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Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.
Digital Object Identifier 10.1109/ACCESS.2022.Doi Number
Network Site Optimization and Clustering
Study Based on Simulated Annealing
Algorithm
LIN-SHEN YANG1*, BIN WEN1*, AND JIE-JUN YAN1*
1 School of Artificial Intelligence, Tiangong University, Tianjin 300387, P. R. China
Corresponding author: Jiejun Yan (e-mail: 719196517@qq.com).
*These authors contributed to the work equally and should be regarded as co-first authors.
ABSTRACT Nowadays, communication networks are becoming increasingly complex. This paper aims to
demonstrate an effective method to achieve the intelligent planning for network base stations (BSs). The
various parameters such as BS coordinates (x, y), the collaboration of multiple types of BS, and the density
of BS construction are taken as design parameters for BS placement. We construct the objective function
using the lowest total cost and the total minimum workload of BS to 90%. To solve the problem of siting
planning with large data volume and mixed placement of multiple BS, we propose a new practical three-step
model for BS siting planning: (Ⅰ) roughly selecting the alternative coordinates for the BS using the
DBSCAN algorithm; (Ⅱ) correcting and further refining the alternative BS coordinates using the K-means
algorithm; (Ⅲ) determining the optimal BS construction solution to meet the requirements using simulated
annealing algorithm (SAA). The real data of a 2500×2500 area have been used for the simulation test. The
simulation result shows that BS placement covers 90.03% of the workload, confirming that the proposed
method can handle site planning for large orders of magnitude of data and use a mix of BS to achieve the best
economics for the demand. This paper provides basic support for future research on network site optimization.
INDEX TERMS DBSCAN algorithm, K-means algorithm, simulated annealing algorithm, base station(BS)
planning
I. INTRODUCTION
Mobile communication technology is proliferating, and the
scale of operation is getting bigger, bringing more complex
communication networks. With the development of 5G,
communication bandwidth is getting bigger. However, the
area that BSs can cover is getting smaller, making the
number of BSs needed to cover the same area more. In
addition, the types of BSs and antennas have also become
more varied. Various BSs make the planning of
communication networks, especially the problem of station
site selection, more complicated. Rational BS placement
plays a key role in the massive data exchange and
communication within cities, which can reduce government
overhead, coordinate the development of communication
quality across regions and improve environmental quality.
Besides within cities, optimal BS placement is also
important: BS location planning at sea [1] can improve the
accuracy of landing point, calculation speed of positioning
and positioning accuracy of high-speed targets at sea[2]；
Most of the BSs were in ruin during rescue and relief in
disaster areas, and planning and research on the placement
method of UAVs(UAVs Unmanned Aerial Vehicles) BSs
was needed[3] This will speed up the rescue process and
maximize the safety of personnel.
Planning an urban communication network is intricate
and complex, and its cost and complexity are closely
related to the location and number of BSs. The problem of
station site selection is: according to the coverage of
antennas of the existing network, a certain number of points
are given to the weak coverage area of the existing network
so that the coverage problem of the weak coverage area can
be solved. Many factors influence it: for example, too many
reference placement points of BSs, the selection of BS
types, whether the total service volume achieves sufficient
coverage, and whether the cost is the lowest. Therefore, a
set of suitable methods for urban communication BS
planning under practical constraints with a large amount of
data is needed to solve the problem of high cost and
complex operation of traditional planning [4].
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2023.3312287
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
2 VOLUME XX, 2017
The site selection and construction of base stations (BSs)
entails three planning objectives: coverage, user demand,
and signal quality[5]. The scientific planning requires using
the BS location and coverage information, combined with
the capacity and transceiver characteristics of the proposed
BS[6]. In addition, the construction cost is a significant
factor in meeting the user service demand while ensuring
the BS radius and coverage design. Therefore, to solve such
problems, there are two main approaches: using the
coverage area[7] or the size of the service volume[6] for
deciding whether to meet the demand. The solution to the
coverage area approach can be divided into two categories:
Set Covering Location Problems (SCLP)[8], which aim to
minimize the cost of meeting the demanding across all
areas, and Maximal Covering Location Problems
(MCLP)[9], which aim to achieve as large an area as
possible at a given cost. Given its practical applications in
fields such as electronic vehicle BSs[10] and Unmanned
Aerial Vehicle (UAV) BSs[11], MCLP has been paid
considerable attention by many scholars.
