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Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.
A98-37006
AIAA-98-4105
REAL-TIME DECISION SUPPORT FOR AIR TRAFFIC
MANAGEMENT, UTILIZING CONCEPT LEARNING
Jun NOGAMI1 , Shinichi NAKASUKA 2 and Koichi HORI3
Downloaded by UNIVERSITY OF FLORIDA on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1998-4105
Department of Aeronautics and Astronautics, Faculty of Engineering,
The University of Tokyo, Kongo 7, Bunkyo-ku, Tokyo, 113, JAPAN
Moreover, the introduction of free-flight concept
must enforce the need of intelligent decision support systems for ATM.
Abstract: Intelligent air traffic management
(ATM) systems will be necessary for future air
traffic control (ATC), which can manage air traffic flows and flight schedules efficiently in a realtime fashion. To meet this objective, in this
paper, an automated decision support system is
described. This system consists of several distributed decision-makers, and uses the concept
learning scheme using neural networks. The system has the capability to find a suboptimal solution without interrupting the actual operations, in
order to deal with various constraints. Simulation
studies show that the proposed scheduling strategy works rather more efficiently than the current
ATC procedures based on fixed heuristic rules.
In this paper, the usefulness of the application of
a machine learning scheme to future ATM functions is first explained. Then, in order to verify its
usefulness, an automated real-time decision support system for ATM in a restricted region such
as a single-unit enroute sector or a terminal area
is proposed. Dynamic selection of scheduling rules
during actual operations, referred to as "dynamic
schedxiling" in this paper, is utilized in this system. For this strategy to work effectively, sufficient knowledge is required that predicts which
rule is the best, reflecting the traffic situations
at the decision time. In this system, an inductive learning algorithm using neural networks is
proposed for acquiring such knowledge. Simulation studies show that the suggested scheduling
scheme works rather more efficiently than the current ATC procedures based on simple fixed heuristic rules such as the first-in first-out discipline.
1. INTRODUCTION
Current air traffic control (ATC) systems have
mainly been conceived to ensure, with tactical interventions, the safety of flights and an orderly
traffic flow, although some functions have been
partly automated. Today, such systems are no
longer efficient because of increasing travel demands and congestion phenomena in major terminal areas. Therefore, it seems necessary and practicable to introduce, in future air traffic management (ATM) systems, not only more-automated
procedures to maintain adequate safety levels, but
also planning and real-time decision support functions. These would have the capability to minimize ATC controllers' interventions that interrupt
the nominal flight plans of the airlines, to deal flexibly with anomalous events, to predict the timevarying traffic evolution as accurately as possible,
and to manage air traffic flows and flight schedules
efficiently and strategically in a real-time fashion in vast air-route and flight networks, in order
to reduce unnecessary airborne delays. To meet
this objective, a fast, intelligent, prediction and
scheduling algorithm has to be designed.
Next, a real-time prediction and decision-making
support system for ATM in a global airspace consisting of many airports and crossing air routes is
further suggested. This system has an ability to
make probablistic forecasts of congestion delays,
etc., and determine the current best control actions in a real-time fashion (e.g., flow regulation,
ground holding or rerouting strategies, etc.) at
any decision time. A graphic network consisting
of various traffic attributes is an evolving knowledge tool for fast prediction and decision making.
Simulation studies on this system are currently
under way, part of which are shown in this paper.
2. ATM AND MACHINE LEARNING
2.1 A hierarchical control model of ATM
1 Graduate Student, jeau'Sspace.t.u-tokyo.ac.jp
2 Associate Professor
3 Professor, hori'Sai.rcast.u-tokyo.ac.jp
Figure 1 shows a hierarchical control model of the
ATM task, which can be decomposed into three
levels, namely, air traffic planning, real-time ATM
and real-time ATC, according to the time scale of
the planning horizon. The main task of air traffic
Copyright © 1998 by the American Institute of Aeronautics and
Astronautics, Inc. All rights reserved.
52
Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.
planning is the regulation of flight schedules. The
main task of the real-time ATM is the on-line forecasting of congestion overloads, and on-line decision making regarding flow control actions to prevent costly airborne delays. The main task of the
5. Negotiation and regulation among multiple
agents, which have individual requirements
conflicting with each other, are needed.
It is impossible to find an optimal solution to this
problem, consisting of the best control actions and
their timings without interrupting the actual operations, by means of exhaustive search-based meth-
real-time ATC is to ensure the safety of air traffic, and to detect and avoid possible collisions. In
Downloaded by UNIVERSITY OF FLORIDA on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1998-4105
this paper, the real-time ATM activity is mainly
considered, which can be further decomposed into
two types of traffic flow management (TFM) actions, according to the scale of the flow control
regions. One type of action, which is addressed
in Section 3, is a microscopic or tactical one, exercised when an aircraft is already airborne. The
ods or model-based mathematical analyses. The
introduction of knowledge-engineering methods is
thought to be one of the most effective strategies
to deal with this problem. Several known expert
systems for flow control in one terminal area such
as CTAS (Erzberger, et al., 1994; Krzeczowski, et
al, 1995; Tobias and Scoggins, 1986) or COM-
other type of action, which is addressed in Section
4, is a macroscopic or strategic one with greater
potential for regulating aircraft flows.
PAS (Volckers and Schenk, 1989) have functions
to make fast, intelligent decisions. But as far as
real-time traffic flow management in a wide region
with many airports is concerned, studies on intelligent, efficient scheduling methods, e.g. ground
holding or rerouting strategies, are at the stage
of trial and error at present. Further, if the freeflight concept is realized, the number of control
variables will increase greatly, because the degree
of freedom of traffic control will extend from a
single dimension (only time) to four dimensions
(time and space), so it will be even more difficult
to find a suboptimal solution using only the known
heuristics that have been empirically obtained by
Right Schedule M"~—— •
• •HnM-ffigl
Gto bai ATM (Row Control)
•*-
*•
-flgM-rauttdbMlion
• greuMttoMng How (Bondon
Untt Sector ATM
ngM4cut» control * namtomcn
flghMpMd control
•M
*•
Safety Surveillance
-*•
•<
ATC controllers, TFM managers etc. Therefore,
intelligent decision support systems are essential
for solving this real-time ATM problem, in which
Figure 1. A control model of the ATM task
new knowledge can be created to assist in making
2.2 Real-time ATM and machine learning
at any decision time.
