IEEE Computational Intelligence Magazine - May 2022 - 92

of two airplanes on the same runway
must have a certain time interval, which
depends on the models of the two airplanes.
First-come-first-serve (FCFS) is
the most direct method to determine
the landing sequence but may not be
the best choice due to the constraint of
the landing interval. As shown in Fig. 5,
the total delay of the three flights in
FCFS is (0 + 110 + 220) = 330 seconds,
while that in intelligent scheduling is (0
+ 250 + 0) = 250 seconds. Certain
exact algorithms (e. g., branch-and-cut
[110] and branch-and-price [111]) have
also been proposed to deal with landing
scheduling. However, these exact algorithms
require specific mathematical features
of the landing scheduling model
Timetable
Flight
AA3024
BB2135
CC7868
Arrival Time
10:30:10
10:31:20
10:32:30
AA3024
Interval = 180
FCFS
10:30:10
AA3024
Interval = 140
Intelligent
Scheduling
10:30:10
10:32:30
FIGURE 5 Example of landing scheduling on a runway.
TABLE II The comparison of the related studies on landing scheduling.
SCENARIO
SINGLE-RUNWAY
MULTI-RUNWAY
REFERENCE
[112]
[113]
[114]
[119]
[121]
[115]
[116]
[117]
[118]
[120]
BASIC OPTIMIZER
GA
GA
ACO
GA
PSO
GA
SIMULATED ANNEALING
SIMULATED ANNEALING
ACO
ACO
10:33:10
CC7868
Interval = 180
10:35:30
10:36:10
BB2135
Model
X
Z
X
and thus cannot be extended in more
complex scenarios. Differently, EC algorithms
have fewer restrictions of the
model and are therefore applicable in
various scenarios. The related studies on
EC algorithms for landing scheduling
are compared in Table II. Xu [112] proposed
a GA-based algorithm to optimize
the landing sequence with the goal
of minimizing the landing time of the
last airplane. Hu and Paolo [113] used an
adjacency matrix to encode the landing
sequence and proposed a binary GA to
minimize the total delay of all flights.
Specifically, the receding horizon control
is incorporated, which divides the
timeline into a set of time windows. The
proposed algorithm sequences airplanes
Minimum Landing Interval
Model X
Model Z
Model X Model Z
90
180
180
250
BB2135
CC7868
Interval = 180
in each time window respectively, rather
than sequencing all expected landing
airplanes simultaneously. Based on the
receding horizon control framework in
[113], Zhan et al. [114] proposed an
ACO-based algorithm with integer
encoding to solve the problem. The
above three studies focused on the single-runway
scenario, but modern airports
usually have multiple runways.
Thus, considering the multi-runway
scenario may be more practical. In this
domain, Liu [115] proposed a GA-based
approach. Salehipour et al. [116] constructed
a mixed-integer programming
model and proposed a simulated annealing-based
algorithm to plan the landing
sequence and landing times of airplanes.
Salehipour [117] also proposed a twostep
approach to solve this mixed-integer
programming model. The first step is
to obtain the landing sequence by a simulated
annealing-based algorithm. With
the landing sequence, the mixed-integer
programming model can be transformed
into a linear programming model and
be solved by an exact solver. Wu et al.
[118] extended the method in [114] to
address multi-runway scenarios. A
greedy heuristic is proposed to distribute
the airplanes to multiple runways
based on the landing sequence obtained
by the ACO algorithm in [114].
Although flights are expected to folCONSIDER
UNCERTAINTY
low
a pre-established timetable, many
uncertainties exist in real operation. For
example, the arrival and taxiing times of
airplanes cannot be as accurate as
planned, and there may be additional
airplanes expecting to land. Caprì and
Ignaccolo [119] considered the uncertainty
of flight arrivals. When new
request-landing airplanes emerge, the
landing sequence must be rearranged.
GA is used to solve this problem, where
the optimization objective is to minimize
the sum of the landing time of airplanes.
In addition, Bencheikh et al.
[120] proposed an ACO-based algorithm
to address the uncertain airplane
arrival scenario. The optimization objective
consists of two parts: the delay penalty
and the rearrangement penalty. The
rearrangement penalty is related to the
change in landing time of an airplane
92 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | MAY 2022
IEEE Computational Intelligence Magazine - May 2022

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