Various methods and tools have been used practically to
determine the optimal construction location of BS for
communication network planning. In the past, researchers
often utilized multi-objective linear programming methods
to solve these problems; however, over time various
approaches such as simulated annealing algorithm[12],
particle swarm optimization algorithm[13], genetic
algorithm[5], discrete fireworks algorithm[6], and greedy
algorithm[14] have gradually become the mainstream
solutions to such problems. Among them, multi-objective
linear programming methods provide higher-quality
solutions by relaxing some constraints[15]. The
performance of population-based evolutionary algorithms,
such as genetic algorithms, extensively depends on the
efficiency of coding[6]. Hence, developing new algorithms
or taking measures to improve the existing methods is
crucial.
In the previous period, many scholars have proposed
various models for constructing BS, among which, the two-
step model proposed by Downs and Camm[16] opened up
new ideas for solving such problems. The first step of this
model is to determine the candidate locations set (CLS),
and the second step is to select the alternative sites that
satisfy the conditions in the corresponding CLS using a
heuristic algorithm to achieve the maximum coverage. This
method can find the optimal solution in most cases. Instead
of the two-step model. He et al. proposed a three-step
model [17], which selects CLSs as the initialization phase
in the first step, like the two-step model. In the second step,
they remove some alternative BS coordinates with low
coverage service from the selected CLSs as the correction
phase. Further, they select alternative sites based on the
correction phase in the third step to achieve maximum
coverage. Besides, Amine et al.[18] considered several
factors for BS construction in a realistic situation,
constrained the traffic demand, and used the optimal
coverage with the lowest economic overhead as the
planning objective. Genetic algorithms were applied to
solve this multi-objective planning problem.
Recently, many scholars have considered several
practical factors in the existing BS siting problems. A
distance-decaying function for the facility coverage was
considered by Haghi et al.[19]. Arana-Jiménez et al.[20]
modeled this problem from a fuzzy perspective producing
suitable fuzzy solutions. The study of Baldomero-Naranjo
et al.[21] considered the demand unknown and distributed
along the edges. In the study of Tedeschi and Andretta[22],
the problem of selecting the optimal site for a BS with
elliptical coverage is considered. Rodriguez et al.[23]
analyzed the effect of vehicles' average utilization on the
siting in a study on facility location and equipment
emplacement led by. Nwelih et al.[24] introduced a
weighted fitness function that combines coverage, capacity,
and transmit power parameters in this field. However, in
most of the articles, only the influence of the selection of
coordinates for a single type of BS was considered,
neglecting the complexity of the practical situation where
multiple types of BSs work in combination[25, 26]. Besides,
only a few papers provide solutions for practical situations
of a large order of magnitude[17, 27].
In summary, the current BS placement methodology has
several challenges and limitations, as follows:
(1) Most of them contain only a single type of base
station construction and do not consider a mixture of
multiple BSs.
(2) The stability problem of coexistence between BSs,
i.e., the threshold between BSs, is not ignored.
(3) Most of the siting schemes have optimization space.
Moreover, only partially utilize the optimization algorithm
to reach the optimal solution for a given situation.
Based on the above analysis, this paper intends to
consider a network planning model that applies to multiple
BS working together and it is suitable for large-scale data
computation adopting the proposed improved three-step
model to meet the multiple requirements of BS planning
(including coverage, user requirements, and signal quality).
The three-step model entirely considers the challenges
and limitations proposed above and expects to use
clustering ideas to solve the stability problem of BS
coexistence and optimization ideas to solve the problem of
mixed construction of multiple BSs and the optimal
solution of the scheme.