The real-time ATM problem, which is a typical
Machine learning is recognised as an effective
on-line decisions, and a suboptimal schedule can
be made in real time using the created knowledge
method by which some novel and evolutionary
knowledge is acquired and generalized systematically. Various machine-learning techniques have
been adopted for other scheduling problems with
large-scale scheduling problem, has the following
characteristics.
1. Immediate decision making at any discrete decision point is needed, so that real operation
is not delayed.
similar characteristics (Grefenstette, et al., 1990;
Nakasuka and Yoshida, 1992; Nakasuka, et al.,
1994). In this paper, an inductive learning technique is adopted in order to search for a suboptimal solution within a practical computational
time, and using the technique, the relationships
2. The environments surrounding this decisionmaking process change dynamically with
time, and involve various uncertain elements, some of which are governed by
stochastic processes and others of which are
difficult to formulate mathematically.
between the time history of the traffic situations
and the best control actions at an arbitrary decision time are explicitly acquired as mapping
3. Optimization criteria cannot be obtained until
functions. Such mapping relations can be estimated inductively using a large number of data
a large number of unspecified successive decision timings occur, requiring the long-term
obtained through off-line simulations and mathematical analyses. In this paper, neural networks
and attribute graphs are used to represent such
anticipation of the discrete events which will
be expected to occur throughout the planning horizon.
4. Various strategies to avoid the so-called combinatorial explosion are needed to deal with
a great number of control variables and constraints.
mapping relations, and some inductive learning
algorithms, such as backpropagation algorithm or
learning vector quantization, are utilized for acquiring the knowledge about such relations.
53
Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.
3. DECISION SUPPORT SYSTEM FOR
SINGLE-UNIT SECTOR REAL-TIME ATM
The control variables s'k, ulkiki, v%, t\ and rk
should be chosen to minimize the multiple objective functions:
3.1 Problem formulation
t6/
In this section, the real-time ATM problem within
a single-unit sector is considered. The inputs, decision items (amendments to the flight plans) and
minJ2 = min E ft { E 4|4 - t}nom\}
constraints in this problem are summarized in Figure 2. The amendments to the flight plans should
(2)
' fc 2 es-
optimize certain requirements, while satisfying the
Downloaded by UNIVERSITY OF FLORIDA on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1998-4105
given constraints: not only the maintenance of the
nominal flight plans as far as possible, but also reducing the total operating costs of all the airplanes
in a prefixed region, are required as optimization
criteria.
Inputs:
1. Nominally Scheduled
Airlines' Flight Flans
2. Radar Data on the
Evolution of Flights
3. Short-term Meteorological Forecasts
4. Restrictions imposed
by Flow Control etc.
Unit-Sector
Horizontal Flow
where, a,-, fa and 7; are weight coefficients depending on the plane class, subject to the flight
path and altitude constraints:
Constarints:
1. Sector Capacity
2. Horizontal & Vertical
=
Separation Criteria
3. Flight Performances
4. Forecasting Accuracy
on Wind Data
5. Navigation Accuracy
= E
(4)
,/orVfci eK<,
the ATC separation constraints:
Decision Items
(5)
1. Rerouting to by-pass
the Congested Areas
2. Variations of Altitude
Levels in comparison
to Nominal Flightplans
3. Imposing Route Delays
through Speed Control
(6)
j
, for Vfc € #'' 0 K , V(i, j) e J, i < j
the initial and terminal conditions:
4. Imposing Holding
Patterns
5. Sequencing Passing
or Landing Orders
*1<>^
, for Vie I
(7)
rL
=0
o
, for Vie I
(8)
K
Requirements of Multiple-Agents
1. Maintenance of the Safety of Flights
2. Prevention of Delay Propagation
(9)
the passage and holding time constraints:
due to Various Anomalies (Emergency, etc.)
3. Maintenance of Nominal Flight Plans
4. Minimization of Total Time Delays or DOCs
Figure 2. Inputs, decision items, constraints and
objectives of the single sector ATM problem
(10)
The control region is described through a network,
whose nodes represent the intersection of the plural airways, etc., and a set of discrete altitude lev-
,/orVfei €«•'", Vt 6 J
els is assigned for each node.
and the overtaking prohibition constraints:
This typical scheduling problem can be formulated
mathematically using nonlinear mixed integer programming (MIP) as the following constrained optimization model.
,/orVfei 6 A " ' ' , V ( t , j ) e / , * < j V
54
Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.
where,
R
This problem is NP-complete, so a fast, intelligent scheduling algorithm is required to solve this
strategic planning region
problem because the scheduler must deal with
(sector region)
strategic planning interval
/°D/
set of indexes of flights
in R in the interval [*„, *„ + TR]
lOk
set of indexes of
three-dimensional nodes in R
set of departure nodes by plane »
set of all the possible trajectory
nodes traversed in R by plane t
A- D fc-
various anomalies such as aircraft accidents, airport closures or changes in weather, etc. Exhaustive search-based strategies cannot be utilized directly, because an optimal solution could not be
found within a practical computational time if
such strategies were used.
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<*i = *',..,*>)
fnom
actual passing time
of plane t on node it
actual holding time
of plane i on node k
nominal departure time
3.2 Current procedures for the control of flights
Bianco and Bielli (1993) indicated that this prob-
lem could be formulated as an optimization problem, with the hypothesis that the nodes to be tra-
from R of plane t
minimum time intervals from
node fci to node fcj of plane t
maximum time intervals from
versed by single airplanes were fixed on the basis of
their nominal flight plans, and altitude levels and
passing times on the node trajectories could be determined by means of the branch-and-bound technique in a real-time fashion, on the assumption
that flight scheduling was carried out according to
the FIFO discipline. That is, this method decomposes the problem into two subproblems that can
node ki to node fcj of plane :'
minimum time separation
at node k between preceding
plane t and trailing plane j
fuel consumed when plane «
holds for time r at node k
fuel consumed when plane i
flies from node fcj to node fcj
ot
''it
be denoted, respectively, as "altitude control" and
"speed control". This is a compromise method to
find an acceptable solution within a short computational time through a large reduction of the
solution space by the use of fixed heuristic rules,
which becomes consistent with the current ATC
procedures. Such rule-oriented reactive scheduling has been widely utilized as a practical and
robust scheduling method. The weak point of this
strategy is, however, that these rules, empirically
extracted from human controllers, only refer to
the local information for decision making, and the
generated schedule cannot always be good in the
global sense.
during the flight time t
set of indexes of nodes following,
when plane :' starts from node k
binary 0-1 variable indicating
whether plane i occupies
the node k, or not
binary 0-1 variable indicating
whether plane t passes over
the flight arc consisting of
nodes k\ and £2, or not
binary 0-1 variable; if plane t
passes over node fc before plane j
does vl£ = 0, otherwise «j? = 1
sufficiently large number.
