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can perform link budget and coverage prediction by considering the surrounding effect.
CloudRF
®
also offers configurable options to simulate the conditions and characteristics
of real equipment by employing a high-resolution topographic graph. Further descrip-
tions of simulation parameters and measurement methods are provided in related parts
of Section
4
.
3.3. Drone Path Planning Optimization
In this study, an industrial agricultural hybrid fixed-wing VTOL drone, known as
AeroHawk [
36
], was utilized to perform measurements. The selected VTOL drone has
the advantages of both fixed-wing and multi-rotor drones, which can take off and land
vertically without a long runway while having the leverage of more extended range and
endurance due to the aerodynamic efficiency generated from the wings during flight. This
key feature is important for farmers with a large area of land.
To find the shortest flight path for the drone, first, the path planning problem was mod-
eled as the TSP, and then both PSO and EPSO algorithms were used to solve the problem.
In the TSP, the nodes and distance between the nodes are given, and the object is to
find the minimum overall distance to travel from one node to other nodes and back to the
starting node without crossing a node twice. According to graph theory, the TSP solves
the Euclidean metric to find a Hamilton loop with the smallest weight in the weighted
completely undirected graph. However, the TSP belongs to the class of non-deterministic
polynomial (NP) problems. To reduce the computational complexity, metaheuristic algo-
rithms such as the GA, PSO, ant colony optimization (ACO), and neural network (NN)
have been used. In this study, we used PSO because of its advantages such as strong
robustness, simulation evolution, ability to store past iterations, and easy implementation.
The PSO algorithm works in such a way that, first, all particles are scattered randomly
on the search space and every particle calculates the objective function based on its position
in the search space. Then, each particle computes its next movement direction based
on a combination of information about its current position, its best position that it has
experienced so far, its current velocity, and information from one or more of the best
particles in the swarm. Then, particles move, one step of the algorithm ends, and, in case
of necessity, the above steps are iterated until the algorithm finds the optimal solution. In
our simulation, we set the PSO algorithm to stop its execution when meeting the defined
number of function evaluation (NFE) value, which is defined as
NFE
(
t
) =
n
pop
+
n
pop
×
t
=
n
pop
(
1
+
t
)
,
(1)
where
n
pop
is the population size (swarm size), and
t
is the number of iterations.
To formulate the behavior of particles, assume there are
n
particles in the swarm, where
the position and velocity of
i
th particle at time
t
are denoted as
x
i
and
v
i
, respectively, for
i
∈ {
1, 2, . . . ,
n
}
.
x
i
,
best
[
t
]
is the best position that the
i
th particle has experienced so far
and
x
gbest
[
t
]
is the best position in the swarm’s experience. In every iteration (generation),
the swarm updates its best position (based on objective value) which is known as the global
best, and each particle updates its best solution (i.e., personal best) and computes its next
position as follows:
v
i
[
t
+
1
] =
wv
i
[
t
] +
c
1
r
1
x
i
,
best
[
t
]
−
x
i
[
t
]
+
c
2
r
2
x
gbest
[
t
]
−
x
i
[
t
]
,
(2)
x
i
[
t
+
1
] =
x
i
[
t
] +
v
i
[
t
+
1
]
,
(3)
where
w
is the inertia coefficient,
c
1
and
c
2
are cognitive and social acceleration coefficients,
respectively, and
r
1
and
r
2
are random numbers in the range of 0–1.
The weakness of the classic PSO algorithm in solving the TSP is that it falls into the trap
of local optimums. To address this problem, we applied three mutation operators, called
swap, reversion, and insertion, into the PSO algorithm, and the modified PSO algorithm is
called EPSO. Figure
7
shows the flowchart of the EPSO algorithm which was implemented
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in MATLAB. The initial parameters are generated through the swarm initialization. As
the adjustment of
w
,
c
1
, and
c
2
plays an important role in the performance of the PSO
algorithm (e.g., it directly affects the convergence speed of the algorithm to the best cost
function) the
w
,
c
1
, and
c
2
parameters were selected as [
68
]
w
=
χ
,
(4)
c
1
=
χφ
1
,
(5)
c
2
=
χφ
2
,
(6)
where variables
φ
1
and
φ
2
are positive numbers,
φ
≡
φ
1
+
φ
1
>
4, and
χ
=
2
φ
−
2
+
p
φ
2
−
4
φ
.
(7)
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of the PSO algorithm (e.g., it directly affects the convergence speed of the algorithm to the
best cost function) the
𝑤
,
𝑐
, and
𝑐
parameters were selected as [68]
𝑤 = 𝜒
, (4)
𝑐 = 𝜒𝜙 ,
(5)
𝑐 = 𝜒𝜙
,
(6)
where variables
𝜙
and
𝜙
are positive numbers,
𝜙 ≡ 𝜙 + 𝜙 > 4
, and
𝜒 =
.
(7)
According to [68], the optimal values for
the above parameters are
𝜙 = 𝜙 = 2.05
,
𝑤 = 0.7298
, and
𝑐 = 𝑐 = 1.4962
.
Figure 8 depicts how the utilized mutation operators operate. The swap operator ex-
changes the places of two randomly chosen nodes. The reversion operator
exchanges the
places of all nodes in a randomly selected range. The insertion operator moves a randomly
chosen node to another random place. Figure 9 presents the pseudocode of the utilized
mutation operators.
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