# MABC: Power-Based Location Planning with a Modified ABC Algorithm for 5G Networks

Authors: Ruchi Sachan; Zahid Muhammad; Jaehoon (Paul) Jeong; Chang Wook Ahn; Hee Yong Youn
Journal: Discrete Dynamics in Nature and Society
 (2017)

---

## Abstract

The modernization of smart devices has emerged in exponential growth in data traffic for a high-capacity wireless network. 5G networks must be capable of handling the excessive stress associated with resource allocation methods for its successful deployment. We also need to take care of the problem of causing energy consumption during the dense deployment process. The dense deployment results in severe power consumption because of fulfilling the demands of the increasing traffic load accommodated by base stations. This paper proposes an improved Artificial Bee Colony (ABC) algorithm which uses the set of variables such as the transmission power and location of each base station (BS) to improve the accuracy of localization of a user equipment (UE) for the efficient energy consumption at BSes. To estimate the optimal configuration of BSes and reduce the power requirement of connected UEs, we enhanced the ABC algorithm, which is named a Modified ABC (MABC) algorithm, and compared it with the latest work on Real-Coded Genetic Algorithm (RCGA) and Differential Evolution (DE) algorithm. The proposed algorithm not only determines the optimal coverage of underutilized BSes but also optimizes the power utilization considering the green networks. The performance comparisons of the modified algorithms were conducted to show that the proposed approach has better effectiveness than the legacy algorithms, ABC, RCGA, and DE.


---

## Body

## 1. Introduction

An increasing number of mobile devices with data intensive applications are generating an enormous amount of data. Considering the growth of mobile devices in day-to-day life, the future networks must be capable of dealing with the ever-increasing mobile data traffic. Nowadays devices are ubiquitous with an expected cellular subscription of over 4.55 billion worldwide [1]. Most of the devices today support the majority of services like 3G and 4G-LTE recently, and next, for the future, it must be capable of handling the rise of the critical factors such as excessive data traffic stress along with 5G networks. Radio access networks almost consume 80% of the power in cellular networks in recent communication technology due to irregular planning [2]. Moreover, it is noted that base stations (BSes) consume a significant amount of the energy (above 50%) in cellular networks [3, 4]. To estimate the locations of BSes to optimize the transmission power concerning the green aspects is required.The vision of 5G wireless communications extends to offer very high data rates, notably low latency, enhanced base station capacity, and significant improvement in users’ perceived good quality of service (QoS) compared to current 4G-LTE networks. A quick look into recent wireless network statistics reports that the global mobile traffic experienced around 70% growth [5] in 2014. Only 26% smartphones (of the total global mobile devices) are responsible for 88% of total mobile data traffic [5] and more than 50% energy consumption spent by the BSes [2, 3].The following information is usually needed to address the network planning problem for systems with 5G air interface: (1) a set of candidate sites that is required where BSes can be installed, (2) a set of possible configuration setting that is needed for each BS’s orientation, height, and maximum power to allocate the location of BSes, (3) traffic distribution parameter which represents the connected users moving around the cell, and (4) propagation radio channel models with allocated frequency which can support the upcoming 5G wireless networks. The mentioned points above can be used to estimate the accurate information of future users in 5G wireless network. By installing the sufficient BSes in a possible position based on the user’s behavior, we can enhance the power efficiency of the network [6]. Location information was also available in previous generations of cellular networks regarding different perspectives in 2G, 3G, and 4G. For instance, cell-ID positioning is used in 2G, timing-based positioning is used in 3G, and dedicated positioning is used in 4G. Even with the above location information, the researchers of 5G [7] have found that the range from hundreds to tens of meters is insufficient for some communication operations. So for the first time majority of user equipments (UEs) can benefit from the positioning technologies which can achieve location accuracy in the order of one meter. 5G should be the first generation to get a benefit from position information for wireless network design and optimization.In this paper, we have modified the Artificial Bee Colony (ABC) algorithm [8] to optimize the location estimation with the minimum power required for the UEs with less activated BSes. Through the comparison of Modified ABC (MABC) with the other mentioned algorithms such as Real-Coded Genetic Algorithm (RCGA) and Differential Evolution (DE) algorithm, we found that even the modified RCGA (MRGA) with the shuffling of their chromosome could not precisely find an optimum solution [4]. However, the standard ABC has performed well, compared to the other implemented techniques, such as RCGA, MRGA, and DE, because of its different methods of playing employed bees and scout bees to optimize the solution efficiently for our targeted problem.The paper is structured as follows: Section2 introduces a literature survey which compares our work with other tasks of optimizing the energy consumption in wireless cellular networks. In Section 3, system model presents a description of the general framework for 5G network planning. Section 4 compares the implementation of the Modified ABC algorithm to the targeted problem with its applications. Section 5 shows the experimental results obtained from our proposed methods with the perspective of 5G networks aspects. Finally, Section 6 concludes our work along with future work.


## 2. Related Work

Till now, many researchers have studied the network design problems related to planning and performance optimization in cellular networks considering the latest advancements in the technologies. There are many possible ways to find a precise location information in wireless network system along with parameters such as distances, velocities, angles, delays, and predictable user behaviors [7]. In 5G networks, a location awareness system can be engaged in a wide range of ways to address several keys challenges. Due to the ability of network planning to perform the resource allocation by expecting the channel quality apart from the traditional time scale mentioned in the CSI- (channel state information-) based solution, it can reduce the overhead and delay of the location-aware resource allocation techniques.In [9], Berrocal-Plaza et al. discussed the optimal location-aware configuration issue by using the Evolutionary Algorithms (EAs), such as Genetic Algorithm (GA) and ABC, to efficiently meet the coverage and traffic requirements for the targeted BSes. They aimed to make a GA in [9] into two versions, named FPS-GA (Genetic Algorithm with Fixed Population Size) and APS-GA (Genetic Algorithm with Adaptive Population Size), to minimize the interference among cells and reduce the energy consumption. It is noted that the balanced load could not completely satisfy the UEs by using the FPS-GA and APS-GA. However, the ABC algorithm required less computational efforts than both FPS-GA and APS-GA.The location area schemes in [10–12] explain the recent developments in the cellular technologies. They partition a network into the multiple regions or location areas, consisting of one or more cells for each region, by updating the performance of the UEs according to the exact optimal locations of the BSes. Another location management scheme is suggested in [13] where a subset of cells in the network are designated as the reporting cells, and each UE performs its location update only when it enters one of the targeted reporting cells. The objective for using the reporting cell is when a call arrives, the search will define the task of the reporting cell which the user has last reported and the neighboring bounded by the nonreporting cells. Taking advantage of targeted reporting cells, the authors have generated the optimized results by using GA, Tabu Search (TS), and Ant Colony Algorithm (ACA) for the location management.In [4], the authors modified the traditional RGA to make novel GAs for the future generation of cellular networks. As they mentioned that because of shuffling all the chromosome in crossover operation, the performance of standard RGA makes worst solution over the generation. So for solving the network planning problem by making MRGA perform better than RGA, they introduced Box Crossover Rate (BCR) with less shuffling in crossover operation and small standard deviation values and also compared the results with DE where they use Scaling Factor 0.5 and Crossover Rate 0.9 for DE over the 50 independent runs.In [14], Ali et al. considered the simultaneous planning of BSes and Relay Stations (RSes) with the link capacity by using EAs. They aimed at finding an optimized set of BSes and RSes that can fulfill the demand of UEs at the lowest cost. Yu et al. in [15] considered a large coverage area that requires high computation time intractable to the network planning problem.For tackling the issue of sustainable energy consumption, some researchers in [16, 17] also examined the methods of achieving optimal energy saving by turning off traffic under loaded BSes. In [16], disabling the unwanted cells with low traffic conserves a significant amount of energy, similar to most of the studies for the power saving progress, where most of the researchers tackle the sleeping mode at UEs [17].


