An Excited Binary Grey Wolf Optimizer for Feature Selection in
Highly Dimensional Datasets
Davies Segera, Mwangi Mbuthia and Abraham Nyete
Department of Electrical and Information Engineering, University of Nairobi, Harry Thuku Road, Nairobi, Kenya
Keywords: Meta-Heuristic, Feature Selection, Evolutionary Algorithm, Binary Grey Wolf Optimizer.
Abstract: Currently, feature selection is an important but challenging task in both data mining and machine learning,
especially when handling highly dimensioned datasets with noisy, redundant and irrelevant attributes. These
datasets are characterized by many attributes with limited sample-sizes, making classification models over-
fit. Thus, there is a dire need to develop efficient feature selection techniques to aid in deriving an optimal
informative subset of features from these datasets prior to classification. Although grey wolf optimizer
(GWO) has been widely utilized in feature selection with promising results, it is normally trapped in the local
optimum resulting into semi-optimal solutions. This is because its position-updated equation is good at
exploitation but poor at exploration. In this paper, we propose an improved algorithm called excited binary
grey wolf optimizer (EBGWO). In order to improve on exploration, a new position-updating criterion is
adopted by utilizing the fitness values of vectors 𝑋
⃗

, 𝑋
⃗

and 𝑋
⃗

to determine new candidate individuals.
Moreover, in order to make full use of and balance the exploration and exploitation of the existing BGWO, a
novel nonlinear control parameter strategy is introduced, i.e. the control parameter of 𝑎⃗ is innovatively
decreased via the concept of the complete current response of a direct current (DC) excited resistor-capacitor
(RC) circuit. The experimental results on seven standard gene expression datasets demonstrate the
appropriateness and efficiency of the fitness value based position-updating criterion and the novel nonlinear
control strategy in feature selection. Moreover, EBGWO achieved a more compact set of features along with
the highest accuracy among all the contenders considered in this paper.
1 INTRODUCTION
The major challenge in analysing big data is the vast
number of features. Out of the many available
features, only a few of them will be useful in
distinguishing samples that belong to different classes
while majority of the of the features will be irrelevant,
noise, or redundant. Foremost, these irrelevant
features lead to noise generation in big data analysis.
In addition, they result in increased dataset
dimensions and a further computational complexity
in both clustering and classification operations. All
these consequently decreases the rate of classification
accuracy. Thus, superior approaches are needed to
identify diverse features, compute the relationship
between the features and optimally select informative
attributes from these highly dimensioned datasets
(Almugren & Alshamlan, 2019).
For a dataset containing 𝑁 number of features,
there exists 2

number of candidate subsets. The
main objective of designing different feature
selection techniques has always been to determine a
compressed and optimal subset with the highest
precision among the possible candidate subsets.
Since the scope of possible solutions is wide and
the size of this set of responses is on the rise due to
the ever-increasing number of features, determining
the best subset of 𝑁 features is extremely difficult
and costly(Pirgazi et al., 2019), (Liang et al., 2018).
Feature selection techniques can be broadly
categorized into two i.e. filters and wrappers. Filter
approaches utilizes the dependency, mutual
information, distance, and information theory in
carrying out feature selection(Shunmugapriya &
Kanmani, 2017). Unlike filters, wrappers utilize
classifiers as the learning algorithm in optimizing the
classification performance by selecting the
informative features. Commonly, filter techniques are
often faster compared to wrappers, which is largely
attributed to their reduced computational complexity
(Sun et al., 2018). Nevertheless, wrapper techniques
can usually offer better performances compared to
filters(Zorarpacı & Özel, 2016). Wrappers apply
metaheuristic optimization approaches, such as
Segera, D., Mbuthia, M. and Nyete, A.
An Excited Binary Grey Wolf Optimizer for Feature Selection in Highly Dimensional Datasets.
DOI: 10.5220/0009805101250133
In Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2020), pages 125-133
ISBN: 978-989-758-442-8
Copyright
c
 2020 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
125

