International Journal of Aeronautical and Space Sciences
these above research are carried out from the point of view
of fuel economy and without taking into account the effect
of airspace operational constraints.
In response to the above issue, the next generation air
transportation system (NextGen) proposed the concept of
required time of arrival (RTA), which requires aircraft to
arrive at designated waypoints within specified time win-
dows [8, 9]. Using RTA operation, aircraft can be separated
and sequenced during approach progress, which is an effec-
tive way to enhance the operational capability and efficiency
for busy airports [10, 11]. Vaddi et al. [12] studied the uncer-
tainty of RTA operation and proposed the significance of
high-fidelity wind models. David and William [13] iden-
tified errors during RTA operation and pinpointed aspects
of trajectory predictions that caused them. Several research
for fuel-saving operation with RTA have been conducted.
Ramon et al. [14], and Adrian et al. [15] studied the contin-
uous descent trajectory within RTA constraint and proposed
that RTA operation is a potential solution to reduce fuel con-
sumption, emissions, and noise without compromising the
airport’s capacity. However, Prins et al. [16]. proposed that
set an RTA constraint would increase fuel consumption for
continuous descent operation versus the same condition. Gar-
cía et al. [17] solved the cruise fuel-efficiency trajectory under
RTA operation using the control optimization algorithm. The
solving performance of the four kinds of optimization control
algorithms were compared at first, and then the rapidity and
validity of Pseudospectral collocation methods were proved
[18]. Alejandro et al. [19] used ABC algorithm to optimize
vertical trajectory by optimizing the Mach number. However,
this study only considered the cruise process.
The above fuel-efficiency problems under RTA opera-
tion mainly fulfill the optimization under a single waypoint’s
constraint, but without considering multiple waypoints’ con-
dition and the convenience during flight process. Beyond that,
the above studies do not reduce the environmental impact due
to aircraft engine gaseous emissions, which is far from the
NextGen’s environmental goals.
The impact of civil aviation on the environment is mainly
the greenhouse effect caused by engine emissions, which
affects global temperature changes. Researches predict that
aircraft emissions will play a larger role in global environ-
mental change as the predicted amount of air traffic increases
[20, 21]. The three types of emissions that have the greatest
environmental impact are: CO
2
,NO
x
, and contrails. Due to
the formation of contrails are strict and the influences of them
are short-term and regional, this paper does not consider the
impact of contrails [22]. Ali and Richard [23] presented the
concept of vertically curved runways for reducing airport
environmental impact and the result shows that CO
2
can be
reduced during takeoff phase. However, this advantage is
regional and the runway in this shape may be expensive. Wei
and Zhang et al. [24] proposed the concept of price weight
of emission, cost index emission factor, and integrated cost
index to consider the effect of aircraft emissions. Although
the total flight cost can be decreased by choosing adequate
integrated cost index, they did not consider the RTA con-
straint. Alfonso and Damián [25] analyzed and optimized
cruise phases in vertical profile using discrete trajectory pat-
terns to minimize the direct operating cost. However, they did
not consider the RTA operation which is a s ignificant mea-
sure to avoid flight conflicts in busy airspaces. Sang and John
[26] studied the vertical trajectory generation problem during
the en route descent phase based on continues descent opera-
tion. However, they did not consider the operational limiting
for air traffic management (ATM). Although the flight man-
agement system can provide a descent profile with various
waypoint limits, it does not take into account environmental
impacts, which does not meet the NextGen’s environmental
goals.
The purpose of present work is optimizing flight perfor-
mance parameters to reduce environmental impact and fuel
consumption with multi-RTA constraints. Only the en r oute
descent process is taking into account. It consists of two seg-
ments: end of a cruise and entire en route descent phase. First,
not only we should reduce the environmental impact and take
a balance between environment and fuel consumption, but
also the speed variation in the optimization process. Second,
multi-RTA constraints include horizontal position constraint,
altitude constraint, and arrival time constraint at each way-
point. Third, the calculation of flight parameters based on
flight model is nonlinear. And the optimization process is
equivalent to solving a multi-constraint, multi-objective, and
nonlinear problem. Therefore, the multi-objective genetic
algorithm was selected to solve this complex problem.
Section 2 presents the optimization problem, which con-
tains the analysis of vertical trajectory pattern, calculation of
flight parameters, and description of the optimization prob-
lem. Section 3 describes the solution method of the problem
that is the genetic algorithm, which includes the selection and
coding of control variables, the establishment of the multi-
objective fitness function, as well as the optimization process.
Section 4 shows numerical examples and analyses the opti-
mization results from different perspectives. Conclusions of
this study are presented in Sect. 5.
2 Problem Modeling
The actual operational limits for airspace are RTA commands
issue by ATM during the en route descent process. The RTA
command requires aircraft to arrive at designated waypoints
within preset time windows and through the correspond-
ing altitude windows. The essence of the RTA instruction
is a multi-constraint waypoint, which consists of distance,
altitude and time. First of all, this section analyzes the ver-
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