## 3. System Model

In this section, we considered a network planning to design the system model which satisfies the area of[
W
×
H
]
k
m
2 for both LTE and 5G networks. In our system model, BSes can be installed at a set of candidate sites H
=
h
1
,
h
2
,
…
,
h
M in the given targeted area. In order to place the BSes, the installation cost is associated with each of the candidate sites such that C
=
c
1
,
c
2
,
…
,
c
M. In our experiment, K denotes the number of BSes; the set of BSes is represented as S
=
s
1
,
s
2
,
…
,
s
K.Our aim is to design a network planning process to minimize the power consumption. The transmission power in a range of 0.1 to 10 watts has been considered as a transmitter attribute for our optimization algorithm. However, the value of antenna gain depends on the manufacture, but we have considered the antenna gain as 18 dBi and frequency as 1800 MHz [18, 19]. We employ the radio propagation model also known as Cost-231 HATA urban propagation model which enlarges the urban HATA model to cover a more expanded range of frequencies [8, 20]. In (1), the Signal-to-Interference-plus-Noise Ratio (SINR) value is calculated, where the coverage probability in the given area around the location h
i with a threshold is less than the SINR value. M
g represents the Mast Head Amplifier (MHA) gain, P
t represents the transmission power, and I and N account for the interference and noise, sequentially:(1)
SINR
=
M
g
×
P
t
I
+
N
.After getting the value of SINR, the path loss (PL) is determined by(2)
PL
dB
=
P
t
+
G
t
-
L
b
-
SINR
,where G
t represents the antenna gain of the transmitter and L
b represents the body loss in dB. Furthermore, the coverage area of a BS is expressed by(3)
CA
b
i
=
3
3
R
2
2
,where R represents the cell radius. The coverage probability in the given area around the location h
i having threshold T is defined in(4)
P
c
h
i
=
P
SINR
h
i
>
T
.


## 4. The Proposed Algorithm

The application of EAs, namely, GA, DE, RCGA, and ABC, is a stochastic exploration search method to resolve both constrained and unconstrained optimization problems, which originates from the natural selection. In this terminology, an individual is referred to as a candidate solution to the targeted optimization problem. These algorithms deal with a set of individuals during their process called the population. ABC is one of the efficient applications of EAs which we have applied and we extended the traditional ABC to a Modified Artificial Bee Colony (MABC) and compared with our previous work of modified RCGA called MRGA. RCGA contains a continuous decision variable where the GA contains a binary coded variable that is a primary difference between GA and RCGA. The application of EAs gives satisfactory solutions to NP-hard problems. Additionally, EAs are also used to solve many practical problems, such as the finding of an optimal position for a BS in an explicitly particular area of interest [21, 22].


### 4.1. Encoding

The fundamental design of chromosomes is a primary phase of any application of EAs. A chromosome is a set of parameters which specify a proposed solution to the targeted problem that the algorithm is trying to resolve. Usually, a set of chromosomes is a possible settlement for gaining a better representation of an optimal solution of any NP-hard problem.This paper defines the available transmit power (Q
i) and location of a BS (X
i
,
Y
i) as a decision variable to the target problem. Here we have used only a constant value for representing a chromosome. The solution of the targeted problem uses these decision variables for chromosomes as described in the following list:Decision Variables
Q
i: available transmit power of a base station s
i  [0.1 to 10.0] Watt
X
i: location of a base station s
i in x-axis
Y
i: location of a base station s
i in y-axis.The structure of chromosome is presented in Figure1 where a set of the populations represents a generation. The population consists of a set of P individuals. In general, a set of individuals is called a population in EAs. Each individual is composed of K BSes where one BS has three decision variables such as its power (Q
i), location-X (X
i), and location-Y (Y
i).Figure 1
The structure of chromosomes.


### 4.2. Artificial Bee Colony

A new and recent application of EAs defines ABC as a swarm intelligence algorithm which is driven by the behavior of honey bees. ABC simulates the intelligent foraging behavior of real honey bees on finding food positions for their nectar source. ABC algorithm contains three groups of bees: employed bees, onlooker bees, and scout bees. The employed bees have always got a chance to start searching for food around the given food source in their memory, and then they share the information about these food sources with the onlooker bees. The onlooker bees get the chance to select good food sources during sharing information by employed bees. The higher quality of the food source has a significant chance to be chosen by the onlooker bees. The scout bees convert from a few employed bees that abandon their food sources in the process and search for new ones [23].In our algorithm, a food source position signifies a possible solution to the optimization problem as an individual in the population, and the nectar quality resembles their fitness function value. The general procedure of ABC is described in the following points.


#### 4.2.1. Initialization of the Population

The initial phase of ABC algorithm first generates an initial population randomly according to a uniform distribution within a possible space. The BS axes (X
,
Y) are represented as a configuration with having the ranges of power Q
=
[
Q
m
i
n
,
Q
m
a
x
]. Here Q
m
i
n and Q
m
a
x are the minimum and maximum power required to each BS in the unit of watts. Consider, for ABC, X
=
1,2
,
…
,
D and Y
=
1,2
,
…
,
D, such as two series of length vector D with required power range [
Q
m
i
n
,
Q
m
a
x
]. Forming the two-time series pairwise results in a set, S
=
s
1
,
s
2
,
…
,
s
D
,
Q, where S
i
=
(
X
i
,
Y
i
). Rearrange BSes according to the values of X
i and Y
i. It gets an order set like S
i
=
X
1
,
Y
1
,
X
2
,
Y
2
,
…
,
X
D
,
Y
D
,
Q
D. All these values are bounded within the range of a lower bound to an upper bound with the random number between r
a
n
d
(
0,1
) during the initialization of the population.An ABC procedure produces a uniformly distributed population of solutions ofP number where each solution refers to the solution of each decision variable taken in our simulation. The solution in our simulation represents BSes as S
i
=
i
=
1,2
,
…
,
P and users as U
i
=
i
=
1,2
,
…
,
P with a given D-dimensional vector. Here D is the number of variables to be optimized as j
∈
1,2
,
…
,
D, and S
i and U
i represent the ith food source in the population. The BS S
i and the user U
i are generated as follows in (5) and (6):(5)
S
i
j
=
S
LB
j
+
rand
⁡
0,1
S
UB
j
-
S
LB
j
,where S
LB
j and S
UB
j are the lower bounds and upper bounds of BSes S
i in the jth directions. (6)
U
i
j
=
U
LB
j
+
rand
⁡
0,1
U
UB
j
-
U
LB
j
,where U
LB
j and U
UB
j are the lower bound and upper bound of given the user U
i in the jth directions.


#### 4.2.2. Employed Bees Phase

In the employed bee phase, employed bees modify the current solution obtained from the neighborhood of the current food source based on the information of individual experiences, and their fitness values mean nectar amount of the new solution. The bee updates their positionA
i by replacing the old one solution of S
i and U
i
. If the fitness value of the new food source is higher than that of the old food source, the updated solution of an ith candidate in this phase is shown in as follows:(7)
A
i
j
=
S
i
j
+
ϕ
i
j
S
i
j
-
S
k
j
,where A
i
j is a new solution of the S
i and k indicates the kth candidate solution index randomly selected from a candidate solution which must be different from the ith candidate solution. k
∈
1,2
,
…
,
P, i
∈
1,2
,
…
,
P, and j
∈
1,2
,
…
,
D are three randomly chosen indices. ϕ
i
j generates a random number within [
-
1
,
1
] with a uniform distribution.An example of the base station’s position update process in the employed bee phase is described in Figure2. Firstly, the current state of bee is represented as S
i and the highlighted box represents the randomly picked direction j. S
k is the randomly chosen bee, towards a direction of j where the randomly selected bee k
≠
i, which is subtracted from the same direction of taken ith bee. The difference is then multiplied by the random number (ϕ
i
j) which varies within [-
1,1]. Finally, this solution is added to the jth vector of S
i to get a jth dimension of a new food position A
i
j, which means the updated solution of the current S
i
j. As shown in Figure 2, it is demonstrated that all other dimensions of A
i
j are the same as those of S
i and are generated in the neighborhood of S
i
j.Figure 2
An example of the base station’s position update.


#### 4.2.3. Onlooker Bees Phase

The procedure of onlooker bee phase comes just after finishing the critical role of the employed bee phase in ABC algorithm. During the procedure, all employed bees share the quality-wise information of the updated solutions and also the position information with the onlooker bees. After getting the information from the employed bees, the onlooker bees analyze the available information and select the promising candidate solutions probabilistically based on the fitness information with its fitness function. The probabilitypro
b
i is calculated using the following expressions in(8)
fitness
i
=
1
F
i
if
F
i
≥
0
,
1
+
abs
F
i
if
F
i
<
0
,
prob
i
=
fitness
i
∑
i
P
/
2
fitness
i
,where F
i is the objective function explained in Section 4.4 in (14) and P is a population size mentioned in simulation parameters in Table 1.Table 1
Simulation parameters.
C
f
15 GHz
P
100
λ
50
G
200
P
t
0.1–10 W
A
g
18 dBi
M
g
2 dB
C
l
2 dB
MNC
3000
N
f
2 dB
L
b
2 dB
K
100
L
G
ul
X
−100
L
T
ul
Y
100
L
G
lr
X
100
L
T
lr
Y
−100
ϕ
rand[0 to 1]
NU
10000


#### 4.2.4. Scout Bees Phase

In the scout bees phase, the employed bees are those whose fitness value of food source is not updated for a predetermined number of cycles. The food source is assumed to be abandoned, and the scout bees phase starts by replacing their old solutions with searching for new solutions randomly according to (5) within the search space. For instance, if the ith solution is abandoned, a new solution is generated to replace the original one using (5), where we set i
=
1. The predetermined number of cycles is a central control parameter which is also named a limit for abandonment. Assume that, for the BS, source S
i is available in the search space; then the scout bees replace the old S
i with a new S
i food source.