binary genetic algorithm (BGA)(De Stefano et al.,
2014), binary grey wolf optimization
(BGWO)(Emary et al., 2016), binary ant colony
optimization (BACO) (Aghdam et al., 2009), binary
particle swarm optimization (BPSO) (He et al., 2009),
to select the optimal informative feature subsets.
BGWO is a recent feature selection approach,
which usually offers better performance compared to
other conventional methods(Emary et al., 2016) .
However, the wolves’ new positions are based on the
experience of leaders i.e. alpha, beta and delta, which
normally leads to premature convergence. In
addition, a proper balance between the diversification
(global search) and intensification (local search) is
still the challenging issue in BGWO (Too et al.,
2018).
In this paper, we propose a new excited binary
grey wolf optimizer (EBGWO) that aims to improve
the performance of BGWO(Emary et al., 2016) in
selecting informative features in highly dimensioned
microarray datasets. Foremost, to overcome the
insufficiency of the existing BGWO regarding its
position-updated equation, which is good at
exploitation but poor at exploration, a new position-
updated equation utilizing the fitness values of
vectors 𝑋
⃗

, 𝑋
⃗

and 𝑋
⃗

is proposed to determine new
candidate individuals. Moreover, inspired by the
concept of the complete current response of a direct
current (DC) excited resistor-capacitor (RC) circuit, a
new nonlinear control parameter strategy for
parameter 𝑎⃗ is introduced in order to make full use
of and balance the diversification and intensification
of the existing BGWO algorithm.
The performance of EBGWO is tested using
seven standard gene expression datasets. To evaluate
the effectiveness of proposed method, EBGWO is
compared with five existing binary metaheuristic
algorithms i.e. BGWO1, BGWO2, BPSO, BDE and
BGA. The experimental results indicate EBGWO has
a very efficient computational complexity, while
keeping a comparative performance in feature
selection.
The rest of paper is organized as follows.
Preliminaries for the work, GWO is presented in
section 2. The proposed excited grey wolf optimizer
(EGWO) is presented in section 3. The binary version
of EGWO i.e. Excited binary grey wolf optimizer
(EBGWO) is presented in section 4. Section 5 reports
the experimental setting and a discussion of the
obtained results. Finally, a conclusion and future
works are given in section 6.
2 GREY WOLF OPTIMIZER
Grey wolf optimizer (GWO) is a recently proposed
metaheuristic optimization technique(Mirjalili et al.,
2014). In nature, grey wolves live in groups ranging
between 5 to 12. GWO mimics the behaviour
portrayed by these grey wolves while hunting and
searching of a prey. In GWO, to simulate the
leadership hierarchy in a pack, the population is
divided into four types of wolves i.e. Alpha (𝛼), beta
(𝛽), delta (𝛿), and omega (𝜔). The alpha wolf is the
overall leader responsible for decision-making. The
beta wolf is the second in command is aids the alpha
in making the decision or other activities. Delta wolf
is referred as the third leader in the group, which
dominates the omega wolves. The three leaders i.e.
𝛼,𝛽 and 𝛿 guide the hunting (optimization) while the
remaining omega wolves ( 𝜔) follow them(El-
Gaafary et al., 2015).
Equation 1 depicts the encircling behaviour of the
pack while hunting a prey.
𝑋𝑡 1 = 𝑋


𝑡


𝐴
.𝐷
(1
)
Where 𝑋

is the position of prey, 𝐴 is the coefficient
vector, and 𝐷 is defined by equation 2.
𝐷 =𝐶.𝑋


𝑡

 𝑋𝑡
(2
)
Where 𝐶 is the coefficient vector, 𝑋 is the position of
grey wolf, and 𝑡 is the number of iterations.
The coefficient vectors, 𝐴 and 𝐶, are determined
by equations 3 and 4 respectively.
𝐴
2.𝑎.𝑟

𝑎
(3
)
𝐶2.𝑟

(4
)
Where 𝑟

and 𝑟

are two independent random
numbers uniformly distributed between 0,1, and 𝑎
is the encircling coefficient that is used to balance the
trade-off between exploration and exploitation.
In GWO, 𝑎 is linearly decreased, from 2 to 0,
according to Equation (5).
𝑎22.



