2: Mean delay and maximum number of aircraft
for the different hypotheses
60
50
40
30
20
10
0
5.2 Comparing 1-to-n to the global strategy
0
10
20
30
number of moving aircraft
40
50
60
Figure 9: Number of generations (random strategy) as
a function of the number of moving aircraft
Figure 7 gives the mean delays as a function of the number of aircraft moving on the taxiways for the different
hypotheses. The 1 to n method produces more delays 5.3 Genetic algorithm efficiency
than the global method using the Genetic Algorithm,
In order to observe the GA efficiency, figure 8 gives the
whatever the chosen hypothesis.
number of generations required by the GA as a function
Table 2 gives for the different hypotheses the mean of time. the different peaks appearing at 7, 8, 10, 11
total delay and the maximum number of aircraft simul- am and 5 pm are the traffic peaks. Figure 9 shows the
taneously moving.
correlation between the number of generation required
The medium hypothesis (GA) penalizes less aircraft by the GA and the number of moving aircraft on the
than the other hypotheses and a smaller number of air- ground.
craft are moving at a time. The random hypothesis
(GA), which is probably more in accordance with reality (the parking position does generally not influence 6 Conclusion and further work
the runway allocation), is more penalizing (each aircraft
is delayed 1 minute more). The 1-to-n strategy is more A preliminary work has shown that it was possible to
penalizing for a number of aircraft that is not bigger, build a taxiway adviser in order to optimize the ground
which can be explained by the weakness of the strategy. traffic on busy airports such as Roissy Charles de Gaulle
7
and Orly. It can be noticed that the modeling was easily improved with new runways on Roissy Charles De
Gaulle, different speeds, uncertainties on speeds etc...
without changing the algorithm itself. Genetic Algorithms are very efficient on the problem as they search
the global optimum of the problem whereas a deterministic algorithm such as an A algorithm can only reasonably be used with a 1-to-n strategy, which is very
poor.
Further work will concentrate in improving the
global criteria for Genetic Algorithms, taking into account for example take off sequencing needs for approach sectors or priority levels for slotted departures.
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