### 4.3. Modified Artificial Bee Colony

The original idea of ABC algorithm performs a hierarchical optimization having a significant drawback in that it considers solutions over generations equally. This inherent disadvantage comes with the most of the population-based stochastic algorithms which relate to a premature convergence or stagnation towards a generation. When ABC tries to solve a complex problem having a large number of variables, the problem is a significant influence on the efficiency and accuracy of ABC [24, 25]. Therefore, the Modified ABC should be able to overcome the issue of the traditional ABC. In our targeted 5G network planning problem, every variable relates to its neighborhood variables. Thus, if the value of one variable changes, it directly affects its neighborhood variables and indirectly the other individual variables. To improve the conventional ABC for getting an optimal solution for our problem is required. Therefore, ABC should be made more efficient.The position updates in the conventional ABC applying (7) cannot make a large difference from the initialization of the population. After some iterations, all potential solutions work within a small proximity. In this issue, (
S
i
j
-
S
k
j
), where i and k make a slight difference without improving, sometimes becomes negligible towards a generation. This phenomenon is called a premature convergence or stagnation if the globally optimal solution is not present in this small proximity. From this point of view, this conventional ABC is not an efficient algorithm according to [26]. Thus, for making convergence rate greater while applying standard ABC to constrained problems, we need to analyze the effect of the perturbation rate which can control the frequency of parameter changes. For controlling the parameters to determine the Scaling Factor (step size), an approach to improve the standard ABC in order to make convergence rate efficient is proposed.In the traditional version of ABC, while producing a new solutionA
i, it changes only one parameter of the parent solution S
i which results in a slow convergence rate. To reduce this obstacle of the ABC optimization methods, the first change was done by the MABC as follows: our MABC proposes a new control parameter called modified mutation rate ∂. Here, for each S
i
j, a uniformly distributed random number R
i
j between 0 and 1 is generated. If the random number R
i
j is less than ∂, parameter S
i
j modifies the following:(9)
A
i
j
=
S
i
j
+
ϕ
i
j
S
i
j
-
S
k
j
,
if
R
i
j
<
∂
,
S
i
j
,
otherwise
,where k
∈
1,2
,
…
,
P, i
∈
1,2
,
…
,
P, and j
∈
1,2
,
…
,
D have randomly chosen indices. Here k must have a different random number from i and ∂ is the modified mutation rate which takes a value between 0 and 1. If ∂ gets a lower value, the solution improves slowly, but while getting a higher one, it becomes a cause of greater diversity in an optimal solution and hence in the population. Additionally, the ratio of the variance operator is also modified in MABC algorithm. In the traditional ABC, taking a random perturbation avoids getting stuck at local minima which add to the current solution in order to produce a new solution.A different random number of the solutions inS
i and S
k where k
≠
i is weighted by a real random number called ϕ
i
j. ϕ
i
j varies in the range [-
1,1], which is called a random perturbation of traditional ABC. In our MABC, the solutions S
i and S
k vary within the range [-
σ
,
σ]; hence, the second improvement of MABC was done by presenting the control parameter (σ) as a Scaling Factor that means a step size to control the magnitude of the perturbation. A smaller value of σ allows for the process in small steps, leading to slow convergence while having a larger value of σ speeds up the steps, but it reduces the exploitation capability of the perturbation method. The function of σ in (10) defines a heuristic rule which assigns different values depending on the number of generations. The mutation step size σ
(
g
) is given as a function for g in (10). The employed bees and onlooker bees both use this expression to search for the neighbor food source. We have more enhancement in the algorithm regarding the fitness function evaluation which is counted as the third improvement for our MABC. If the number of fitness evaluations decreases, the algorithm runs faster than having more fitness evaluations. In our modified MABC, what we have done differently for the traditional ABC is described in Algorithm 1 of modified employed bees and Algorithm 2 of modified onlooker bees. As we have used this expression in employed bees and onlooker bees during the process of these bees, the MABC algorithm is set only to evaluate those chromosomes which are already modified in the greedy selection method. If we apply this expression for selecting the neighbor food source, it does not always repeat a new food source position due to the constraints given in algorithms. It means that the MABC algorithm checks whether a food source has been modified or not before proceeding with the fitness function evaluation. This checking-in MABC helps to eliminate a number of fitness evaluations for the modified individuals that have already been evaluated in the past generation. We also considered that the algorithm can converge to an optimal solution.(10)
σ
g
=
1
-
0.9
×
g
G
,where G is a maximum generation number and current generation number (g) varies from 0 to G. The mutation step size σ
(
g
) follows all variables of each vector in the population. In the start, it will decrease slowly from 1 at the beginning of the run during (g
=
0) to 0.1 as the number of generations g approaches G. Thus, this decrease of σ
(
g
) performs the best tuning capability of the proposed algorithm.Algorithm 1:The modified employed bees.
(1)Begin
(2) Cycle (T) = 0, t
j
=
1
(3)For  i
=
0 to i
=
P
/
2 (Food source)
(4)
S
i
j
=
S
L
B
j
+
r
a
n
d
0,1
S
U
B
j
-
S
L
B
j
(5) Another solution S
i
j found using (Equation (11)) for each P
i called the neighborhood of the current food source
(6) Randomly pick an element j after each modified solution of ∀
i
j,  where  i
≠
k
(7) Check the fitness (F) for the new solution S
i
j
¯ taking an objective fuction using (Equation (14))
(8)
t
j
=
t
j
+
1
(9)
If  fitness of (
F[S
i
j
¯
]
≠
F
[
S
i
j
]
)  Then
(10)
Evaluate  F
[
S
i
j
¯
]
(11)
F
[
S
i
j
]
=
F
[
S
i
j
¯
]
(12)
t
j
=
0
(13)
End If
(14)End For
(15)
T
=
T
+
1
(16)EndAlgorithm 2:The modified onlooker bees.
(1)Begin
(2) Cycle (T) = 0, t
j
=
1
(3) Onlooker bee counter (OBC = 0)
(4) Another solution∀
i
k found using (Equation (11)) for each P
i called neighborhood of the current food source
(5)
While  (OBC < P
/
2 (Food source))
(6)
If  (
r
a
n
d
(
0,1
)
<
p
r
o
b
i
)  Then
(7) Onlooker bee select the employed bee and become an employed bee,
(8) OBC = OBC + 1,
(9) Repeat employed bee phase Algorithm
1
(10) Check the fitness (F) for the new solution S
i
j
¯ taking an objective fuction using (Equation (14))
(11)
t
j
=
t
j
+
1
(12)
If  fitness of (
F[S
i
j
¯
]
≠
F
[
S
i
j
]
)  Then
(13)
Evaluate  F
[
S
i
j
¯
]
(14)
F
[
S
i
j
]
=
F
[
S
i
j
¯
]
(15)
t
j
=
0
(16)
End If
(17)
End If
(18)
End While
(19)
T
=
T
+
1
(20)EndThe fourth innovative point of our MABC is that it solves the problem of exploitation and the also convergence speed has a better tuning capability than the traditional ABC. After getting a different random perturbation ofS
i and S
k, the proposed MABC calculates a neighborhood solution ∀
i
j introduced in (11) using an inertia weight given in (12):(11)
∀
i
j
=
S
i
j
×
w
+
2
ψ
i
j
-
0.5
S
i
j
-
S
k
j
+
ϕ
i
j
B
i
j
-
S
k
j
,
(12)
w
=
0.5
+
rand
⁡
2
,where w is a random inertia weight which controls the impact of the previous solution S
i
j, the best-so-far solution is represented as B
i
j of jth dimension, ϕ
i
j is a random number within [0 to 1], and ψ
i
j follows a mutation step size process instead of varying in the range of [-
1
,
1]. The modified employed bees phase is described in Algorithm 1.MABC uses (11) instead of calculating the neighborhood solution of conventional ABC in (7) in order to proceed with a better result in the employed bee phase. After completing the employed bee phase in our proposed MABC, the onlooker bees calculate a probability in (13) as follows:(13)
prob
i
=
0.9
×
F
i
max
⁡
F
+
0.1
,where F
i is the fitness value of the ith solution in the population. The modified onlooker bees phase is described in Algorithm 2. The rest of all the procedures after the onlooker bees and scout bees phases follow the same steps as conventional ABC. In addition to these innovative points mentioned above, a new control parameter ∂ (called modified mutation rate) and a step size σ both produce a greater diversity to an optimal solution and eliminate a number of fitness evaluations for modified individuals that have already been evaluated in the past generation. As a result, they solve the problem of exploitation with the convergence speed having a better tuning capability. Therefore, our MABC has so far obtained better results than the standard ABC. The overall procedure of our proposed MABC is described in Algorithm 3.Algorithm 3:Pseudocode of MABC.
(1)Begin
(2) Initialize Users phase ()
(3) Initialize Population phase ()
(4) Memorize best solution ()
(5) Memorize the best solution S
i
j achieved so far
(6) Cycle (T) = 1
(7)While  Termination criteria is not satisfied  do
(8) SendEmployedBees () (Algorithm
1)
(9) SendOnlookerdBees () (Algorithm
2)
(10) SendScoutBees ()
(11)
If  Exist  Then
(12) Re-initialize the individual S
i
j using (Equation (5)), s
=
0
(13) Memorize the best new solution B
i
j achieved so far
(14)
If  (
B
i
j
-
S
i
j
) > Limit  Then
(15)
s
=
s
+
1
(16)
Else
(17)
s
=
max
⁡
(
1
,
s
-
1
)
(18)
B
i
j
=
S
i
j
(19)
End If
(20)
End If
(21)
T
=
T
+
1
(22)End While
(23)untill  T = MNC
(24)End