(5
)
Where 𝑡 and 𝑇 represent the number of iterations and
maximum number of iterations respectively.
In GWO, the three leaders 𝛼,𝛽 and 𝛿 leaders are
deemed knowledgeable of the potential position of
the prey. Thus, they guide the remaining omega
wolves to move toward the optimal position.
ICINCO 2020 - 17th International Conference on Informatics in Control, Automation and Robotics
126

Mathematically, the new position of wolf is updated
as per Equation (6).
𝑋

𝑡1










(6)
Where 𝑋

,𝑋

and 𝑋

are determined according to
Equations (7)-(9)
𝑋


|
𝑋


𝐴

.𝐷

|
(7)
𝑋

𝑋


𝐴

.𝐷


(8)
𝑋


|
𝑋


𝐴

.𝐷

|
(9)
Where 𝑋

,𝑋

and 𝑋

are the position of 𝛼,𝛽 and 𝛿
respectively during iteration 𝑡.
𝐴

,𝐴

and 𝐴

are determined using Equation 3;
and 𝐷

,𝐷

and 𝐷

are defined in Equations (10)-(12)
respectively.
𝐷


|
𝐶

.𝑋

𝑋
|
(10)
𝐷

𝐶

.𝑋

𝑋
(11)
𝐷


|
𝐶

.𝑋

𝑋
|
(12)
Where 𝐶

,𝐶

and 𝐶

are determined using Equation
(4).
3 EXCITED GREY WOLF
OPTIMIZER (EGWO)
3.1 Nonlinearly Controlling Parameter
𝒂 via the Complete Current
Response of the DC Excited RC
Circuit
It is a well-established fact that for population-based
metaheuristics, both exploration (diversification) and
exploitation (intensification) are conducted
concurrently.
Exploration is termed as the ability of a
population-based metaheuristic to examine new areas
within the defined search space with the aim of
determining the global optima. On the hand,
exploitation is the ability to utilize the information of
already identified individuals in deriving better
individuals(Long et al., 2018; Luo et al., 2013).
In every population-based metaheuristic, both
exploration (diversification) and exploitation
(intensification) abilities are attained by applying
specific operators.
In the conventional GWO algorithm, the control
parameter 𝑎 plays a critical role in balancing between
diversification and intensification of an individual
candidate search (Long et al., 2018). A larger value
of 𝑎 enhances global exploration, while its smaller
value promotes local exploitation. Thus, selection of
a suitable control strategy for parameter 𝑎 is critical
in attaining an effective balance between local
exploitation and global exploration. From literature,
one proved way to achieve the required balance is
critically studying the control of parameter 𝑎. To
date, various approaches have been proposed to
control the conventional GWO’s parameter 𝑎 (Long,
2016; Long et al., 2018; Mittal et al., 2016).
However, in the conventional GWO, 𝑎 linearly
decreases from 2 to 0 using Equation (5). Since
GWO incorporates a highly complicated nonlinear
search process, the utilized linear control of
parameter 𝑎 doesn’t reflect the actual search process
(Long et al., 2018). Moreover, (Mittal et al., 2016)
suggested that the performance of GWO would
improve if parameter 𝑎 is nonlinearly controlled.
Motivated by both the above consideration and
the complete current response of a direct current (DC)
excited resistor-capacitor (RC) circuit(Alexander &
Sadiku, 2016), a novel nonlinear adaptation of
parameter 𝑎 is proposed in this paper.
The complete current response of the RC circuit
to a sudden application of a dc voltage source, with
the assumption that the capacitor is initially not
charged is given in Equation 13.
𝑖𝑡 










(13
)
Where 𝜏𝑅𝐶 is the time constant that expresses
the rapidity with which the value if 𝑖 decreases from
the initial value



to zero over time . 𝑉

is value of a
constant DC voltage while 𝑅 and 𝐶 are the resistor
and capacitor values of the circuit.
We adopt this concept i.e. the exponential decay
of 𝑖 over time to develop a new nonlinear control
strategy of parameter 𝑎 as presented in Equation 14.
𝑎
,
𝑎