Several objective functions [Eqs.(l-S)] can be considered relative to the individual requirements of
the various agents (e.g., ATC controllers, or airline operators). In this section, only /2 is utilized
3.3 Basic idea of dynamic scheduling
as the optimization criterion, which represents the
sum of the differences between the actual sector
To compensate for such shortcomings of the reactive scheduling method, a "dynamic scheduling
departure times and the nominal ones for all the
(DS)" method has been adopted in this paper. In
aircraft which are predicted to exist in the sector
this method, many scheduling rules are prepared,
R within the planning interval [t0, t0
from which one is selected dynamically during
actual operations, considering the instantaneous
T* in Eq.(7) indicates the minimum possible passage time of the node k'0 for the plane i. If the
traffic situations at each decision time. Therefore,
the scheduling rule to be used is not fixed, but
switches from time to time. Mapping knowledge
1
plane t is not in the sector R at the time t0, T 0 depends not only on its speed performance but also
as to the relationships between the "traffic situation vs. best heuristic rule" is required, because
rule selection must be completed in such a short
time that real operation is not delayed. A powerful inductive knowledge-acquisition mechanism is
on the maximum allowable number of aircraft at
any time within the planning interval in the sector R, denoted as QR^TR), which can be determined by both a maximum controller workload
and flow restrictions between the sector R and its
needed, so that the effect of the DS method can
be fully exploited. For this objective, in this pa-
neighboring sectors. In this section, Qfl(t 0 »2fl) is
assumed as infinite, and the restrictions imposed
per, a finite set of basic attributes, approximately
representing the instantaneous traffic situations,
by flow control are not considered.
55
Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.
2.Basic Attributes Attributes
is extracted and the nonlinear mapping relationships between the "basic attribute set vs. best
reflecting
the
characteristics of overall traffic situations at
the decision time, and the status of the ATC
heuristic rule" are obtained inductively using neural networks. This type of machine learning is
named "concept learning", and is a kind of inductive learning technique. A DS method, based on
infrastructure, axe prepared for every manager. More local traffic attributes, e.g. congestion level in the local area around aircraft
the concept learning scheme and using binary decision trees or neural networks, has already been
with a similar priority, are further prepared
for Managers 2 to 4.
applied to other scheduling problems (Nakasuka
and Yoshida, 1992; Nakasuka, el al, 1994), and
good results have been reported.
3.Scheduling Rules Several rules with quite
different characteristics are prepared foi
each manager.
Build Time Module (BTM)
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3.4 Proposed Scheduler DS1/DS2
To solve the real-time ATM problem within a
single-unit sector, an intelligent scheduling system
named DS1 has been developed, which is based on
hierarchical and iterative cooperation by four distributed managers. Each manager has, a priori,
a set of several heuristic rules, from which one
is selected during actual operations by means of
the DS method, reflecting the instantaneous traffic situations at each decision time. Manager No.
1 determines the priorities for single airplanes, and
Figure 3.
scheduling
extracts the cooperating aircraft with similar priorities. Manager No. 1 has a preferential rule, in
which an emergency aeroplane can have the highest priority. Once the priorities of single airplanes
Detailed configuration of dynamic
Every manager in DS1 has its own individual neural network consisting of three layers, whose input
layer is a set of basic attributes and whose output layer dictates the most suitable decision rule
among the candidate rules prepared for that manager. In the build time module, the best heuris-
have been determined by Manager No. 1, Managers 2, 3 and 4 are activated for airplanes with
similar priorities. Manager No. 2 assigns for each
airplane, either a runway in a terminal area, or an
altitude level at which it leaves an enroute sector.
Manager No. 3 determines a flight strategy criterion for each airplane. Manager No. 4 assigns
an air-route consisting of nodes to be traversed
and an altitude level for each node for each airplane. Once the trajectories and flight strategies
have been assigned by these managers, modified
time schedules for a group of airplanes with simi-
tic rule of each manager is exhaustively sought,
through simulation, for an arbitrarily generated
sample problem which is randomly set according
to a priori knowledge about the possible situations
of the traffic environment. The criterion determining the best solution is the sum of delays for
all the aircraft which are predicted to be in the
sector within the planning interval [Eq.(2)j. The
delay of an aeroplane is defined as the difference
between its nominal departure time from the sector, and its actual one. Then the pair of data
on the basic attribute set vs. the best scheduling
rule is extracted for each manager. As for Managers 2 to 4, a generated problem in the build time
module produces simultaneously a large number of
subproblems, corresponding to individual groups
of aircraft, classified according to their priorities
by Manager No. 1, and one learning data sample is extracted from each subproblem. A large
number of such data are input into the inductive
learning part, and the mapping knowledge as to
the relationships between the basic attribute set
vs. the best heuristic rule for each manager is
lar priorities are made, assuming the premodified
flight plans of airplanes with higher priorities as
constraints, by means of the combined techniques
of non-linear programming and the branch-andbound technique. This process is iterated until
rescheduling is completed for the group of airplanes with the lowest priority.
Figure 3 depicts the detailed configuration of this
system. The build time module (BTM) in DS1
acquires the mapping knowledge between the traffic situation vs. the best heuristic rule in off-line
simulation. The following three types of a priori
human knowledge are utilized.
l.Possible Situations This module has the capability to generate various different traffic
acquired by means of the backpropagation algorithm. The learned weight matrix of the neural
situations, including possible anomalies such
as runway closures, aircraft accidents, etc.
network is stored in the manager. Figure 4 shows
the neural networks for managers 1 to 4, each of
56
Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.
which consists of three layers which respectively
have ni, "2 and ns nodes. Table 1 summarizes a
set of basic attributes and sets of a priori heuristic
Table 1 Basic attributes and heuristic rules
No. Attribute Content
1 No. of aircraft considered
(overall traffic density)
2 Variance of density distribution
rules of these four managers. The run time module
(RTM) in DS1 selects one scheduling rule for each
manager at each decision point during the real operations, using the mapping knowledge stored in
dependent upon local regions
3 Ratio of different aircraft types
the neural network of the manager.