### 4.4. Fitness Evaluation

A fitness function uses a type of objective function in EAs which helps to get a solution from the evaluation of each for the survival of next generation. In ABC, each single solution exists in the target search space, which we call the type of bees. All of the bees have fitness value which is evaluated by the taken objective function to be optimized. Our approach is formulated by using the objective function given in (14) for getting the fitness (F
i) of the optimal network configuration as follows:(14)
F
i
=
U
E
2
T
P
×
ActiveBSe
s
2
,where UE is the number of connected users to the BSes, T
P represents the total transmit power, and ActiveBSes represent the number of BS such that T
P is configured for each user to be connected to a BS. We defined the maximum number of generations G as for the termination criteria. The proposed algorithm terminates after executing simulation T
g generations and returns the best-so-far solution.


## 4.1. Encoding

The fundamental design of chromosomes is a primary phase of any application of EAs. A chromosome is a set of parameters which specify a proposed solution to the targeted problem that the algorithm is trying to resolve. Usually, a set of chromosomes is a possible settlement for gaining a better representation of an optimal solution of any NP-hard problem.This paper defines the available transmit power (Q
i) and location of a BS (X
i
,
Y
i) as a decision variable to the target problem. Here we have used only a constant value for representing a chromosome. The solution of the targeted problem uses these decision variables for chromosomes as described in the following list:Decision Variables
Q
i: available transmit power of a base station s
i  [0.1 to 10.0] Watt
X
i: location of a base station s
i in x-axis
Y
i: location of a base station s
i in y-axis.The structure of chromosome is presented in Figure1 where a set of the populations represents a generation. The population consists of a set of P individuals. In general, a set of individuals is called a population in EAs. Each individual is composed of K BSes where one BS has three decision variables such as its power (Q
i), location-X (X
i), and location-Y (Y
i).Figure 1
The structure of chromosomes.


## 4.2. Artificial Bee Colony

A new and recent application of EAs defines ABC as a swarm intelligence algorithm which is driven by the behavior of honey bees. ABC simulates the intelligent foraging behavior of real honey bees on finding food positions for their nectar source. ABC algorithm contains three groups of bees: employed bees, onlooker bees, and scout bees. The employed bees have always got a chance to start searching for food around the given food source in their memory, and then they share the information about these food sources with the onlooker bees. The onlooker bees get the chance to select good food sources during sharing information by employed bees. The higher quality of the food source has a significant chance to be chosen by the onlooker bees. The scout bees convert from a few employed bees that abandon their food sources in the process and search for new ones [23].In our algorithm, a food source position signifies a possible solution to the optimization problem as an individual in the population, and the nectar quality resembles their fitness function value. The general procedure of ABC is described in the following points.


### 4.2.1. Initialization of the Population

The initial phase of ABC algorithm first generates an initial population randomly according to a uniform distribution within a possible space. The BS axes (X
,
Y) are represented as a configuration with having the ranges of power Q
=
[
Q
m
i
n
,
Q
m
a
x
]. Here Q
m
i
n and Q
m
a
x are the minimum and maximum power required to each BS in the unit of watts. Consider, for ABC, X
=
1,2
,
…
,
D and Y
=
1,2
,
…
,
D, such as two series of length vector D with required power range [
Q
m
i
n
,
Q
m
a
x
]. Forming the two-time series pairwise results in a set, S
=
s
1
,
s
2
,
…
,
s
D
,
Q, where S
i
=
(
X
i
,
Y
i
). Rearrange BSes according to the values of X
i and Y
i. It gets an order set like S
i
=
X
1
,
Y
1
,
X
2
,
Y
2
,
…
,
X
D
,
Y
D
,
Q
D. All these values are bounded within the range of a lower bound to an upper bound with the random number between r
a
n
d
(
0,1
) during the initialization of the population.An ABC procedure produces a uniformly distributed population of solutions ofP number where each solution refers to the solution of each decision variable taken in our simulation. The solution in our simulation represents BSes as S
i
=
i
=
1,2
,
…
,
P and users as U
i
=
i
=
1,2
,
…
,
P with a given D-dimensional vector. Here D is the number of variables to be optimized as j
∈
1,2
,
…
,
D, and S
i and U
i represent the ith food source in the population. The BS S
i and the user U
i are generated as follows in (5) and (6):(5)
S
i
j
=
S
LB
j
+
rand
⁡
0,1
S
UB
j
-
S
LB
j
,where S
LB
j and S
UB
j are the lower bounds and upper bounds of BSes S
i in the jth directions. (6)
U
i
j
=
U
LB
j
+
rand
⁡
0,1
U
UB
j
-
U
LB
j
,where U
LB
j and U
UB
j are the lower bound and upper bound of given the user U
i in the jth directions.


### 4.2.2. Employed Bees Phase

In the employed bee phase, employed bees modify the current solution obtained from the neighborhood of the current food source based on the information of individual experiences, and their fitness values mean nectar amount of the new solution. The bee updates their positionA
i by replacing the old one solution of S
i and U
i
. If the fitness value of the new food source is higher than that of the old food source, the updated solution of an ith candidate in this phase is shown in as follows:(7)
A
i
j
=
S
i
j
+
ϕ
i
j
S
i
j
-
S
k
j
,where A
i
j is a new solution of the S
i and k indicates the kth candidate solution index randomly selected from a candidate solution which must be different from the ith candidate solution. k
∈
1,2
,
…
,
P, i
∈
1,2
,
…
,
P, and j
∈
1,2
,
…
,
D are three randomly chosen indices. ϕ
i
j generates a random number within [
-
1
,
1
] with a uniform distribution.An example of the base station’s position update process in the employed bee phase is described in Figure2. Firstly, the current state of bee is represented as S
i and the highlighted box represents the randomly picked direction j. S
k is the randomly chosen bee, towards a direction of j where the randomly selected bee k
≠
i, which is subtracted from the same direction of taken ith bee. The difference is then multiplied by the random number (ϕ
i
j) which varies within [-
1,1]. Finally, this solution is added to the jth vector of S
i to get a jth dimension of a new food position A
i
j, which means the updated solution of the current S
i
j. As shown in Figure 2, it is demonstrated that all other dimensions of A
i
j are the same as those of S
i and are generated in the neighborhood of S
i
j.Figure 2
An example of the base station’s position update.