𝑀𝑎𝑥𝐼𝑡𝑒𝑟 
𝑀𝑎𝑥𝐼𝑡𝑒𝑟


,
(14
)
Where 𝑎
,
is the value of the control parameter 𝑎
assigned to grey wolf 𝑖 during iteration 𝑡.
𝑀𝑎𝑥𝐼𝑡𝑒𝑟
indicates the total number of iterations (generations)
and 𝑎

is the initial value of the control
parameter 𝑎. 𝜏
,
is a nonlinear modulation index
assigned to the grey wolf 𝑖 during iteration 𝑡.
An Excited Binary Grey Wolf Optimizer for Feature Selection in Highly Dimensional Datasets
127

To ensure that the value of the control parameter 𝑎
,
is proportional to the fitness value of grey wolf 𝑖
during iteration 𝑡, a new formulation of the value of
the nonlinear modulation index 𝜏
,
is given in
Equation (15).
𝜏
,




 









 







(15)
Where 𝐹𝛼

, 𝐹𝛽

and 𝐹𝛿

are the fitness values of
𝛼,𝛽 and 𝛿 wolves (the 3 best wolves) respectively
during the current iteration 𝑡. 𝐹𝑋

is the fitness value
of grey wolf 𝑖 during iteration 𝑡 and finally 𝐹𝑤

is
the worst fitness value among the omega (𝜔) wolves
during iteration 𝑡 .
Consequently, 𝐴

,𝐴

and 𝐴

are determined using
Equation (16) which is a variant of Equation 3.
𝐴
2.𝑎
,
.𝑟

𝑎
,
(16)
From the literature of conventional GWO
(Mirjalili et al., 2014), when 𝐴1 the grey wolves
are compelled to attack the prey (exploitation) and
when 𝐴1 the grey wolves are compelled to move
away from the current prey with the hope of finding
another fitter prey. This implies that smaller values of
the control parameter 𝑎 promotes local exploitation
while larger values facilitates global exploration.
According to Equation (5) of the conventional
GWO algorithm, it is evident that half of the iterations
are committed to exploration and the remaining half
to exploitation. This strategy fails to consider the
impact of effective balancing between these two
conflicting milestones to guarantee accurate
approximation of the global optimum.
The nonlinear control strategy of parameter 𝑎
proposed in Equation (14), tries to overcome this
challenge by adopting a variant of decay function to
strike a proper balance between exploration and
exploitation. Since this strategy promotes allocates a
large proportion of the iterations to global exploration
compared to local exploitation, the convergence
speed of the proposed EGWO algorithm is enhanced
while minimizing the local minima trapping effect.
Moreover, since the proposed scheme is
proportional to the fitness values of the individual
grey wolves in the search space and the current
iteration (generation), diversity and the quality of the
solutions is enhanced.
3.2 Socially Strengthened Hierarchy
via a Fitness-value based
Position-updating Criterion
In the conventional GWO, social hierarchy is the
cornerstone in both the internal management and the
hunting patterns of the pack(Tu et al., 2019) . All the
wolves in the pack conduct hunting under the
guidance of the 𝛼,𝛽 and 𝛿 wolves. An assumption
that these three dominant wolves have a better
knowledge of the prey’s location. Consequently, the
omega (𝜔) wolves update their positions with the aid
of these three leaders during the hunting process. This
implies that the conditions of the 𝛼,𝛽 and 𝛿 wolves
are key in updating the whole pack. Meanwhile, the
higher the rank a wolf attains during the search, the
closer it gets to the global optimum.
In addition, all the wolves including the three
leaders utilize Equation (6) to update their positions.
That is to say the 𝛼 wolf will utilize the lowly ranked
𝛽 and 𝛿 wolves to update its position. Likewise, 𝛽
wolf will utilize the lowly ranked 𝛿 wolf to update
itself. Since the conditions of the 𝛽 and 𝛿 wolves are
worse compared to that of the 𝛼 wolf, there are higher
chances that the two wolves will compel the 𝛼 wolf
to move away from the global optimum. Likewise, 𝛽
wolf may also be misled by the 𝛿 wolf. Ultimately,
the accumulative error will have an adverse effect on
updating the positions of the all the wolves in the pack
and the convergence efficiency of the GWO will
drastically reduce(Tu et al., 2019).
On the other hand, since all the omega (𝜔) wolves
are attracted towards the 𝛼,𝛽 and 𝛿 wolves, they may
prematurely converge due to limited exploration
within the search space. Thus, the conventional GWO
is good at exploitation but poor at exploration.
Thus, to overcome the GWO’s premature converge
and still maintain the social hierarchy of the pack, a
different scheme for updating both the dominant (𝛼,𝛽
and 𝛿) and the omega (𝜔) wolves is needed. To attain
this, a new position-updated equation utilizing the
fitness values of vectors 𝑋
⃗