4 Variance of aircraft type distribution
dependent upon local regions
DS2 is an extended system of DS1. It has the
Downloaded by UNIVERSITY OF FLORIDA on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1998-4105
capability to modify schedules reflecting the local or detailed traffic situations, on the basis of
schedules obtained by DS1. DS2 also uses the
12 Conflict probability, estimated
on the assumption that every aircraft
flies according to its nominal flight plan
( Attributes 13 to 18 are
DS method and the knowledge acquisition mechanism using neural networks. Sequencing, flight-
not used for Manager No. 1. )
13 No. of the rule chosen by Manager No. 1
time changes, rerouting, etc., are executed by additional distributed Managers 5 to 8 for an extracted group of neighboring aircraft. A fixed
rule is used for classifying the aircraft into groups,
and the number of aircraft belonging to the same
group is limited to less than nine. The distribution pattern of current 3D positions, nominal landing sequence pattern (e.g., LHLLE...), variation
in assigned routes, etc., of aircraft belonging to a
chosen group, the congestion level of a particular
node (e.g., runway No. 2 or waypoint No. 10),
and so on, are given as basic attributes as to the
local traffic situation. Local attributes, which indicate the relationships between neighboring aircrafts, such as previous relative order, controllability, normalized separation distance, speed difference, flight level difference, etc., are also included in input attributes of DS2 and they are utilized to make efficient resequencing. Heuristic and
optimal constrained position-shift methods (Neuman and Erzberger, 1990), and knowledge-based
sequencing and runway allocation algorithm utilizing fuzzy logic (Krzeczowski, et al., 1995) are
14 Congestion level in the local area around
aircraft belonging to the same priority group
18 Traffic flow ratio among routes and altitudes
___of the airplanes with higher priorities_____
Manager No. 1 (ni=8, n2=12, 713=6)
No. Heuristic Rule Description_________
1 FIFO (first-in first-out)
2 The earlier the nominal sector departure
time, the higher the priority
6 The larger the estimated conflict
______probability, the higher the priority
Manager No. 2 (ni=18, n2=20, na=4)
No. Heuristic Rule Description__________
1 Choose the same point
as the nominal flight plan
4 Choose a point with the shortest distance
________from the current position______
Manager No. 3 (m=18, n2=24, n$=6)
No. Heuristic Rule Description______
1 Minimum flight time
2 Minimum difference of time
from the nominal flight plan
partly utilized, but rule selection process utilizing
machine learning is added in this paper. Figure 5
depicts the overall configuration of DS1 and DS2.
Of course, use of the DS method does not guarantee that the optimal selection can be made in
an actual unknown traffic situation, that is different from the situations generated in the off-line
5 Common flight time for
constant descent angle
6 Common flight time with
________mninimized-DOC descent
build time phase. Neural networks are-often said
to be bad at extrapolation. However, a satisfactory sub-optimal schedule can be achieved, which
Manager No. 4 (r»i=18, n2=30, n3=8)
No. Heuristic Rule Description____________
1 Choose the same path
as the nominal flight plan
is well verified by computer simulation studies, examples of which are shown in Sections 3.5 and 3.6.
2 Choose the shortest path
3 Choose a path with the lowest
number of passage waypoints
8 Choose a path with
the lowest degree of congestion
Attributes of
Situation (nl)
Hidden
Layer(n2)
(Degree of congestion of every possible path is
Best Heuristic
recalculated, based on the premodified flight
plans of all the airplanes with higher priorities.)
Rules (n3)
Figure 4. Neural networks stored in managers
57
Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.
- Ctasslf (cat on Into
Groups of Aircraft
• Ranking of Each Group
basad on Tim* Urn
pfjortty-jp
Downloaded by UNIVERSITY OF FLORIDA on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1998-4105
Flight Schriufcj of
Aircraft wtth Higher Priorities
QQ.J
Constraints:
Flight Schedules of Aircraft
with Higher Group-Ranking
DS2
Figure 5. Overall configuration of DS1 and DS2
3.5 Simulation results 1 : terminal area
landing sequence, due to wake vortices, as given
in Table 2.
Traffic model. A model of one extended terminal area, including the neighboring cruise sectors,
limited to the arrival flow, is assumed, as shown
in Figure 6. There are four entry points, located
at 200nm from the airport, and two close parallel runways. The total number of intersection
nodes is 16, and three flight levels are considered
for the cruise section, namely FL310, 330 and 350.
Two aircraft types belonging to different weight
classes are considered, i.e. B747-200 (Heavy) and
B737-300 (Large), each of which has a different
speed performance. The actual traffic flow is generated in the run time module by the Montecarlo method according to the Poisson distribution, whose average number of aircraft entering
the terminal area per hour is given as N (ACPH).
Several types of descent trajectories are also considered, and the vertical minimum separation is
1000ft below FL290.
I] run way
Learning effect. Table 3 shows the growth of mapping knowledge stored in the neural network of
Managers 1 to 4 during the learning phase of DS1.
Q
"Prediction accuracy" indicates the percentage of
times that the neural network generated in each
manager by the build time module predicts the
best rule correctly in the run time module. For
example, 76 trials can predict the best rule of manager No. 1 correctly, out of 100 problems tried online, based on the neural network stored in Manager No. 1, which is acquired by 1000 samplegenerated problems of the DS1 build time module. Overfitting often occurs for a large number
of learning data. So, the learning phase is terminated when 2000 problems have been generated in
Radar
^Separatla
> <l
J
I Radar
^parade
Final
Approach
Figure 6. Terminal area model
Table 2 Matrix of separation distance
minima for final approach
trailing aircraft
the DS1 Build Time Module. As for Managers 2
to 4, the learning phase is terminated when 25437
Large
5 nm
about 77, 84 and 72 percent respectively at that
3 nm
preceding
Heavy
Heavy
4 nm
aircraft
Large
3 nm
subproblems have been generated, and the prediction accuracies of Managers 2, 3 and 4 reach
time. Based on the acquired knowledge of DS1,
the learning phase is repeated in DS2. 1000 problems, which produce approximately 50000 subproblems, are generated as learning data in the
DS2 build time module, and the average predic-
In-trail longitudinal minimum separation is 5nm.