The ideas of the model mainly consist of the following
three points:
(1) Preliminary clustering of a large number of BS
coordinates data points based on the DBSCAN algorithm,
where (the radius parameter)
is set to a given threshold
of 10 between BSs and (the neighborhood density threshold)
parameter is 1. Computer simulation can obtain the set of
coordinates of the proposed station site;
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2023.3312287
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
3 VOLUME XX, 2017
(2) Optimizing the set of proposed site coordinates
obtained by the DBSCAN algorithm in (1) and using the K-
means algorithm to cluster the obtained set of site
coordinates can avoid some of the data clusters in (1) being
too large to ensure the stability of the BS operation (the
radius of the cluster exceeds a given threshold distance),
where the parameter K of the algorithm is one-tenth of the
maximum value of the horizontal and vertical distance of
the cluster in which it is located.
(3) Considering the actual situation of mixed
construction of multiple BSs, the set of coordinates of the
proposed BSs obtained in (2) is optimized again, and the
station coordinates are used to select which BS to be
constructed as the decision variable, the total cost of
construction is minimized as the objective function, and the
service volume in the coverage area is greater than 90% of
the total service volume as the constraint for planning.
Finally, based on the simulated annealing algorithm
(algorithm parameters: initial temperature of 1000,
maximum number of iterations of 1000, number of
iterations at each temperature of 10000, and temperature
decay coefficient of 0.95), the final station plan is obtained.
The planning model can be applied to various BS
network planning models. It represents a breakthrough
from most traditional BS planning models that include only
a single type of BS and can combine different types of BSs
to achieve optimal planning objectives. Also, the model has
a flexible structure, and the BS site planning for any
requirement can be accomplished by converting the
specified constraints and established objectives of the
actual problem into the corresponding parts of the model.
Besides, with the aid of the clustering algorithms, the
method proposed in this paper (combining initialization in
step 1 with correction of optional station coordinates in step
2) can greatly reduce the amount of data to be processed
during the optimization of the planning scheme (in step 3).
The effectiveness of the model is verified in a 2500×2500
test data set.
This paper uses a real dataset with a size of 2500×2500
as an example to explain how the model works. The
remaining parts of this paper are organized as follows.
Section 2 discusses the BS data pre-processing. Section 3
demonstrates how the three-step model works to obtain the
best plan for BS arrangement. Section 4 summarizes the
final scheme and model characteristics and presents ideas
for future research.
II. BASE STATION DATA MUNGING
This paper uses a fixed area of size 2500×2500 raster as an
example to construct new base stations (BSs). Information on
the indicators of each raster area includes whether it is a weak
coverage point, the service volume in the raster area, and the
latitude and longitude coordinates (simplified to geographical
horizontal and vertical coordinates).
Firstly, for the given data, careful observation was made,
and it was found that the amount of weakly covered raster data
needed to be more robust and conducive to the subsequent
solution of the model. Fig. 1 shows the location of the 182,807
data points in the planning area.
FIGURE 1. Visualization of the location of weak coverage points.
Considering the temporal complexity of the calculation, it
is decided to pre-process the data. Since the plan requires
coverage of more than 90% of the services, this paper sorts all
the weak coverage data in ascending order by service volume.
It is found that the number of data points accounts for 70.01%
of the total data when the service volume accumulates to 5%.
Although these data are extensive, they have little impact on
demand, and will hardly appear in the later planning coverage
calculation. Therefore, we decide to eliminate this part of the
data and complete the data simplification. A random sample
of 2,000 data points from the BS data source is analyzed
descriptively, and a significant degree of dispersion between
the data is found. Fig. 2 displays that eliminating some points
with minimal service volume not only facilitates the
calculation but also facilitates the subsequent clustering of the
features presented, thereby ensuring the coverage of the
service requirements. Thus, this processing is reasonable and
scientific.
FIGURE 2. Descriptive statistics chart for business volume sampling.
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2023.3312287
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
4 VOLUME XX, 2017
The data were then checked for outliers and missing values,
and all data were found to be present and reasonable. At this
point, the analysis and pre-processing of the data are
completed. The locations of the 54,817 data points filtered
after pre-processing the data are illustrated in Fig. 3.
FIGURE 3. Visualization of weak coverage point locations after filtering.