### 4.2.3. Onlooker Bees Phase

The procedure of onlooker bee phase comes just after finishing the critical role of the employed bee phase in ABC algorithm. During the procedure, all employed bees share the quality-wise information of the updated solutions and also the position information with the onlooker bees. After getting the information from the employed bees, the onlooker bees analyze the available information and select the promising candidate solutions probabilistically based on the fitness information with its fitness function. The probabilitypro
b
i is calculated using the following expressions in(8)
fitness
i
=
1
F
i
if
F
i
≥
0
,
1
+
abs
F
i
if
F
i
<
0
,
prob
i
=
fitness
i
∑
i
P
/
2
fitness
i
,where F
i is the objective function explained in Section 4.4 in (14) and P is a population size mentioned in simulation parameters in Table 1.Table 1
Simulation parameters.
C
f
15 GHz
P
100
λ
50
G
200
P
t
0.1–10 W
A
g
18 dBi
M
g
2 dB
C
l
2 dB
MNC
3000
N
f
2 dB
L
b
2 dB
K
100
L
G
ul
X
−100
L
T
ul
Y
100
L
G
lr
X
100
L
T
lr
Y
−100
ϕ
rand[0 to 1]
NU
10000


### 4.2.4. Scout Bees Phase

In the scout bees phase, the employed bees are those whose fitness value of food source is not updated for a predetermined number of cycles. The food source is assumed to be abandoned, and the scout bees phase starts by replacing their old solutions with searching for new solutions randomly according to (5) within the search space. For instance, if the ith solution is abandoned, a new solution is generated to replace the original one using (5), where we set i
=
1. The predetermined number of cycles is a central control parameter which is also named a limit for abandonment. Assume that, for the BS, source S
i is available in the search space; then the scout bees replace the old S
i with a new S
i food source.


## 4.2.1. Initialization of the Population

The initial phase of ABC algorithm first generates an initial population randomly according to a uniform distribution within a possible space. The BS axes (X
,
Y) are represented as a configuration with having the ranges of power Q
=
[
Q
m
i
n
,
Q
m
a
x
]. Here Q
m
i
n and Q
m
a
x are the minimum and maximum power required to each BS in the unit of watts. Consider, for ABC, X
=
1,2
,
…
,
D and Y
=
1,2
,
…
,
D, such as two series of length vector D with required power range [
Q
m
i
n
,
Q
m
a
x
]. Forming the two-time series pairwise results in a set, S
=
s
1
,
s
2
,
…
,
s
D
,
Q, where S
i
=
(
X
i
,
Y
i
). Rearrange BSes according to the values of X
i and Y
i. It gets an order set like S
i
=
X
1
,
Y
1
,
X
2
,
Y
2
,
…
,
X
D
,
Y
D
,
Q
D. All these values are bounded within the range of a lower bound to an upper bound with the random number between r
a
n
d
(
0,1
) during the initialization of the population.An ABC procedure produces a uniformly distributed population of solutions ofP number where each solution refers to the solution of each decision variable taken in our simulation. The solution in our simulation represents BSes as S
i
=
i
=
1,2
,
…
,
P and users as U
i
=
i
=
1,2
,
…
,
P with a given D-dimensional vector. Here D is the number of variables to be optimized as j
∈
1,2
,
…
,
D, and S
i and U
i represent the ith food source in the population. The BS S
i and the user U
i are generated as follows in (5) and (6):(5)
S
i
j
=
S
LB
j
+
rand
⁡
0,1
S
UB
j
-
S
LB
j
,where S
LB
j and S
UB
j are the lower bounds and upper bounds of BSes S
i in the jth directions. (6)
U
i
j
=
U
LB
j
+
rand
⁡
0,1
U
UB
j
-
U
LB
j
,where U
LB
j and U
UB
j are the lower bound and upper bound of given the user U
i in the jth directions.


## 4.2.2. Employed Bees Phase

In the employed bee phase, employed bees modify the current solution obtained from the neighborhood of the current food source based on the information of individual experiences, and their fitness values mean nectar amount of the new solution. The bee updates their positionA
i by replacing the old one solution of S
i and U
i
. If the fitness value of the new food source is higher than that of the old food source, the updated solution of an ith candidate in this phase is shown in as follows:(7)
A
i
j
=
S
i
j
+
ϕ
i
j
S
i
j
-
S
k
j
,where A
i
j is a new solution of the S
i and k indicates the kth candidate solution index randomly selected from a candidate solution which must be different from the ith candidate solution. k
∈
1,2
,
…
,
P, i
∈
1,2
,
…
,
P, and j
∈
1,2
,
…
,
D are three randomly chosen indices. ϕ
i
j generates a random number within [
-
1
,
1
] with a uniform distribution.An example of the base station’s position update process in the employed bee phase is described in Figure2. Firstly, the current state of bee is represented as S
i and the highlighted box represents the randomly picked direction j. S
k is the randomly chosen bee, towards a direction of j where the randomly selected bee k
≠
i, which is subtracted from the same direction of taken ith bee. The difference is then multiplied by the random number (ϕ
i
j) which varies within [-
1,1]. Finally, this solution is added to the jth vector of S
i to get a jth dimension of a new food position A
i
j, which means the updated solution of the current S
i
j. As shown in Figure 2, it is demonstrated that all other dimensions of A
i
j are the same as those of S
i and are generated in the neighborhood of S
i
j.Figure 2
An example of the base station’s position update.


## 4.2.3. Onlooker Bees Phase

The procedure of onlooker bee phase comes just after finishing the critical role of the employed bee phase in ABC algorithm. During the procedure, all employed bees share the quality-wise information of the updated solutions and also the position information with the onlooker bees. After getting the information from the employed bees, the onlooker bees analyze the available information and select the promising candidate solutions probabilistically based on the fitness information with its fitness function. The probabilitypro
b
i is calculated using the following expressions in(8)
fitness
i
=
1
F
i
if
F
i
≥
0
,
1
+
abs
F
i
if
F
i
<
0
,
prob
i
=
fitness
i
∑
i
P
/
2
fitness
i
,where F
i is the objective function explained in Section 4.4 in (14) and P is a population size mentioned in simulation parameters in Table 1.Table 1
Simulation parameters.
C
f
15 GHz
P
100
λ
50
G
200
P
t
0.1–10 W
A
g
18 dBi
M
g
2 dB
C
l
2 dB
MNC
3000
N
f
2 dB
L
b
2 dB
K
100
L
G
ul
X
−100
L
T
ul
Y
100
L
G
lr
X
100
L
T
lr
Y
−100
ϕ
rand[0 to 1]
NU
10000


## 4.2.4. Scout Bees Phase

In the scout bees phase, the employed bees are those whose fitness value of food source is not updated for a predetermined number of cycles. The food source is assumed to be abandoned, and the scout bees phase starts by replacing their old solutions with searching for new solutions randomly according to (5) within the search space. For instance, if the ith solution is abandoned, a new solution is generated to replace the original one using (5), where we set i
=
1. The predetermined number of cycles is a central control parameter which is also named a limit for abandonment. Assume that, for the BS, source S
i is available in the search space; then the scout bees replace the old S
i with a new S
i food source.


