Recent Researches in Applied Economics and Management - Volume II
Heuristics for Limiting Pollution in Ground Control Optimization
ADACHER LUDOVICA
Dipartimento di Ingegneria,
Università degli Studi Roma Tre
Via della Vasca Navale, 79, Roma
ITALY
[email protected]
FLAMINI MARTA
Università Telematica Internazionale UNINETTUNO
Corso Vittorio Emanuele II, 39, Roma
ITALY
[email protected]
MASI MARCO
Dipartimento di Ingegneria
Università degli Studi Roma Tre
Via della Vasca Navale, 79, Roma
ITALY
[email protected]
Abstract: - In this paper we deal with the problem of scheduling aircraft maneuvering on ground in the specific
case study of Malpensa Airport. Given a fixed route and a landing/take off time instant for each
landing/departing aircraft, we propose local heuristics to reduce the pollution problem. Considering the
complexity of the problem, we examine three objective functions in different lexicographical order: (i) the
maximization of the number of on time aircraft; (ii) the maximization of the safety; (iii) the minimization of
pollution and noise. Problem constraints are related to the safety rules. We model the problem as a job-shop
scheduling problem. We develop heuristic procedures based on an alternative graph formulation of the problem
to construct and improve feasible solutions. Experimental results based on real data and analysis is reported.
Key-Words: - Aircraft Ground control, pollution, heuristic
determined such that safety rules are satisfied.
Local control is responsible of runways control
and consists in sequencing and timing the use of
the runway by the aircraft. Ground control is
responsible for aircraft traffic management in
the Terminal Maneuvering Area (TMA), that
generally includes all taxiways, runways, yards,
aprons or intersections. At present, human
controllers perform ATC operations supported
only by graphical representations of the aircraft
position and speed. Decision support systems
would be useful both to optimize management
performances and to face unexpected events
without neglecting the optimization of traffic
management even in such cases. Problems
arising in ATC are usually hard to perform in
1 Introduction
The increase of air traffic leads airports to be
the major bottleneck in Air Traffic Control
(ATC) operations. Aviation authorities are thus
studying methods to optimize the use of the
existing airport infrastructures and aircraft
movements in the vicinity of airports, subject to
a certain required level of safety. Airports
management is entrusted to dispatchers in air
control, local control and ground control. Air
control tasks concern with routing decisions,
where a route for each aircraft has to be chosen
from its current position to its destination, and
scheduling decisions in the vicinity of the
airports, where routes are fixed and feasible
aircraft sequencing and timing have to be
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Recent Researches in Applied Economics and Management - Volume II
safety and aims to limit the event in which two
aircraft are physically close. Regarding to the
third objective function, we associate the
production of pollution and noise with the total
time the aircraft keep the engine on, therefore
our aim is to minimize such total time. The
problem of pollution is very popular in different
areas (i.e. see[9]). The constraints of the
problem are given by the safety rules
concerning the moving of the airplanes in the
terminal. We consider the ASP as a job shop
scheduling problem with additional constraints.
We model the problem by an alternative graph
([4], [8]) and we propose some heuristic
procedures producing fast feasible solutions
able to face the real time nature of the problem.
The paper is organized as follows. In Section 2
reader can find the detailed description of the
problem that is modelled as a job-shop
scheduling problem with additional constrains.
Solution heuristic procedures are described in
Section 3 and experimental results are reported
in Section 4. Section 5 is dedicated to the
conclusions.
terms of both designing adequate models and
projecting efficient and effective solution
techniques, due to the complex real aspects that
have to be included in the model representation
in order to produce solutions that can be
practically implemented. Several approaches
have been proposed for solving both air and
ground scheduling problems ([1], [2], [3]), but
most of the early contributions suffer for a
substantial lack of information due to the usage
of very simplified models. Recent models ([4])
introduce an increased level of realism and
incorporate a larger variety of constraints and
possibilities, such as no-wait constraints, and
earliness/tardiness penalties for each early/tardy
aircraft. Most of the research efforts focus on
local control ([5], [6], [7]) where runway
scheduling problems are analyzed. Due to the
complexity of such problems researchers often
propose the developing of heuristic procedures.
Bianco et al. [7] model the single runway
landing problem as a job-shop scheduling
problem and propose a solution based on a
mixed integer linear programming formulation.