, 𝑋
⃗

and 𝑋
⃗

is utilized in
determining new candidate individuals.
Foremost, for each wolf in the pack,
vectors 𝑋

, 𝑋

and 𝑋

are computed using
Equations (17)-(19).
𝑋



𝑋


𝑗



(17
)
𝑋



𝑋


𝑗



(18
)
ICINCO 2020 - 17th International Conference on Informatics in Control, Automation and Robotics
128

𝑋



𝑋


𝑗



(19)
Where 𝑑 is the dimension of the search space and
𝑋


𝑗

,𝑋

𝑗 and 𝑋

𝑗 are determined using
Equations (7)-(9) respectively.
Next, the fitness values 𝐹𝑋

,𝐹𝑋

and
𝐹𝑋

for vectors 𝑋

, 𝑋

and 𝑋

respectively are determined and the one with the best
fitness forms the new position as depicted by
Equations (20)-(21).

𝑓
𝑖𝑡𝑡𝑒𝑠𝑡,𝑃𝑜𝑠𝑚𝑖𝑛 

𝐹𝑋




(20)
𝑋

𝑡1



𝑋





(21)
4 EXCITED BINARY GREY
WOLF OPTIMIZER (EBGWO)
Feature selection (FS) is a significant problem in
pattern recognition and machine learning areas. The
aim of FS is to select the most informative feature
subset guided by a given evaluation criterion(Salesi
& Cosma, 2017; Tu et al., 2019).
In essence, FS is a broad-based optimization problem
that is characterized by huge computations.
Since the FS problem utilizes a binary search space,
it is important to convert the proposed continuous
EGWO to binary i.e. EBGWO. One of the commonly
adopted approach for this transformation is the
utilization of transfer functions(Salesi & Cosma,
2017; Tu et al., 2019).
In our experiments, the transfer function we utilized
in converting the real values of each solution to binary
is depicted by Equation (22).
𝑋


𝑡1


1,𝑖𝑓 𝑆𝑋


𝑡1

𝜌,
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(22)
Where 𝜌∈0,1 depict a random threshold and 𝑆 is
the considered sigmoid function as expressed by
Equation (23).
𝑆

𝑥


1
1  exp 10𝑥  0.5
(23)
𝑋


𝑡1

=1 imply that the 𝑗

element of 𝑋𝑡1
is selected as an informative attribute while 𝑋


𝑡
1

=0 imply that the corresponding 𝑗

element is
ignored.
For instance, if 𝑋

𝑡1

0.55,0.21,0.35,0.8
and 𝜌0.5, the output of Equation (21) becomes
𝑋

𝑡1

1, 0,0,1 which imply that the 1

and
4

features be selected while the 2

and 3

features will be ignored.
By doing so, the number of features is reduced
without affecting the classification performance.
Since the FS task aims at attaining better
classification accuracy with the utilization of fewer
attributes, the objective function 𝐹𝑖𝑡 utilized in this
paper is given by Equation (24)(Salesi & Cosma,
2017).
𝐹𝑖𝑡𝜀 ∗
|
𝑆
|
|
𝑁
|


1𝜀

∗
𝐴
𝑐𝑐
(24)
Where 𝐴𝑐𝑐 is indicates the accuracy of a given
classifier,
|
𝑆
|
is the size of the selected feature subset
and
|
𝑁
|
is the number of the total features of a
dataset. Thus, FS is turned into a problem of
determining the minimum value of Equation (24).
Herein, 𝜀 and