## 4.3. Modified Artificial Bee Colony

The original idea of ABC algorithm performs a hierarchical optimization having a significant drawback in that it considers solutions over generations equally. This inherent disadvantage comes with the most of the population-based stochastic algorithms which relate to a premature convergence or stagnation towards a generation. When ABC tries to solve a complex problem having a large number of variables, the problem is a significant influence on the efficiency and accuracy of ABC [24, 25]. Therefore, the Modified ABC should be able to overcome the issue of the traditional ABC. In our targeted 5G network planning problem, every variable relates to its neighborhood variables. Thus, if the value of one variable changes, it directly affects its neighborhood variables and indirectly the other individual variables. To improve the conventional ABC for getting an optimal solution for our problem is required. Therefore, ABC should be made more efficient.The position updates in the conventional ABC applying (7) cannot make a large difference from the initialization of the population. After some iterations, all potential solutions work within a small proximity. In this issue, (
S
i
j
-
S
k
j
), where i and k make a slight difference without improving, sometimes becomes negligible towards a generation. This phenomenon is called a premature convergence or stagnation if the globally optimal solution is not present in this small proximity. From this point of view, this conventional ABC is not an efficient algorithm according to [26]. Thus, for making convergence rate greater while applying standard ABC to constrained problems, we need to analyze the effect of the perturbation rate which can control the frequency of parameter changes. For controlling the parameters to determine the Scaling Factor (step size), an approach to improve the standard ABC in order to make convergence rate efficient is proposed.In the traditional version of ABC, while producing a new solutionA
i, it changes only one parameter of the parent solution S
i which results in a slow convergence rate. To reduce this obstacle of the ABC optimization methods, the first change was done by the MABC as follows: our MABC proposes a new control parameter called modified mutation rate ∂. Here, for each S
i
j, a uniformly distributed random number R
i
j between 0 and 1 is generated. If the random number R
i
j is less than ∂, parameter S
i
j modifies the following:(9)
A
i
j
=
S
i
j
+
ϕ
i
j
S
i
j
-
S
k
j
,
if
R
i
j
<
∂
,
S
i
j
,
otherwise
,where k
∈
1,2
,
…
,
P, i
∈
1,2
,
…
,
P, and j
∈
1,2
,
…
,
D have randomly chosen indices. Here k must have a different random number from i and ∂ is the modified mutation rate which takes a value between 0 and 1. If ∂ gets a lower value, the solution improves slowly, but while getting a higher one, it becomes a cause of greater diversity in an optimal solution and hence in the population. Additionally, the ratio of the variance operator is also modified in MABC algorithm. In the traditional ABC, taking a random perturbation avoids getting stuck at local minima which add to the current solution in order to produce a new solution.A different random number of the solutions inS
i and S
k where k
≠
i is weighted by a real random number called ϕ
i
j. ϕ
i
j varies in the range [-
1,1], which is called a random perturbation of traditional ABC. In our MABC, the solutions S
i and S
k vary within the range [-
σ
,
σ]; hence, the second improvement of MABC was done by presenting the control parameter (σ) as a Scaling Factor that means a step size to control the magnitude of the perturbation. A smaller value of σ allows for the process in small steps, leading to slow convergence while having a larger value of σ speeds up the steps, but it reduces the exploitation capability of the perturbation method. The function of σ in (10) defines a heuristic rule which assigns different values depending on the number of generations. The mutation step size σ
(
g
) is given as a function for g in (10). The employed bees and onlooker bees both use this expression to search for the neighbor food source. We have more enhancement in the algorithm regarding the fitness function evaluation which is counted as the third improvement for our MABC. If the number of fitness evaluations decreases, the algorithm runs faster than having more fitness evaluations. In our modified MABC, what we have done differently for the traditional ABC is described in Algorithm 1 of modified employed bees and Algorithm 2 of modified onlooker bees. As we have used this expression in employed bees and onlooker bees during the process of these bees, the MABC algorithm is set only to evaluate those chromosomes which are already modified in the greedy selection method. If we apply this expression for selecting the neighbor food source, it does not always repeat a new food source position due to the constraints given in algorithms. It means that the MABC algorithm checks whether a food source has been modified or not before proceeding with the fitness function evaluation. This checking-in MABC helps to eliminate a number of fitness evaluations for the modified individuals that have already been evaluated in the past generation. We also considered that the algorithm can converge to an optimal solution.(10)
σ
g
=
1
-
0.9
×
g
G
,where G is a maximum generation number and current generation number (g) varies from 0 to G. The mutation step size σ
(
g
) follows all variables of each vector in the population. In the start, it will decrease slowly from 1 at the beginning of the run during (g
=
0) to 0.1 as the number of generations g approaches G. Thus, this decrease of σ
(
g
) performs the best tuning capability of the proposed algorithm.Algorithm 1:The modified employed bees.
(1)Begin
(2) Cycle (T) = 0, t
j
=
1
(3)For  i
=
0 to i
=
P
/
2 (Food source)
(4)
S
i
j
=
S
L
B
j
+
r
a
n
d
0,1
S
U
B
j
-
S
L
B
j
(5) Another solution S
i
j found using (Equation (11)) for each P
i called the neighborhood of the current food source
(6) Randomly pick an element j after each modified solution of ∀
i
j,  where  i
≠
k
(7) Check the fitness (F) for the new solution S
i
j
¯ taking an objective fuction using (Equation (14))
(8)
t
j
=
t
j
+
1
(9)
If  fitness of (
F[S
i
j
¯
]
≠
F
[
S
i
j
]
)  Then
(10)
Evaluate  F
[
S
i
j
¯
]
(11)
F
[
S
i
j
]
=
F
[
S
i
j
¯
]
(12)
t
j
=
0
(13)
End If
(14)End For
(15)
T
=
T
+
1
(16)EndAlgorithm 2:The modified onlooker bees.
(1)Begin
(2) Cycle (T) = 0, t
j
=
1
(3) Onlooker bee counter (OBC = 0)
(4) Another solution∀
i
k found using (Equation (11)) for each P
i called neighborhood of the current food source
(5)
While  (OBC < P
/
2 (Food source))
(6)
If  (
r
a
n
d
(
0,1
)
<
p
r
o
b
i
)  Then
(7) Onlooker bee select the employed bee and become an employed bee,
(8) OBC = OBC + 1,
(9) Repeat employed bee phase Algorithm
1
(10) Check the fitness (F) for the new solution S
i
j
¯ taking an objective fuction using (Equation (14))
(11)
t
j
=
t
j
+
1
(12)
If  fitness of (
F[S
i
j
¯
]
≠
F
[
S
i
j
]
)  Then
(13)
Evaluate  F
[
S
i
j
¯
]
(14)
F
[
S
i
j
]
=
F
[
S
i
j
¯
]
(15)
t
j
=
0
(16)
End If
(17)
End If
(18)
End While
(19)
T
=
T
+
1
(20)EndThe fourth innovative point of our MABC is that it solves the problem of exploitation and the also convergence speed has a better tuning capability than the traditional ABC. After getting a different random perturbation ofS
i and S
k, the proposed MABC calculates a neighborhood solution ∀
i
j introduced in (11) using an inertia weight given in (12):(11)
∀
i
j
=
S
i
j
×
w
+
2
ψ
i
j
-
0.5
S
i
j
-
S
k
j
+
ϕ
i
j
B
i
j
-
S
k
j
,
(12)
w
=
0.5
+
rand
⁡
2
,where w is a random inertia weight which controls the impact of the previous solution S
i
j, the best-so-far solution is represented as B
i
j of jth dimension, ϕ
i
j is a random number within [0 to 1], and ψ
i
j follows a mutation step size process instead of varying in the range of [-
1
,
1]. The modified employed bees phase is described in Algorithm 1.MABC uses (11) instead of calculating the neighborhood solution of conventional ABC in (7) in order to proceed with a better result in the employed bee phase. After completing the employed bee phase in our proposed MABC, the onlooker bees calculate a probability in (13) as follows:(13)
prob
i
=
0.9
×
F
i
max
⁡
F
+
0.1
,where F
i is the fitness value of the ith solution in the population. The modified onlooker bees phase is described in Algorithm 2. The rest of all the procedures after the onlooker bees and scout bees phases follow the same steps as conventional ABC. In addition to these innovative points mentioned above, a new control parameter ∂ (called modified mutation rate) and a step size σ both produce a greater diversity to an optimal solution and eliminate a number of fitness evaluations for modified individuals that have already been evaluated in the past generation. As a result, they solve the problem of exploitation with the convergence speed having a better tuning capability. Therefore, our MABC has so far obtained better results than the standard ABC. The overall procedure of our proposed MABC is described in Algorithm 3.Algorithm 3:Pseudocode of MABC.
(1)Begin
(2) Initialize Users phase ()
(3) Initialize Population phase ()
(4) Memorize best solution ()
(5) Memorize the best solution S
i
j achieved so far
(6) Cycle (T) = 1
(7)While  Termination criteria is not satisfied  do
(8) SendEmployedBees () (Algorithm
1)
(9) SendOnlookerdBees () (Algorithm
2)
(10) SendScoutBees ()
(11)
If  Exist  Then
(12) Re-initialize the individual S
i
j using (Equation (5)), s
=
0
(13) Memorize the best new solution B
i
j achieved so far
(14)
If  (
B
i
j
-
S
i
j
) > Limit  Then
(15)
s
=
s
+
1
(16)
Else
(17)
s
=
max
⁡
(
1
,
s
-
1
)
(18)
B
i
j
=
S
i
j
(19)
End If
(20)
End If
(21)
T
=
T
+
1
(22)End While
(23)untill  T = MNC
(24)End


## 4.4. Fitness Evaluation

A fitness function uses a type of objective function in EAs which helps to get a solution from the evaluation of each for the survival of next generation. In ABC, each single solution exists in the target search space, which we call the type of bees. All of the bees have fitness value which is evaluated by the taken objective function to be optimized. Our approach is formulated by using the objective function given in (14) for getting the fitness (F
i) of the optimal network configuration as follows:(14)
F
i
=
U
E
2
T
P
×
ActiveBSe
s
2
,where UE is the number of connected users to the BSes, T
P represents the total transmit power, and ActiveBSes represent the number of BS such that T
P is configured for each user to be connected to a BS. We defined the maximum number of generations G as for the termination criteria. The proposed algorithm terminates after executing simulation T
g generations and returns the best-so-far solution.