In this paper, the main focus is on the real time
local and ground Aircraft Scheduling Problem
ASP with fixed routes. The case study we refer
is related to the TMA of Malpensa Airport (from
now on TMA). The TMA has a specific layout
implying the traversing of one of the runways
by most part of routes. For the safety problem
of TMA it is important to develop a detailed
model able to adequately represent all the safety
constraints. The traversing of the runway is
regulated by stop bars. Whenever an aircraft has
to cross the runway while another aircraft
occupies the runway, the first one has to wait at
a stop bar. Here the spatial safety rules are less
pressing, since a reduced distance between the
aircraft is allowed. In our problem we consider
three objective functions in lexicographical
order, namely (i) the maximization of the
number of on time aircraft; (ii) the minimization
of the mean waiting time at the stop bars close
to one of the runways; (iii) the minimization of
pollution and noise. The first objective function
represents one of the most analyzed indices in
literature, which gives a measure of the
performance of the control operations. The
second objective function concerns with the
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2
Problem Description
The case study we deal with is related to an
aircraft scheduling problem (ASP) in the
Terminal Maneuvering Area (TMA) of
Malpensa Airport. The TMA has two parallel
runways, namely 35R and 35L, two yards, two
aprons A1 and A2, and a taxiway network. The
runways are divided into segments, each
between two consecutive intersections with the
taxiway network. Yards are areas positioned at
the beginning of the runways, in which aircraft
wait before departing. Aprons include parking
bays in which the aircraft are parked. Stop bars
regulate the access to the cross points. Runway
35L has to be crossed by aircraft
departing/landing on runway 35R and coming
from/going to apron A1. This peculiarity of the
TMA makes the safety a crucial aspect while
modelling and optimizing problems related to
the ground control. We consider both arriving
and departing aircraft, in a given time interval.
Each arriving aircraft has associated a fixed
ground route from its current position to the
parking bay and each departing aircraft has
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Recent Researches in Applied Economics and Management - Volume II
mean waiting time at the stop bars regulating
the crossing of the runway. The third objective
function is evaluated by associating the
production of pollution and noise with the total
time the aircraft keeps the engine on, therefore
our aim is to minimize such total time.
associated a fixed ground route from its current
position to the runway. We are given a nominal
landing time and an arrival time for the arriving
aircraft. The nominal landing time is the
minimum time instant in which the aircraft
would be able to land. The landing time is a
variable of the problem, since in practice the
landing instant could be postponed for
optimization scopes. The arrival time represents
the time instant in which the aircraft should
reach the parking bay. For each departing
aircraft we are given a departing time that is the
time instant in which the aircraft should takeoff. The arrival times and departing times are
considered as due dates for the aircraft. Problem
constraints are described in Subsection 2.1 and
correspond to the safety rules regulating the
movings of the aircraft in the TMA. The
problem briefly consists in scheduling the
movings of the aircraft through the TMA, in
order to avoid deadlocks and collisions, subject
to the safety.
We consider three objective functions: (i) the
maximization of the number of on time aircraft;
(ii) the minimization of the mean waiting time
at the stop bars close to runway; (iii) the
minimization of pollution and noise.
The first objective function gives a measure of
performance of the management and control
operations. An aircraft is a on time aircraft if its
arrival or departing time meets its due date.
Naturally, if the lateness is negative we have an
early aircraft, if positive a tardy aircraft and if
equal to zero a on time aircraft. Note that it is
impossible to meet exactly the due date, for this
reason we have introduced a time interval for
each aircraft, instead of time instant, in which it
is on time. On the other hand, this really small
interval is trivial respect to the whole flight.
Note that even early flights which could cause
coordination discomforts in the TMA
management. Obviously, a tardy aircraft causes
major costs with respect to an early aircraft
When evaluating the quality of a solution we
are also interested in considering some other
performance indices, such that the average
tardiness and absolute average lateness. The
second objective function concerns with the
safety and aims to limit the event in which two
aircraft are physically close, by minimizing the
ISBN: 978-960-474-324-7
2.1 Problem constraints
ASP can be modelled as a job-shop scheduling
problem with additional constraints. Jobs are
represented by aircraft and resources by parts of
the TMA. An operation is the occupation of a
resource by an aircraft, therefore the processing
time of an operation corresponds to the time
necessary to run/occupy a certain resource.
Constraints implied by safety rules, typically
regulating spatial or temporal security
distances, hold for each pair of aircraft moving
in the TMA. We model the TMA as a set of
resources of limited capacity. The resources we
consider are runway segments, taxiway
segments, parking bays, stop bars, yards. All
such resources but the yards have unitary
capacity. Yards are assumed to have unlimited
capacity. Each route associated to an aircraft
corresponds to a list of resources. Standard jobshop constraints hold, namely: (i) precedence
constraints: resources composing a routes have
to be run in a precise order; (ii) capacity
constraints: resources with unary capacity can
be occupied at most by an aircraft at a time; (iii)
pre-emption constraints: operations can not be
interrupted. Additional constraints, that is nowait, blocking and incompatibility constraints,
are introduced to model real aspects of the
problem related to the safety rules. No-wait
constrains state that a given set of consecutive
resources in a route has to be occupied without
interruption. This is the case, for instance, of
segments composing a runway. Blocking
constraints model the absence of buffer between
two resources, therefore the occupation of a
resource of unary capacity by an aircraft makes
such resource unavailable for other aircraft for
the
entire
occupation
time
interval.
Incompatibility constraints hold when two
different resources can not be occupied at the
same time. In this case the two resources are
said incompatible. For instance, all the
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Recent Researches in Applied Economics and Management - Volume II
the idea of repeatedly choose an arc at a time from
set A and by selecting the other arc of the alternative
pair until an improvement is found. The exchange is
not accepted if a cycle is detected or the solution
does not improve. At each step the arc is selected in
an ordered list, constructed on a local rule. Every
time an improved is obtained the solution is
updated.