The minimum spacing distances for final approach
depend on the weight classes of the aircraft in the
58
Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.
Case 2 L/H: 50/50, E/W: 50/50 (percent)
tion accuracy for Managers 5 to 8 finally reaches
about 73 percent. In order to maximize the prediction accuracy of each manager, similar types
Case 3 L/H: 50/50, E/W: 70/30 for Ihr
alternating with 30/70 for Ihr (percent)
of generated traffic samples are automatically removed in the build time module, and the parameters for the back propagation algorithm are carefully selected.
Table 4 Average delay D (min.) performance
Case 1
Table 3 Growth of mapping knowledge
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of Managers No.l to No.4
Generated
Problems (and
Subproblems)
in BTM
100 (1871)
500 (7068)
1000 (13954)
1500 (20112)
2000 (25437)
Tried
Problems
in RTM
10
50
100
150
200
Scheduling FIX2 2.44 9.93 3.28 12.58 4.36 16.58
Algorithm DS1 1.89 8.97 2.75 11.54 3.70 14.95
Prediction Accuracy
(percent)
Manager
No.l No.2 No.3 No.4
20.0 5.1 7.5 5.2
58.0
76.0
88.0
89.5
Case 2
N(ACPH)
60
90
60
90
60
90
FIX1 2.48 10.24 3.33 12.95 4.45 17.06
DS2 1.78 8.28 2.58 10.40 3.32 14.05
OPT 1.73 7.95 2.44 9.93 3.04 13.52
For example, for Case 3, when N is 90 (ACPH),
19.0 23.1 15.8
53.5 59.8 52.5
73.2 81.7 69.3
77.4 84.4 72.3
DS1 and DS2 can mitigate congestion delays by
2.1 (min.) and 3.0 (min.) respectively on average, and they can increase arrival throughputs by
7.8 and 10.6 percent respectively on average, as
compared with FIX1. Table 4 indicates that DS1
works more effectively when the traffic flows are
unbalanced route by route, and DS2 works more
effectively when aircraft with different weight cat-
Final performance. In order to evaluate the effect of DS1 and DS2, the following two schedulers
have been prepared. FIX1 uses fixed rules at each
Manager, i.e. "FIFO" as Manager No. 1, "nomi-
egories and speed classes exist together. This
means that DS1 can skillfully modify trajectories
nal runway" as Manager No. 2, "minimum flight
time" as Manager No. 3 and "nominal trajectory"
as Manager No. 4. FIX2 uses different fixed rules,
i.e. "FIFO" as Manager No. 1, "nominal runway"
and flight strategies, and DS2 can skillfully modify landing orders and control air speeds slightly
for every well-extracted group of aircraft.
as Manager No. 2, "common flight time with minimized DOC" as Manager No. 3 and "trajectory
with the lowest congestion degree" as Manager
No. 4. OPT, described in Table 4, means a suboptimal solution obtained off-line by the combined
techniques of nonlinear programming, genetic algorithms and the branch-and-bound method.
Figure 7 shows the cumulative probability distributions for the average delay per aircraft Dk in a
given traffic sample k, with the parameter N, for
Case 3. The benefits of the proposed schedulers
can clearly be seen for greater traffic densities.
This is valid, because longer groups occur in heavy
traffic, and long groups can be optimized more efficiently than short ones. For example, when N
equals 90 (ACPH), for FIX2, an average delay oi
12 (min.) or less is realized for 41 percent of all
Tables 4 and 5 and Figure 7 summarize the typical performance for these schedulers. 1000 traffic
samples are made by Montecarlo simulation for
each traffic situation case and each scheduling algorithm. The time-length of each traffic sample is
the traffic samples generated. For that case, on
the other hand, the same average delay per aircraft is realized for 57 percent for DS1, and this
delay or less is realized for 72 percent of all the
samples for DS2.
4hrs. The average time delay per aircraft Dj. for
a random traffic sample k (k = 1,2,—,1000),
which is defined as the sum of the individual aircraft arrival-time delays divided by the number of
aircraft in the sample, is calculated. Each performance data in Tables 4 and 5 represents the
average delay D, which is defined as the sum of
DI, for a random traffic sample k divided by the
number of trial samples.
1000
(13)
fc=i
Table 4 shows the effect of the traffic flow imbalance and the mix of aircraft types. The following three cases of the traffic flow mix, i.e.
s
10
is
Average Delay per Aircraft (min.)
East/West (E/W), and the aircraft type mix, i.e.
20
Figure 7. Cumulative probability distributions
in Case 2
Large/Heavy (L/H), are considered.
Case 1 L/H: 70/30, E/W: 50/50 (percent)
59
Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.
Moreover, an analysis of the correlation between
the input and the output of the trained neural networks using partial differentiation has been undertaken to see what kinds of basic attributes have a
large impact on a switch of rules in each manager.
As an example, in Manager 3, a "nominal flight
Final performance. In the learning phase, 3000
and 2000 problems tried off-line are generated for,
respectively, Managers 1 to 4 and 5 to 8. The average prediction accuracies finally reach 77 and 72
percent, respectively.
time" rule is used when the traffic is not heavy,
a "minimum flight time" rule is used when it is
slightly heavy and a "common flight time" rule is
Table 6 Average delay D (min.) performance
Htype
1
V t y p e 1
used when it is very heavy. Such rule switching,
Downloaded by UNIVERSITY OF FLORIDA on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1998-4105
reflecting the degree of traffic congestion, seems to
be understandable. When the traffic flow is overloaded, it is preferable to speed up every aircraft,
even if this causes additional fuel consumption, in
order to prevent the propagation of delays into the
traffic that follows, and it is preferable to assign
the same flight time to every aircraft, in order to
minimize its conflict possibility.
Table 5 Average delay D (min.) performance
Emergency
No
Emergency Missed
Event
Anomaly Landing Approach
FIX1 12.95
14.83
13.60
Scheduling FIX2
14.24
12.58
13.19
Algorithm DS1
11.54
11.94
12.81
DS2
10.40
10.78
1
2
1
3
1
2
1
3
FIX1 7.05 8.98 9.66 9.47 12.52
Scheduler DS1 5.82 7.35 7.50 7.58 10.25
DS2 5.48 6.96 7.08 6.62 9.29
Table 6 shows the effect of the imbalance of either
horizontal or vertical flow distribution, and compares the performance of three schedulers, namely
FIX1, DS1 and DS2. FIX1 uses the same rules
as FIX1 adopted in Section 3.5. In all the data,
scheduling is performed 500 times and the performance is averaged. Each item of performance
data represents the average delay per aircraft of
its departure time from the sector. The average
entry rate N into the sector according to the Poisson distribution is assumed as 120 (ACPH), and
11.57
the ratio of B747-to-B737 is 50 to 50 percent.