III. MODELLING AND SOLVING
When investigating the demand data of Base Stations(BSs) in
the selected area, three things need to be taken into
consideration: latitude and longitude coordinates, signal
coverage strength, and total service volume in this grid. To
improve the signal coverage strength of the area, the coverage
demand should reach at least 90% of the total service volume
when the network BSs planning is completed. In addition, to
ensure signal stability, the distance between the BSs must be
greater than the given threshold value. In the actual network
planning, the signal coverage strength and stability, the cost of
building BSs, and some other practical factors must be taken
into consideration. This paper divides BSs into macro and
micro BSs. In this article, the coverage area of macro BSs is
30 grid units in radius, and the cost is 10 value units. In
comparison, the coverage area of micro BSs is 10 grid units in
radius, and the price is 1 value unit. The following part of this
section illustrates how our model works to deploy BSs.
A. Step 1: Roughly Selecting the Alternative
Coordinates for the BS Based on DBSCAN Algorithm
The site selection and construction of base stations(BSs) have
the following characteristics:
1. The number of base stations to be constructed is still
being determined. More base stations may be required in areas
with high traffic density. In contrast, areas with low traffic
density may require fewer base stations.
2. There is a constraint between the base station coverage
radius and the coordinates of weak coverage points. If the
service volume demand of two weak coverage points is
satisfied by the same BS, the distance between the two weak
coverage points should be less than twice the distance of the
BS coverage radius (i.e., the diameter of the BS coverage area).
The DBSCAN clustering algorithm has the following
characteristics:
1. Compared with other clustering algorithms, the
DBSCAN algorithm does not need to determine the number
of clusters in advance.
2. The parameter that needs to be determined for the
DBSCAN algorithm is the maximum coverage radius. The
idea of this algorithm is that if the distance between two data
points is less than or equal to a certain threshold, then these
two points belong to the same cluster.
By continuously performing simulation iterations, the
DBSCAN algorithm can determine the number of clusters
actively and combine the coordinates of weak coverage point
locations with the base station coverage radius. Therefore, we
choose the DBSCAN algorithm in the initial base station
construction coordinates selection.
To simplify the planning complexity, this paper first
considers only micro BSs when selecting BS sites. A single
macro BS is subsequently used to replace multiple similar
micro BSs to save the cost. Since the coverage of the micro
BSs is 10, we set
(the radius parameter) to 10 and
MinPts
(the neighborhood density threshold) parameter to 1, i.e., no
noise points by default [28, 29]. By inputting pre-processed
weak coverage raster data, preliminary clustering results can
be obtained, and the results are shown in Fig. 4.
FIGURE 4. DBSCAN clustering results.
Next, the center coordinate of each cluster in the clustering
result is denoted as
( , )
center center
XY
for a cluster containing
n
data points:
1
1n
center i
i
XX
n=
=
(1)
1
1n
center i
i
YY
n=
=
(2)
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2023.3312287
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
5 VOLUME XX, 2017
Where
i
X
represents the horizontal coordinate of the i-th
point in a certain cluster, and
i
Y
represents the vertical
coordinate of the i-th point in a certain cluster.
FIGURE 5. Scatter plot of DBSCAN clustering centers.
It is observed from Fig. 5 that the clustering effect is
relatively significant, and the goal of clustering the weak
coverage points is initially achieved. After continuous iterative
calculations in Matlab, the results of some clustering centers
and the number of points they contain are shown in Table 1.
TABLE 1. Results of the DBSCAN clustering center calculation.
No.
x coordinate
y coordinate
Number of
points in the
cluster
1
1963
1341
556
2
1901
874
442
3
1956
2146
433
4
1098
421
402
5
1844
2432
352
6
1872
2214
337
...
...
...
...
3353
869
2292
1
3354
1356
2271
1
3355
844
1962
1
Table 1 demonstrates that, after clustering, the largest
cluster contains 556 coordinates, which is larger than the
maximum value of the coverage (314) for a single micro BS.
It can be seen in Fig. 6 that the DBSCAN clustering method
only allows the existence of two points whose distance is less
than the given radius parameter. However, not all the points
within the cluster are necessarily within a circle whose radius
is the parameter (
)[30]. The cluster centers generated only
by the iterative DBSCAN clustering method may not be used
as alternative coordinates for the initial micro BSs, as they
may ignore some points and may not meet the 90% service
demand requirement. Therefore, further clustering is required
for some clusters with a more substantial coordinate coverage.