## 5. Computational Complexity

In this section, we discuss the complexity of our proposed MABC algorithm. The proposed algorithm is described in the following five parts: (i) the initialization of the food source, (ii) the search operation of modified employed bees, (iii) the probability of food sources, (iv) the search operation of onlooker bees, and (v) the search operation of scouts bees. First, the computational complexity of the initialization isO
(
F
K
D
) where F is the food number that is equal to the half of the colony size; K is the number of base stations (BSes); D is the vector dimension. Second, the complexity of the search operation of employed bees is O
(
F
K
D
+
F
K
D
N
u
) where N
u is the number of users. Third, the complexity of food source’s probability is O
(
F
K
). Fourth, the complexity of search operation of onlooker bees is O
(
F
K
D
+
F
K
D
N
u
). Last, the complexity of search operation of scout bees is O
(
F
K
D
). Therefore, the overall computational complexity of our proposed scheme is O
(
1
/
N
f
e
(
F
K
D
+
λ
(
F
K
D
N
u
+
F
K
+
D
)
)
) where N
f
e is number of fitness evaluations; λ is the number of iterations. Now we analyze the time complexity of the original ABC algorithm. The total time complexity of the traditional ABC is O
(
F
K
D
+
λ
(
2
F
K
D
N
u
+
2
F
K
+
D
)
) [27]. This original ABC algorithm has more than one fitness evaluation for each individual during the generation. Each employed bee tests a neighbor food source for their quality based on the fitness function. It means that the fitness function evaluates double for all the individuals during the search operations through these bees. Compared to the traditional ABC algorithm, our approach MABC does not add any extra operations regarding the complexity effect. Even MABC does not run the fitness function evaluation for all the individuals twice during the search process of employed bees and onlooker bees if they already found better nectar food source at the first time of the evaluation. With these constraints, our MABC has a better fitness value than original ABC and other EAs without losing the good performance as mentioned in Table 6. However, this operation can help MABC to run faster than ABC. If it does not happen, then, in the worst case, our MABC and the original ABC keep the same computational complexity. For RCGA, its total time complexity is O
(
P
K
+
G
(
P
2
+
P
K
2
+
P
(
N
u
+
K
N
u
)
)
) where P is the population size; G is the maximum number of generations [28]. The complexity of the MRGA is the same as that of RCGA because of having same operations used in MRGA except a difference between the operation of crossover and mutation [4]. These operations do not affect the computational complexity between RCGA and MRGA. For DE, its computational complexity is O
(
P
K
+
P
K
N
u
+
G
P
(
N
u
+
K
N
u
)
) where all the notations are described above [29]. Therefore, MABC has the same complexity as that of the original ABC. MRGA also has the same complexity as that of RCGA because of no additional operations used in the algorithm regarding complexity. DE has less computational complexity than MRGA and RCGA, but it has the same complexity as both our MABC and the original ABC.