The following three horizontal flow types are compared, each of which is given as a matrix of the
Table 5 shows the robustness of DS1 and DS2
against anomalies. The average entry rate N is
assumed as 90 (ACPH). The ratio of L/H is 50/50
traffic flow ratio (percent) between an entry node,
i.e. AI, AI or AS, and a departure node, i.e. BI,
percent and the ratio of E/W is also 50/50 percent. Two cases, i.e. emergency landing and
B2, or B3.
missed approach, are considered, both of which
are assumed to occur once per hour, and compared with the no-anomaly case. It indicates that
Htype
11 11
11 11
11 11
the DS method, especially DS2, can suppress the
divergence of delay even if anomalies do occur.
1
11
11
11
Htype 2
20 10 5
10 10 10
5 10 20
HtypeS
5 10 20
10 10 10
20 10 5
The following three vertical flow types are also
3.6 Simulation results 2 : single-unit enroute
sector
compared, each of which is given as a vector of the
traffic flow ratio (percent) among three altitude
Traffic model. A model of a single-unit enroute
sector is assumed, shown in Figure 8, and consisting of 20 nodes and three flight levels. The diameter of this sector is 400nm. In-trail longitudinal
levels, i.e. FL310, 330 and 350.
minimum separation is assumed as 15nm. Other
Table 6 indicates that DS1 and DS2 can work more
Vtype 1
[33 33 33]
assumptions are the same as those in Section 3.5.
.Al
Vtype 2
[35 30 35]
VtypeS
[30 40 30]
effectively when the traffic flows are unbalanced
either horizontally or vertically; namely they can
acquire some knowledge to change routes or altitudes skillfully into a non-congested area for every
well-extracted group of aircraft.
Vertical Flow
FL3SO
3.7 adequate sector region
The greater the sector region, the more the free-
dom of scheduling and the more the number of decision items. The magnitude of each sector should
Figure 8. Enroute sector model
60
Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.
be determined by the trade-off between traffic
flow efficiency and computational load. Simulation studies show that the suggested system (DS2)
becomes more effective if the sector region and
predicted time horizon become greater and it can
get good solution in real-time if the predicted time
horizon lies within 2 hours.
4. DECISION SUPPORT SYSTEM
FOR REAL-TIME ATM
IN A VAST TRAFFIC NETWORK
4-2 Previous research 1
Bianco and Bielli (1993) designed a constrainec
linear optimization model for flow control among
multiple sectors, and several strategies to perform optimal flow-control actions were suggested
Vranas (1992) indicated that several integer programming formulations could be given for th<
multi-airport ground-holding problem and the influence of airlines' flight networks on the various
ground-holding policies was analyzed by means oi
operations research (OR). Other researchers alsc
suggested an extended integer programming for-
mulation. Several suboptimized strategies to mitigate congestion delays, both in terminal areas
and in vast air traffic networks, have been numerically studied, utilizing various techniques includ-
Downloaded by UNIVERSITY OF FLORIDA on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1998-4105
4-1 Problem formulation
Table 7 Decision items and requirements
Decision Items_______________________
ing classical branch-and-bound method, genetic
algorithms, and so on.
1. aircraft currently in a terminal area
- flexible rescheduling for missed-approach etc.
- landing order, landing time, runway allocation
2. aircraft currently in an enroute sector
Several factors which have a great influence on
the suboptimized flow-control, ground-holding oi
- destination change for airport closure etc.
- flow regulation among sectors
(auto-tuning of sector capacities)
rerouting strategies have been identified by these
OR-like numerical analyses. Detailed observation
- rerouting and changes in flight levels
- speed control
of suboptimal solutions searched for by means of
various OR-like methods would be very useful to
acquire refined heuristic strategies for real-time
3. aircraft currently awaiting take-off
- flight cancellation
decision support for the TFM activity. These ORlike methods, however, cannot be utilized directly
in the real-time ATM problem, because they cannot find a good solution within a practical compu-
- permission for takiag-off
- ground-hold time allocation
- rescheduling flight-plan (rerouting, etc.)____
Requirements________________________
tational time, and their analyses neglect the uncertainty in predicting weather events.
1. Nominal prescheduled flight plans should be
maintained as far as possible
2. Total direct operating costs (DOCs) dependent
on the additional fuel usages and delays
must be made as low as possible_________
4-3 Previous research 2
Selecting the correct amounts of control activ-
In this section, the real-time ATM problem in a
ity such as ground holding time is made difficult
because of the uncertainty in predicting weather
events that produce congestion delays. Qiao, ei
al., (1994) indicated that the air traffic flow could
be modelled on the assumption that the flight time
error of an aeroplane occurred only in the enroute
region, whose capacity was assumed to be infinite.
global airspace with many airports and airroutes,
the so-called '^traffic flow management" (TFM)
problem, is considered. A fast, intelligent prediction and scheduling algorithm is required to predict the future congestion overload at each element
of the vast air traffic network using the information available from radar, satellites, etc., and to
ules so as to minimize the total delay cost using
Such an error could be given as a specific probablistic distribution function, and the equations for
the predicted performance data. Further, the algorithm has to have the capability to mitigate dis-
minal entry, mean delay time in the terminal, air
determine the best amendments of flight sched-
calculating the mean air holding time at the terholding probability and delay probability of the
ruptions resulting from severe weather or various
emergencies, flexibly. The decision items and requirements in this scheduling problem are summarized in Table 7. The control actions for an aircraft
departure aeroplane were derived. In addition,
several ground-holding policies based on these online predictions were proposed, to alleviate costly
airborne congestion.
which is already airborne must be determined, not
only by the scheduler described in Section 4.4, but
also based on the parallel distributed cooperation
among the individual schedulers corresponding to
single-unit sectors, which have already been suggested in Section 3.