FIGURE 6. Schematic diagram of DBSCAN clustering result.
B. Step 2: Correcting and Further Refining the
Alternative BS Coordinates Based on K-means
Algorithm
The K-means clustering algorithm is used for the secondary
clustering, which is to further separate the clusters that exceed
the coverage of the micro BS. This algorithm divides the
sample into K clusters and minimizes the sum of the distances
between all objects in the sample space and their cluster
centers[31-33]. The clusters that do not meet the predefined
threshold in the initial clustering are subjected to a secondary
clustering analysis. The K value for each cluster is selected
individually. The two furthest data distance from the
x
coordinate in a single cluster is called
max
x
, and the two
furthest data distance from the
y
coordinate is called
max
y
.
Since the micro base radius parameter
is 10, the number of
clusters K for a single sample space is expressed as follows.
max max
max{ , }
10 10
xy
K
=
(3)
By updating the DBSCAN clustering results with the
clustering results of K-means, 5,815 clustering centers can be
chosen for BS sites. If all 5,815 clustering centers are built
with micro BSs, the entire service volume can be covered.
Alternatively, if some of the 5,815 clustering centers are
selected to establish macro BSs, some to build micro BSs, and
the rest to remain BS-free, the construction cost can be
significantly reduced while still reaching the planning target
of a 90% service volume. The 5,815 clustered centers have
been identified as potential sites for new BSs and are shown in
Fig. 7 for visualization purposes.
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2023.3312287
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
6 VOLUME XX, 2017
FIGURE 7. Site planning model visualization results.
Some summary results of the final clustering centers are
given in Table 2.
TABLE 2. Summary results of the final clustering centers.
Serial number
x coordinate
y coordinate
1
444
640
2
123
1053
3
938
678
4
303
663
5
1672
768
6
711
254
...
...
...
5813
833
1011
5814
273
555
5815
660
753
C. Step 3: Objective optimization model based on SAA
Nowadays, the architecture of a 5G network is more complex
than that of a 4G network, and the emergence of 5G microbes
can effectively improve the cost-effectiveness of network BS
construction and optimize the service capacity of the system.
Since the above two clustering steps have ensured signal
coverage and stability, the third optimization step can be
performed by combining the results of the above two
clustering steps with the minimum total cost as the objective
function and the minimum workload as the constraint to form
a planning model. The intelligent optimization based on a
simulated annealing algorithm is used to further improve the
network base station siting scheme by adjusting the number of
stations and macro and micro BS types and changing the
station layout.
In addition, it should be emphasized that the signal coverage
of the network BS construction scheme and the signal
interference generated by the coexistence of macro and micro
BSs are also factors and objectives that we need to consider.
However, in the first two steps of clustering, the DBSCAN
algorithm in the first step ensures the signal coverage, and the
K-means algorithm in the second step ensures the stability of
the coexisting signals of macro and micro BSs, so both of them
play a simplified contribution to the overall optimization
objective.
To obtain the optimal construction plan for BSs, this paper
considers the selection of new BSs as the decision variable,
the minimum total cost of new BSs as the objective function,
and the constraint that the service volume within the
coverage area is greater than 90% of the total service volume.
In summary, the following model can be obtained.
Objective function:
min 10
Micro Base Station Macro Base Station
P num num=+
(4)
Binding conditions:
1
( ) 90%
n
i
i
Traffic Total Traffic
=
(5)
The work described in this paper chooses possible station
coordinates randomly, and the range of choices is as follows.
0,
1,
2,
no base stations
Micro base stations
Macro base stations
(6)
At the same time, to avoid the new-generated macro BS
coverage including the surrounding micro BS coverage, the
alternative sites within both the macro BS and the micro BS
coverage are set as the first choice by Matlab, i.e., no BS is
established. According to this model, this problem can be
solved using the SAA, which is a heuristic optimization
algorithm that theoretically finds the optimal global
solution[34, 35]. Therefore, it is employed to provide the
optimal siting solution. The initialization parameters for SSA
in this paper are set as shown in the following Table 3.