1𝜀

are weights corresponding to
the feature subset size and average accuracy
respectively. The parameter of 𝜀 in Equation (24) is
set 0.2 (Salesi & Cosma, 2017).
The pseudocode of the proposed excited binary
grey wolf optimizer (EBGWO) algorithm is
presented in Algorithm 1.
Algorithm 1: Pseudo-code for the EBGWO.
Input: labelled gene dataset D, Total number of
iterations 𝑀𝑎𝑥𝐼𝑡𝑒𝑟, Population size N, Initial value of
the control parameter
𝑎

Output: Optimal Individual’s position
𝑋

, Best
fitness value Fit (
𝑋

)
1. Randomly initialize N individuals’ positions to
establish a population
2. Using Equation (23), evaluate the fitness of all
wolves, Fit (
𝑋)
3.
[~, Index] =Sort (𝐹𝑖𝑡 
𝑋,′𝐴𝑠𝑐𝑒𝑛𝑑′)
4.
𝐹𝛼 =𝐹𝑖𝑡 𝑋

5.
𝐹β =𝐹𝑖𝑡 𝑋

6.
𝐹δ =𝐹𝑖𝑡 𝑋

7.
𝐹w =𝐹𝑖𝑡 𝑋

8.
𝑋

=𝑋𝐼𝑛𝑑𝑒𝑥1
9.
𝑋

=𝑋𝐼𝑛𝑑𝑒𝑥2
10.
𝑋

=𝑋𝐼𝑛𝑑𝑒𝑥3
11.
For t=1 To 𝑀𝑎𝑥𝐼𝑡𝑒𝑟
12. For i=1 To N
13.
Determine
𝑎
,
using Equation (14)
14.
Compute 𝑋

,𝑋

and 𝑋

using
Equations (17)-(19)
15.
Generate
𝑋
𝑣𝑒𝑐1

, 𝑋
𝑣𝑒𝑐2

and
An Excited Binary Grey Wolf Optimizer for Feature Selection in Highly Dimensional Datasets
129

𝑋
𝑣𝑒𝑐3

using Equation (21)
16. Evaluate the fitness values
𝐹𝑋

, 𝐹𝑋

and 𝐹𝑋

of the binary
vectors
𝑋
𝑣𝑒𝑐1

𝑋
𝑣𝑒𝑐2

and
𝑋
𝑣𝑒𝑐3

respectively using Equation (24)
17. Determine the minimum value(fittest) of the
three evaluated fitness values and its Index
using Equations (20)
18.
If (fittest<𝐹𝑖𝑡 
𝑋

) Then
19.
𝐹𝑖𝑡 
𝑋

= fittest
20.
Update
𝑋

using Equation (21)
End If
21. Next i
22. Repeat steps 3 to 10
23. Next t
5 EXPERIMENTAL RESULTS
AND DISCUSSION
All the experiments were conducted in Windows
Windows 10 Home Single Language 64-bit operating
system; processor Intel(R) Core (TM) i7-3770CPU ,
processor speed of 3.4GHZ; 12GB of RAM. All the
considered algorithms were implemented using
MATLAB 2017 environment.
5.1 Dataset Description
In order to evaluate the performance of the proposed
algorithm, seven gene expression datasets were
utilized. The datasets were selected to have a variety
of instances (sample-size), genes and classes as a
representative of various issues. Table 1 outlines the
detailed distribution of instances, genes and classes
for each considered dataset.
Table 1: Microarray datasets used in the experiments.
Dataset
No. of
Instances
No. of
Genes
No. of
Classes
Brain_Tumour1 90 5920 5
Brain_Tumour2 50 10367 4
CNS 60 7129 2
DLBCL 77 5469 2
Leukemia 72 7129 2
Colon 62 2000 2
Lung Cancer 203 12600 4
5.2 Parameter Setting
The proposed EBGWO is benchmarked with two
novel binary grey wolf optimizations (i.e. BGWO1
and BGWO2) (Emary et al 2016), binary particle
swarm optimization (BPSO), binary differential
evolution (BDE) and binary genetic algorithm(Too et
al., 2019). The optimizer- specific settings of the
considered algorithms are presented in Table 2.
Table 2: Parameter settings for each considered algorithm.
Algorithm Year Parameter settings
EBGWO
N=10,𝑀𝑎𝑥𝐼𝑡𝑒𝑟
100, 𝑎