Figure 9, which is taken from the reference (Qiao,
et al., 1994), indicates that, as compared with the
case where no ground regulation is imposed, the
proposed ground-holding policies, where a depart-
ing aeroplane is permitted to take off only when
61
Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.
the expected value Ew about the airborne delay
time of the aeroplane is, respectively, below 30,
Downloaded by UNIVERSITY OF FLORIDA on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1998-4105
60, 90 and 120(sec.), can greatly reduce its airborne delay, without increasing its total travel
time, which is the sum of its air travel time and
its ground-holding time. The value Ew is derived
by the proposed equations. Detailed assumptions
assuming as its inputs the current traffic situation, the information about weather events and
the specific scheduling rules selected by the control
mode. Fast, lookahead prediction is needed, so
the knowledge representing the relationships between such inputs into this mode, and a large number of data on the future traffic performance, are
and parameters are given in the reference (Qiao, et
acquired inductively from various learning data
al., 1994). This method is excellent in that it has
the capability to make fast decisions considering
the uncertainty in predicting future traffic situations. However, in the method, ground holding is
imposed on a departing aeroplane, on the assump-
obtained through off-line simulations and modelbased mathematical analyses. A hierarchical attribute graph, an extended version of KFM (Kohonen Feature Map), is used as the knowledge representation scheme, whose nodes consist of
tion that every aeroplane which will depart later
will fly according to its nominally scheduled flight
• a set of discrete events which will occur
throughout the planning horizon,
plan. Such an assumption hinders both the accurate prediction of future traffic situations, and the
making of optimal decisions throughout the longterm planning horizon. Furthermore, the method
is based on an oversimplified traffic model, which
neglects airlines' flight connection networks, airroute networks in enroute regions, changes in sec-
• the scheduling rules selected by the control
mode,
• the useful attributes representing the structure of the airroute and flight networks,
current traffic situations, forecast data on
weather events, etc.,
tor capacities with time, sequencing in terminal
areas, timing regulations among take-off and ar-
and so on, and whose arcs consist of the mapping relationships described by nonlinear functions among attribute nodes. Several algorithms
rival flights, etc., which play important roles in
alleviating congestion delays (Vranas, 1992).
for the inductive acquisition of the refined graph
structure, such as LVQ (learning vector quantization), are currently under investigation.
1000
0-No Regulation
30Sec.
—— 2-Ew«60Sec.
—— 3-Ew = SOSec.
—— 4-Ew=120Sec.
20
25
X(Alrcraft/Hour)
Figure 9. Amount of the average airborne delay
(Mean Wait Time) based on the ground
holding policy using the value Ew
(Qiao, et al., 1994)
Figure 10. Proposed system architecture
The control mode is based on cooperation between distributed decision makers such as the
flight schedule planner, the ground holding manager, the rerouting manager, the flow control manager, the negotiation manager, etc. For exam-
4-4 Proposed decision-maker
It is necessary to supplement the above shortcomings of both of the methods in Sections 4.2 and 4.3,
ple, the negotiation manager has the capability
to arbitrate between the conflicting requirements
in order to construct intelligent decision-makers
for this TFM problem. Figure 10 shows a proposed system, which consists of a prediction mode
of multiple agents, such as airline planners, ATC
controllers, etc. In each manager, many a priori
decision candidates are prepared, from which one
and a control mode.
is selected at each decision point, on the basis of
the instantaneous flight and airroute network situations and the performance data on congestion
The prediction mode can make an approximate
estimate of the future traffic performance, such as
the distribution pattern of future arrival demands
at an airport, or the delay probability of a flight,
delays, etc., forecast by the prediction mode. For
62
Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.
example, either permission to take-off, or a request
diction mode is activated to make fast-time predictions about the future performance data, using
the decision point where the recursion is cut off
as the starting point. This strategy, of course, degrades the reliability of the performance data obtained. But, the more skillful the cut-off control
of the recursive process, the more accurate are the
estimates of the performance data in the prediction mode, and better heuristic rules used in the
control mode would be able to aid the proposed
for ground holding, is determined for an aeroplane
waiting for its take-off. If the latter is selected,
the allocation of appropriate gate-holding times
must be decided further. Such decision making is
so difficult that a human cannot implement sufficient knowledge to pin-point a single best candidate. Therefore, the scheduling should be made
according to a time line, and at each future decision point, one decision candidate must be selected.
method in making better decisions. An analogous
recursive scheduling is used in the reference (Nakasuka, et al., 1994) and good results have been reported. Simulation studies on this system are currently being performed, some of which are shown
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| Overall Scheduling PrecMs|
in Section 4.5.
4-5 Simulation results
Virtual traffic-network model. A model of air traffic network, including multiple airports and enroute sectors, is assumed, as shown in Table 8.
The actual traffic flow is generated in the run time
module by the Montecarlo method according to
the Poisson distribution, whose mean number of
aircraft generated per airport per hour is given
as N (ACPH). 5000 traffic samples are made by
Montecarlo simulation for each scheduling algorithm and each N (ACPH). The time-length of
each traffic sample is lOhrs.
Figure 11. Recursive scheduling to deal
with combinatorial explosion
Figure 11 shows this process in more detail. The
Table 8 Traffic flow model
prediction of the accurate performance data on
the assumption that a specific candidate is to
be selected will be required, in order to select
the correct candidate. But to obtain this performance data, a "virtual scheduling" from the de-
Number of Airports
5
Number of Enroute Sectors
10
cision point into some point in the future must
Number of Intersection Waypoints
Distance between Airports
44
800-2200(nm
be made, corresponding to the first move of each
of these candidates, which gives birth to another
Max No. of A/C in one Terminal
Max No. of A/C in an Enroute Sector
10
20-40
level of scheduling problem. If this new schedul-
Average Flight Connection Ratio
Ground Delay Cost
0.4
550(USD/hr
ing is badly made, the performance data obtained
may be unreliable, which degrades the selection
optimality at the upper level. Therefore, the lower
level must also make a sufficiently good schedule,
which requires another lower-level scheduling for
prediction at each decision point, and so on. So,
in order to make optimal decisions, the recursion
will continue almost infinitely, which results in the
Airborne Delay Cost
2200(USD/hi
Traffic Mix (Heavy:Medium)
50:50
Aircraft Generation Process:
______ Poisson Distribution per Airport
Synergistic effect due to the combination of multiple TFM strategies. Figure 12 and Table 9 indicate the typical performance of the proposed
schedulers. Figure 12 shows the average DOC
loss per aircraft for several TFM strategies. Intelligent scheduling in terminal and flow control
in enroute use DS method, addressed in Section
3. Airroute change, take-off regulation and departure time regulation use the proposed prediction
and control mode, addressed in Section 4.4.
so-called "combinatorial explosion". To avoid this
problem, the proposed system has the capability
to control this recursion, and cut the recursion at
the specified level by approximating the optimal
decision making process by using heuristic rules.