TABLE 3. Initialization parameter settings for the SAA
Parameters
Value
Initial temperature
1000
Maximum number of iterations
1000
Number of iterations at each temperature
10000
Temperature decay coefficient
0.95
In this paper, macro BSs are established at all optional sites
as the initial condition. Finally, the construction cost of these
BSs converges to 2,149 after about 482 iterations. During this
process, 102 macro BSs and 1129 micro BSs are established,
covering 90.03% of the total service volume and achieving the
target of providing service coverage to 90% service volume.
The change in the cost of each iteration and the siting options
for some BSs is shown in Fig. 8.
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2023.3312287
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
7 VOLUME XX, 2017
FIGURE 8. The plot of the number of iterations versus minimum cost.
The final visualization of the BS is depicted in Fig. 9.
FIGURE 9. Final site plan.
IV. MODEL COMPARISON
The optimal BS construction plan and its required cost are
finally obtained through the optimization calculation of the
above steps. On this basis, we selected some calculation
results of the same context as this problem, used the same
data set for comparison, and confirmed the superiority and
practicality of the three-step model. The specific results are
shown in the following table：
TABLE 4. Comparison of different models
Method
Number
of
micro
BSs
Number
of
macro
BSs
Total
Cost
Coverage
area
SAA[36]
7168
1566
22828
98.23%
DBSCAN
[37]
1058
868
9738
>=90%
K-means
+PSO[38]
942
365
4592
91.28%
Three-step
model
1129
102
2149
90.03%
Compared with the optimization scheme using SAA alone,
it is found that without the constraint of pre-clustering, the
calculation results show more serious deviations, and the
coverage areas of the BSs overlap significantly. Although the
coverage areas are very substantial, the resulting cost
increase is not reasonable for applying the practical problem.
The BS site planning using the DBSCAN algorithm
combined with the exhaustive method is the opposite of the
model solution process proposed in this paper, in which the
type of BSs that can be built at each point is first determined.
Then the location of the new BSs is determined by clustering
using the DBSCAN algorithm. From the comparison of the
results of the two planning schemes, it is easy to see that the
use of the DBSCAN algorithm for site planning leads to a
high total cost. Although the problem of the coverage
threshold of the BS is well solved, the traversal algorithm
using only methods such as the exhaustive enumeration
method will make the results not optimal, and the results
have strong randomness. In contrast, the use of some
combinatorial optimization algorithms and intelligent
optimization algorithms can solve this problem well.
In this method, the weak coverage points to be planned are
first clustered using the K-means clustering method to
determine the approximate location of the BS construction
points. Then PSO is used to optimize the solution of specific
station sites considering the cost and benefit factors. The
total cost of this method is lower than the above two methods,
and it combines the ideas of clustering and optimization to
solve the problem. However, it needs to fully consider the
threshold of BSs and the waste of resources caused by
repeated planning, while the three-step model of two-layer
clustering can solve such problems very well.
V. CONCLUSION
In this paper, we present a new three-step model with practical
implications for planning optimal BS construction solutions.
The model consists of initialization, correction, refining as
well as optimization. The design parameters for BS placement
are BS coordinates (x, y), the collaboration of multiple types
of BS, and the density of BS construction. We construct the
objective function using the lowest total cost and setting the
total minimum workload of BS to 90%. The real data of a 2500
×2500 area are used for the simulation test and the results are
reasonable, confirming the effectiveness of this method for
large orders of magnitude of data and multi-types BS. This
study also leads to the following conclusions:
1. Combining the DBSCAN and K-means algorithms can
yield more accurate results. The DBSCAN clustering
algorithm identifies more concentrated points in the
alternative area and distinguishes more discrete points;
however, it may lead to the merging of adjacent clusters. In
contrast, the K-means clustering algorithm can refine the
decomposition of connected clusters, but it is more affected by
noise points.
2. The SAA can provide an optimal solution for BS siting
and construction relatively quickly to minimize costs and
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2023.3312287
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
8 VOLUME XX, 2017
satisfy the constraint of covering at least 90% of the service
volume. 1129 micro BSs and 102 macro BSs are established
in this paper, at a total cost of 2,149, covering 90.03% of the
total service volume in the area.