## 6. Results and Discussion

In this section, we represent some numerical results obtained from the application of Evolutionary Algorithms such as DE, RGA, MRGA, ABC, and MABC. The performance evaluation of our proposed Modified ABC is performed with these algorithms in a fair manner. The aim of these experiments does show not only the effectiveness of our algorithm on realistic network planning but also the impact that energy consumption issues have pointed out in our simulation. Firstly, the modified algorithm is evaluated by concerning the best-optimized power level and its location problem for 5G BSes with the standard ABC, RGA, and DE. In this scenario, we obtained our experiment results regarding the number of active BSes and transmission power as an energy consumption with the connected users in comparison with conventional DE, RGA, and ABC.Simulation parameters are considered in Table1. In this table, we have taken some of the constant variables such as carrier frequency (C
f), FDD frame structure, receiver antenna gain (A
g), bandwidth, MHA gain (M
g), cable loss (C
l), noise figure (N
f), and body loss (L
b). Our decision variables are defined as a population size (P), maximum number of iterations (λ), transmission power (Q), and so forth. In our operations, the environment area is assumed to represent (X
,
Y) as (-
100.00,100.00) and (100.00
,
-
100.00) in meter where BSes and UEs are considered to be connected in the given area of interest. The users are supposed to be allocated as an specific point by using their accuracy range in the given area as this takes a new feature in 5G wireless networks and for the future generation, too. The possible users connect to those BSes which are active for servicing the best quality based on the network planning. We have performed our experiment and reported values to estimate the best location for 5G base stations. The proposed simulation environment has been shown in Figure 3, where hexagon boxes represent centers with an entirely covered area with users occupied in an urban area. The circle shape represents an area which is allocated by an optimum BS in our proposed and the standard algorithms such as ABC, RGA, and DE. All useful notations are used in our paper mentioned in “Notations.”Figure 3
Simulation environment.Our simulation results are calculated with over 50 independent runs. The comparison terms are taken for the modified RGA with Box Crossover Rate (BCR) = 0.1 and Mutation Rate (M
r) = 0.2. For standard DE, the Scaling Factor (SF) = 0.5 and Crossover Rate (CR) = 0.9 are used. For standard RGA, M
r = 0.2 is used. The proposed MABC takes mutation rates with their step size as described in Section 6. The convergence graph has been shown in Figure 4 where MABC performs better towards the upcoming generations than the MRGA and all other application of Evolutionary Algorithms such as the standard ABC, RGA, and DE. While comparing our modified algorithms with these existing algorithms, we found that the standard RGA gets lightly equal and even worse fitness value towards a generation because the shuffling happens again and again by using Box Crossover which is used in RGA algorithms. The modified RGA gets better fitness than RGA and DE. This is because they are not changing their chromosome every time in crossover operation. RGA has better fitness value than the standard RGA, ABC, and DE but is not better than our MABC as we have performed the modification in their bees of standard ABC which give better fitness value than that of the standard ABC, RGA, and DE for the best network planning in 5G networks.Figure 4
Convergence graphs.Figure5 shows the number of active BSes with the standard ABC, RCGA, DE and our MRGA, and MABC. We can see that MABC can have more active BSes than even MRGA [4] and the standard ABC, RCGA, and DE. The EAs such as DE, RCGA, and ABC hold less activated BSes and serve less users at the same time in comparison with the MRGA and ABC. The results lead to less fitness value as it depends on the fitness function. The randomness of the EAs produces more chances for the network operator to find better BS combinations. However, the MABC and MRGA keep more active base stations than the standard ABC, RCGA, and DE which uses the advantage of the higher computational complexity that depends on their level of crossover and mutation of RCGA and DE. For ABC, it depends on the standard role of bees. We emphasize that standard RCGA and DE have performed well in terms of the less active base stations but serve users insufficiently and also could not perform well regarding their power consumption. That is why the MRGA and MABC increase the number of active base stations more with less power consumption than the standard ABC, RCGA, and DE to achieve better fitness.Figure 5
The number of active base stations towards a generation.Figure6 shows a number of connected users towards a generation with MABC, MRGA, and the standard ABC, RCGA, and DE. As this figure shows, that all of the algorithms performed well regarding the coverage area by users with the connection of their active base stations. But there is still a difference in performance after reaching the 40th generation to provide excellent coverage in our simulation environment among these standard and modified algorithms. Figure 6 showed the difference is how these algorithms are performing slightly different from the starting generation till 40th generation.Figure 6
The number of connected users towards a generation.The performance of the transmission power consumption among the proposed MABC, MRGA, and traditional ABC, RCGA, and DE has been shown in Figure7. Our proposed MABC has performed well for consuming less power than the other algorithms [4]. According to the generation, this statement is true because the power is almost constant in most of the scheme except for DE. As we see in Figure 7, the performance of DE and MRGA [4] was quite similar after reaching over the 60th generation and later DE performed well in comparison to MRGA. In the starting generation, we can see that MRGA has less total power consumption than all of three mechanisms named ABC, MRGA, and RCGA except MABC but while going to the next generation, its consumption goes high because of the shuffling of their chromosome during the reproduction by crossover. According to ABC performance, the traditional ABC could not perform better than MRGA and DE but have performed better than RCGA. Thus we have modified the traditional ABC as MABC where we achieved very less power consumption from the initial point of the generation because of modifying their mutation step size on their bee phases. By making traditional ABC as a novel ABC after modifying, we got the good results regarding the power consumption. The statistical results have been tabulated in Tables 2–5, respectively. Firstly, Table 2 shows the performance of our proposed MABC and the traditional ABC where we get t-value 2.00086
E
-
07. Table 3 shows the performance of MRGA where we are getting t-value 0.023381. Table 4 shows the comparison of our MABC and RCGA where we get t-value 4.03195
E
-
29. Lastly, the results of our proposed MABC are shown, compared with the traditional DE where t-value gives 4.05318
E
-
20 in Table 5. Hence this proves that the MABC is statistically better than the traditional ABC, RCGA, and DE.Table 2
Thet-value for MABC and ABC in 49 degrees of freedom is significant at a QoS level of significance by two-tailed t-test.
The modified ABC
ABC
t-value
Average
308.68278
145.654808
2.00086
E
-
07
Stdev
77.82408737
15.8800909196Table 3
Thet-value for MABC and MRGA in 49 degrees of freedom is significant at a QoS level of significance by two-tailed t-test.
The modified ABC
The modified RGA
t-value
Average
308.68278
277.270614
0.023381
Stdev
77.82408737
56.70863407Table 4
Thet-value for MABC and RCGA in 49 degrees of freedom is significant at a QoS level of significance by two-tailed t-test.
The modified ABC
RCGA
t-value
Average
308.68278
39.76453
4.03195
E
-
29
Stdev
77.82408737
2.399219965Table 5
Thet-value for MABC and DE in 49 degrees of freedom is significant at a QoS level of significance by two-tailed t-test.
The Modified ABC
DE
t-value
Average
308.68278
145.654808
4.05318
E
-
20
Stdev
77.82408737
15.8800909Table 6
Comparison of results obtained for their fitness value by MABC, ABC, MRGA, RCGA, and DE with 50 test numbers getting in 200th-generation time.
Fitness value
Iteration
MABC
ABC
MABC
MRGA
MABC
RCGA
MABC
DE
1
336.569
220.5592
336.569
288.199
336.569
38.4158
336.569
122.4345
2
326.7795
232.8575
326.7795
256.7098
326.7795
38.138
326.7795
122.4345
3
136.3359
178.0451
136.3359
184.0869
136.3359
38.9982
136.3359
147.3075
4
478.0451
263.1525
478.0451
263.0525
478.0451
37.4129
478.0451
147.3413
5
363.8525
206.3958
363.8525
243.324
363.8525
38.8615
363.8525
157.4405
6
399.3313
229.994
399.3313
266.0057
399.3313
38.9466
399.3313
168.3165
7
497.6723
343.9293
497.6723
343.9293
497.6723
38.2377
497.6723
182.6838
8
343.9293
279.6975
343.9293
217.4483
343.9293
39.747
343.9293
138.1339
9
413.9853
217.6088
413.9853
257.755
413.9853
38.792
413.9853
137.7067
10
221.5153
243.5444
221.5153
270.0002
221.5153
41.7116
221.5153
133.2046
11
320.0002
217.1254
320.0002
240.9877
320.0002
40.4955
320.0002
133.0904
12
317.9254
223.4749
317.9254
282.6575
317.9254
42.9836
317.9254
144.4086
13
382.6575
223.1256
382.6575
282.9843
382.6575
45.9056
382.6575
150.9968
14
223.1256
216.3692
223.1256
306.8127
223.1256
44.3962
223.1256
139.5661
15
270.1614
245.5956
270.1614
313.6375
270.1614
38.0587
270.1614
137.1016
16
254.719
185.7675
254.719
204.5175
254.719
39.0704
254.719
176.6061
17
287.0222
205.4735
287.0222
240.775
287.0222
41.1525
287.0222
150.9161
18
321.2165
178.1283
321.2165
185.5978
321.2165
41.6386
321.2165
131.9684
19
378.1283
247.4768
378.1283
265.8708
378.1283
36.8584
378.1283
132.8054
20
247.9118
267.8852
247.9118
310.4483
247.9118
44.0629
247.9118
162.799
21
297.8852
215.574
297.8852
261.19
297.8852
35.4141
297.8852
172.6942
22
220.0042
210.3367
220.0042
309.0168
220.0042
40.118
220.0042
125.2206
23
210.9367
190.0167
210.9367
235.3166
210.9367
43.9276
210.9367
142.237
24
227.8001
197.3563
227.8001
204.8888
227.8001
37.6756
227.8001
160.4762
25
197.3063
229.4653
197.3063
280.4655
197.3063
37.1763
197.3063
129.5167
26
233.043
274.8593
233.043
301.5113
233.043
36.6548
233.043
132.8081
27
301.5113
198.5159
301.5113
224.5502
301.5113
37.8516
301.5113
181.9633
28
291.0059
187.1543
291.0059
237.3015
291.0059
37.8559
291.0059
128.0427
29
321.4146
226.2556
321.4146
331.5433
321.4146
41.3885
321.4146
161.0378
30
257.9592
265.8664
257.9592
265.8664
257.9592
40.9125
257.9592
135.5947
31
365.8994
276.1566
365.8994
330.5423
365.8994
39.8699
365.8994
132.1572
32
308.9495
242.4229
308.9495
289.2582
308.9495
39.6183
308.9495
143.372
33
342.9229
229.6357
342.9229
287.8494
342.9229
42.3116
342.9229
158.5198
34
262.8943
288.9151
262.8943
345.6238
262.8943
40.8357
262.8943
147.5854
35
292.465
125.2196
292.465
197.748
292.465
38.8482
292.465
147.7685
36
397.748
402.1246
397.748
452.8917
397.748
36.3569
397.748
136.2769
37
402.1916
303.3515
402.1916
312.0491
402.1916
43.8927
402.1916
129.7897
38
271.1631
283.7516
271.1631
313.1315
271.1631
37.1562
271.1631
149.7464
39
213.1315
202.5987
213.1315
259.6116
213.1315
39.0499
213.1315
164.2077
40
202.5987
262.1589
202.5987
291.0349
202.5987
40.5539
202.5987
134.8221
41
230.1549
315.8854
230.1549
386.4251
230.1549
41.4009
230.1549
137.6344
42
316.4251
163.4352
316.4251
191.4861
316.4251
39.7959
316.4251
145.1443
43
323.0682
158.5565
323.0682
258.3565
323.0682
40.3688
323.0682
178.4081
44
458.3565
270.9059
458.3565
343.0924
458.3565
39.3066
458.3565
133.0197
45
289.0719
197.5141
289.0719
206.7901
289.0719
44.3265
289.0719
143.9841
46
397.5341
256.4257
397.5341
389.7103
397.5341
39.494
397.5341
125.5549
47
356.4256
169.1989
356.4256
228.2749
356.4256
39.791
356.4256
153.9786
48
214.6505
233.8152
214.6505
248.5624
214.6505
38.7579
214.6505
156.4837
49
333.8152
281.1153
333.8152
374.9021
333.8152
37.5592
333.8152
131.4135
50
374.9021
251.4721
374.9021
279.7401
374.9021
36.0738
374.9021
146.0198
t-test
0.03
t-test
4
E
-
29
t-test
4.1
E
-
20
t-test
2
E
-
07
F-test
0.029
F-test
5.6
E
-
61
F-test
1.4
E
-
21
F-test
0.00188Figure 7
The total transmitting power towards a generation.


## 7. Conclusion

In this paper, we formulate a network planning optimization problem with our proposed Modified ABC (MABC) algorithm, the standard ABC, RCGA, and DE. The key objective of this network planning problem is to minimize the power consumption while using the minimum number of active base stations with their connected users in order to assure a certain quality of service to the users. Since this optimization problem is an NP-hard problem, it consumes tremendous resources such as computation time and requires the evaluation of a number of expensive fitness functions for a high-quality solution using the application of Evolutionary Algorithms (EAs). Therefore, the insight of the EAs has a better tradeoff between resources and the quality of solutions. The application of EAs is an intelligent tool which provides us with an optimum high-quality solution to the optimization problems with a huge search space. We have compared the three legacy algorithms (i.e., ABC, RCGA, and DE) with our MABC in performance evaluation. The MABC has successfully found much better configuration by comparing with the conventional DE and RCGA and even the modified RCGA (MRGA) in order to locate a proper location and also to adjust the range of the power along with their connected users. Experimental results classified the application of EAs regarding the performance and the number of function evaluations. This indicates that our MABC can guide us towards choosing an efficient way to achieve high transmit power saving and to satisfy coverage constraints for 5G wireless networks. As for future work, we will enhance our MABC algorithm for handover scenarios (e.g., vehicular networks) where UEs are moving fast in the 5G wireless networks.



---

*Source: 4353612-2017-07-06.xml*