That is, the selection of decision candidates at every decision point which follows the decision point
at which the recursive process is cut off, is made by
a priori heuristic rules. The dynamic scheduling is
applicable, instead of using fixed rules. The pre63
Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.
Table 9 Synergistic effect of delay perfonnance due to the combination of multiple TFM actions
Average total delay
per aircraft (sec)
(total=airborne+ground)
recursive
airroute sector ATC
N/hour
N/hour
prediction distribution intelligence 20.0 22.5 25.0 27.5 20.0 22.5 25.0 27.5
no
101.7 125.8 163.0 208.1 142.6 212.4 415.4 1209.3
fixed
FCFS
no
98.8 122.2 159.1 201.4 138.3 205.6 405.9 1193.0
fixed
DS
no
95.2 117.3 149.7 186.5 134.4 196.1 388.7 1168.4
free
FCFS
Downloaded by UNIVERSITY OF FLORIDA on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1998-4105
Average airborne delay
per aircraft (sec)
no
free
yes
free
DS
DS
88.7 108.8 139.2 173.0 121.9 182.0 365.9 1132.7
79.5 93.2 119.3 146.2 106.8 161.5 323.8 1047.5
tion of the number of rules is also needed.
The direct observation of sub-optimal solutions searched for exhaustively, utilization
of structured classifiers (Iba and Higuchi,
1992), application of genetic algorithms,
learning from negative instances of traffic
situations where the best scheduling rule
cannot be estimated correctly during real
operation, and so forth, may be useful for
the evolution and generalization of heuristic
Table 9 shows the synergistic effect due to the
combinational use of both schedulers, as compared with the single use of each scheduler, as
well as it indicates that the proposed schedulers
with fast-prediction mode and recursive decisionmaking mode works more effectively than the simple schedulers without such lookahead planning
functions.
1,200.0
»
Ho
+ DS MtOwd in Tenmal
1,000.0
g | 300.0
e a.
O
£
3. Neural networks are not good at extrapolation and representing the mapping relationships explicitly. Decision trees are not
good at nonlinear classification. A refined
mapping scheme to compensate for both
^•Tote-off Regalaua
OJ: 600.0
O g 400.0
strategies.
•f Flaw Control in Emote
+Rertiaatg (AimtU Change)
+Dcparttrt Tina Regulation
Ground Detay Cost: SSWflir
Airborne Dtlay Cost: 2MOSflirJ
200.0
0.0
14.0
18.0
shortcomings is urgently required. Various
other machine-learning techniques, such as
case based reasoning (Levin and Fearnsides,
1994) or reinforcement learning, should also
be considered.
22.0 26.0 30.0
N (ACPH)
Figure 12. Effect of multiple TFM actions
4. An interactive decision support between human managers and machine systems is required, so that human managers can intervene in the generation of useful traffic
5. ENHANCEMENT OF DYNAMIC
SCHEDULING
attributes and novel, improved scheduling
strategies, and the regulation of multiple
agents' conflicting requirements.
Enhancement of dynamic scheduling is essential
for further improvement of the capability of the
proposed schedulers described in Sections 3 and
4. When it has been sufficiently improved, the
whole schedule could be drawn up by the dynamic scheduling method alone, shown in Figure
13, without any hierarchy or iterative process.
A breakthrough in solving these problems is currently being pursued.
To do this, the following problems must be solved,
which have been identified as fundamental problems in the field of artificial intelligence.
1. The most important attributes must be utilized for rule selection, which is a difficult
problem, far beyond what a human can
do. The automatic generation of useful attributes from raw data on the traffic situations is required for solving this problem.
ProManSpMe
Sotadoo Space
Figure 13. Concept of the enhanced dynamic
scheduling method
2. The automatic creation of new, better,
scheduling rules is required. Minimiza64
Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.
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6. CONCLUSIONS
Erzberger, H., Davis, T.J. and Green, S. (1994).
Design of Center-TRACON Automation
System. In: Proc. of the AGARD Guidance
and Control Panel, 56th Symposium on Machine Intelligence in Air..
An automated decision support system for realtime, efficient ATM is proposed, which consists of
several distributed decision-makers. Large-scale
scheduling problems of this kind are so complicated that man alone cannot implement enough
intelligence into each decision-maker. Therefore,
the empirical knowledge extracted from ATC controllers, TFM managers, etc., is not sufficient to
make optimal decisions, and to deal with sudden
anomalies. In the proposed system, this insufficiency is compensated for with the internal simulations for prediction, as well as the dynamic selection of scheduling rules using neural networks.
The simulation results verify the versatility and
flexibility of the proposed scheduler for the realtime ATM problem within a single-unit sector and
in a global airspace. Aspects which will be addressed in future studies include:
Future Air Traffic Control and Navigation Systems. (1991). AIAA SP-050-1991.
Grefenstette, J.J., Ramsey, C.L. and Schultz.
A.C. (1990). Learning Sequential Decision
Rules using Simulation Models and Competition. Machine Learning.
Hollnagel, E., Cacciabue, P.C. and Bagnara, S.
(1994). The Limits of Automation in Air
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Vol.40, pp.561-566.
Iba, H. and Higuchi, T. (1992). Evolutionary Learning of Predatory Behaviors Based
on Structured Classifiers. ETR-TR92-34,
• Application of the proposed dynamic
scheduling technique to existing methods
of handling heavy traffic arrival flows at
major terminals (Krzeczowski, et aJ., 1995;
Synnestvedt, et al., 1995).
SAB92, MIT Press.
Izumi, K.H. (1986). An Evaluation of Descent
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Krzeczowski, K. J., Davis, T. J. and Erzberger,
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AIAA-95-3366-CP.
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Control Panel, 56tb Symposium on Machine
Intelligence in Air..
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time-varying traffic evolution as accurately
as possible.
Nakasuka, S. and Yoshida, T. (1992). Dynamic
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computational time.
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could generate conflict-free trajectories in
real time.
Neuman, F. and Erzberger, H. (1990). Analysis
of Sequencing and Scheduling Methods for
Arrival Traffic. NASA TM 102795.
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