Introducing clustering algorithms in station site
optimization reduces spatial and temporal complexity. The
SAA, using heuristic ideas, allows the model to be solved
accurately. However, our experiments are based on Matlab
simulations, and no field experiments are conducted, so we
have neglected the height of actual geographical locations and
the issue of frequency interference between signals in real-
world scenarios. Also, in the algorithmic approach, the
selection of initial values may affect the final alternative BS
coordinates due to the multiple uses of clustering
algorithms[39] In addition, the stability of the clustering
algorithm as an unsupervised pattern recognition method[40]
is also worth considering[41]. Therefore, to meet this
experiment's needs, we over-constrained the model. In the
future, we will gradually relax certain constraints to evaluate
the model, and we will also try to improve the model by
randomly adding loss functions such as altitude and signal
interference.
Appendix A
Notes:
⚫ The DBSCAN algorithm used in the first step of
clustering
Application object: coordinate points of BSs that reach a
specific service volume;
Parameter settings:
(the radius parameter) is 10, which is
the minimum coverage radius of the BS, and
MinPts
(the
neighborhood density threshold) parameter is 1 to ensure that
all points are considered.
⚫ The K-means algorithm used in the second step of
clustering
Application object: the set of BSs whose core points and
boundary points in the cluster in the clustering result in the first
step exceed the BS threshold distance;
Parameter setting: K (number of clusters) is the maximum
value of the horizontal and vertical distance within the selected
cluster, and the formula is as follows. The 10 in the formula
depends on the stability distance of the BS threshold.
max max
max{ , }
10 10
xy
K
=
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content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2023.3312287
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⚫ SAA used in the third optimization step
Application object: a planning model in which the station
coordinates are used to select which BS to build as the decision
variable, the least total cost of construction as the objective
function, and the service volume in the coverage area is more
significant than 90% of the total service volume as the
constraint;
Parameter settings: The specific parameter settings of the
simulated annealing algorithm are shown below. The values
of these parameters are obtained by comparing multiple
simulations.
Parameters
Value
Initial temperature
1000
Maximum number of iterations
1000
Number of iterations at each temperature
10000
Temperature decay coefficient
0.95
Appendix B
The data in this article represents the existing network
coverage in a specific city area. The data has been rasterized
for computational convenience, dividing the area into a
2500x2500 coordinate grid.
The dataset contains information about 182,808 weak
coverage points within this 2500x2500 coordinate grid. The
information includes each weak coverage point's X and Y
coordinates and the corresponding traffic volume. In this area,
the minimum traffic volume among the weak coverage points
is 0.000192, the maximum traffic volume is 47,795.01, and the
average traffic volume of the weak coverage points is 38.59.
Appendix C
The abbreviations of terms used in the article are as follows:
Full name
abbreviation
Base Station
BS
Simulated Annealing Algorithm
SAA
Set Covering Location Problems
SCLP
Maximal Covering Location Problems
MCLP
Unmanned Aerial Vehicle
UAV
Candidate Locations Set
CLS
Particle Swarm Optimization
PSO
Appendix D
The explanations of the parameters in this article are as follows:
Parameter
Explanation
in DBSCAN algorithm
neighborhood radius
MinPts
in DBSCAN
algorithm
minimum number of points
K in K-means algorithm
Number of clustering
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This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2023.3312287
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
/ VOLUME XX, 2017
LIN-SHEN YANG was born in Tianjin, China, in
2002. He is currently pursuing a B.E. degree in
artificial intelligence from Tiangong University,
Tianjin, China. His main research interest includes
pattern recognition and deep learning.
BIN WEN was born in Hubei, China, in 2002. He
is currently pursuing a B.E. degree in artificial
intelligence from Tiangong University, Tianjin,
China. His main research interest includes
machine learning and data mining.
JIE-JUN YAN was born in Jiangsu, China, in
2001. He is currently pursuing a B.E. degree in
artificial intelligence from Tiangong University,
Tianjin, China. His main research interest includes
data clustering and regression calculations,
modeling estimation, and data prediction.
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2023.3312287
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