The basic idea is to try and iteratively invert
precedence between two aircraft. An inversion is
accepted only if the new solution is feasible and
improved. Obviously, the LS inverts precedence
between aircraft if and only if the early aircraft
precedes the tardy aircraft, otherwise it is not
possible to improve the solution since we can
improve the first objective function only if we delay
a early aircraft or if anticipate a tardy aircraft.
The local search (LS) is applied to maximize the on
time aircraft.
We proposed a binary search (BS) to maximize the
safety and minimize the pollution. We try, only for
the departing aircraft, to impose the waiting times at
the parking bay. We calculate the waiting time for
departing aircraft and we try to shift the waiting
time at the parking bay, utilizing the binary
research. We start the research by transferring the
total waiting time to the parking bay. If BS does not
find a feasible solution BS tries with half waiting
time, and so on. If a feasible solution is constructed,
BS has reduced the total waiting time at the stop
bars/taxiways, improving the safety, and it has
increased the time with the engines turned off,
reducing the pollution.
This change on the waiting time with the engines
turned off is approved only if the number of on time
aircraft don't worsen.
segments of a runway can be occupied only by
an aircraft at a time. This make each pair of
segments of the same runway incompatible. A
conflict arises when two aircraft have to run the
same resource or two incompatible resources at
the same time. A conflict is solved by fixing a
precedence between the two aircraft. Therefore,
a feasible solution for ASP consists in solving
all the conflicts among aircraft, avoiding
deadlocks. ASP, as the majority of the problems
belonging to the class of job-shop scheduling
problems, is hard to resolve. Our aim is both to
design a valid model, representative of most of
the practical aspects and to develop fast
heuristic algorithms, based on such model, in
order to face the real time nature of the
problem.
3 Heuristics
In this Section we describe the heuristics procedure
we use to improve a given initial feasible solution.
The model we use to determine an initial feasible
solution and to measure the effect of a local
modification of it, implemented by a heuristic
procedure, is the Alternative Graph [4] (AG). For
any detail concerning the AG modeling the TMA we
consider, we refer to [8].
Due to the real nature of the problem we first
compute fast initial solutions, then we tray to
improve the quality by applying local search
heuristics based on the alternative graph
representation.
Any potential conflict on resources between landing
and departing aircraft must be detected and solved.
We consider a list of real dispatching criteria to
assign the precedence.
Ordered all the aircraft according to the FIFO rule
respect to nominal landing/departing time, the
precedence between two consecutive landing
(departing) airplanes is given on FIFO rule, if a
conflict occurs

in the runway a landing aircraft always
precedes a departing aircraft

and if occurs in taxiway, stop bars, parking
bays, a departing aircraft precedes a landing
one.
4 Computational Results
Experiments are carried out considering as a
reference test case one busy hour of arrivals and
departures at the Malpensa international airport.
From the study a we have tested different instances
(denoted as n\_m\_x\_t) based on four parameters
(n,m,x,t):
 n: number of departures (4,5,6,8,10,15)
 m: number of arrivals (4,5,6,8,10,15)
 x: number consecutive arrivals/departures
(2,3,4,5,6)
 t: simulation constant ( 4,5,6,8,10,12,20)
This admissible solution represents a good
estimation of the solution currently produced by
controllers in terms of both safety and quality.
Once a feasible solution x has been constructed, it is
modeled by the alternative graph and local search
procedures are applied. The local search is based on
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Recent Researches in Applied Economics and Management - Volume II
The simulation constant t and the TMA average
throughput time X defines the simulation time
interval T =t*X .
The routing problem is solved off-line in a
preliminary step and the main focus is on real-time
scheduling decisions with fixed routes (we have
tested only real routing). The heuristic to optimize
the routing problem is under study.
In particular we deal with the problem of scheduling
airplanes moving on ground, with different
objectives. Different lexicographic order is tested.
If we considered first the number of on time aircraft,
the local search gives better results in comparison
to FIFO rule, for the on time aircraft the
improvement is attested around 30% and respect to
the average lateness is 3%. The binary search,
applied to waiting time at the stop bars, gives a
reduction of pollution around 15% instead the BS
applied at the whole waiting time (stop bars and taxi
ways) gives a reduction of pollution around 40%.
We have also tested first the binary search to
minimizing the pollution and after the local search
to maximize the on time aircraft. In this case, for the
on time aircraft the improvement is attested around
60% , the average lateness is -2%, and the reduction
of pollution around 32%.
[3]
[4]
[5]
[6]
[7]
[8]
[9]
4 Conclusions
In this paper we introduced the alternative graph
model for ASP in the TMA of Malpensa airport. We
show that even a simple greedy heuristic is able to
improve on time aircraft and average absolute
lateness when compared to commonly adopted
policies. We observe that an advanced real-time
scheduling system may be useful to optimize the
traffic conditions, improving the safety and the
pollution on ground.
We have tested that the changing of the
lexicographic order improves remarkable the
pollution index. We have transferred the whole
waiting time from the taxyways /stop bars to the
parking bays, by the binary research , achieving a
reduction of the time with the engine on.
We are investigating rules to optimize the aircraft
routing that, in this paper, is considered fixed.
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