2
BGWO1 2016
N=10,𝑀𝑎𝑥𝐼𝑡𝑒𝑟
100, 𝑎

2
BGWO2 2016
N=10,𝑀𝑎𝑥𝐼𝑡𝑒𝑟
100, 𝑎

2
BPSO 2019
N=10,𝑀𝑎𝑥𝐼𝑡𝑒𝑟
100, 𝐶

𝐶

2, 𝑉


6, 𝑊

0.9, , 𝑊


0.4
BDE 2019
N=10 ,𝑀𝑎𝑥𝐼𝑡𝑒𝑟
100, 𝐶𝑅0.9
BGA 2019
N=10,𝑀𝑎𝑥𝐼𝑡𝑒𝑟
100, 𝐶𝑅0.8, MR=0.01
Additionally, all the considered algorithms are
repeated over 10 independent runs to ensure both
stability and statistical significance of the obtained
results. Furthermore, the commonly utilized 10-fold
cross validation scheme is used to divide the
considered microarray datasets into training and
testing (Arlot & Celisse, 2010).
A wrapper approach based on the K-Nearest
Neighbour (K-NN) classifier(Emary et al., 2016;
Pirgazi et al., 2019) is used for feature selection in this
paper. The K-NN classifier (where k=5) is utilized to
obtain the classification accuracy of the solutions.
Table 3 presents the performance of all the
algorithms considered for the feature selection task
using the gene expression datasets whose details are
presented in Table 1.
The following information is presented in each
column of Table 3:
i) Algorithm: Provides the abbreviations of the
considered algorithms i.e. Excited Binary
Grey Wolf Optimizer (EBGWO), Binary Grey
Wolf Optimizer 1(BGWO1), and Binary Grey
Wolf Optimizer 2 (BGWO2)
ii) 𝑀𝑎𝑥_𝐴𝑐𝑐 Maximum Accuracy value obtained
when a given algorithm is repeated for 10
independent runs.
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130

Table 3: Experimental Results.
Algorithm Accuracy Number of Genes Dataset
𝑀𝑎𝑥_𝐴𝑐𝑐 𝑀𝑖𝑛_𝐴𝑐𝑐 𝐴𝑣𝑔
_
𝐴𝑐𝑐 𝑀𝑎𝑥
_
𝑁𝑓𝑒𝑎𝑡 𝑀𝑖𝑛
_
𝑁𝑓𝑒𝑎𝑡 𝐴𝑣𝑔
_
𝑁𝑓𝑒𝑎𝑡
EBGWO (Ours)
0.933 0.911 0.919 673 440 501.9
Brain_Tumour1
BGWO1 0.889 0.856 0.871 3831 2952 3356.9
BGWO2 0.911 0.878 0.894 1656 1094 1343.3
BPSO 0.854 0.823 0.843 2972 2763 2863.9
BDE 0.864 0.834 0.854 3017 2737 2937.6
BGA 0.869 0.844 0.859 2950 2840 2889.4
EBGWO (Ours)
0.920 0.84 0.884 2811 712 1151.5
Brain_Tumour2
BGWO1 0.840 0.820 0.838 7415 6103 6813.4
BGWO2 0.880 0.820 0.846 4019 2528 3083.8
BPSO 0.800 0.780 0.798 5126 5090 5122.4
BDE 0.728 0.713 0.714 5198 5076 5172.3
BGA 0.767 0.753 0.752 5139 5039 5089.5
EBGWO (Ours)
0.85 0.8 0.827 1020 564 710.3
CNS
BGWO1
0.783 0.750 0.760 4942 4217 4606.4
BGWO2
0.800 0.750 0.780 2502 1842 2175.8
BPSO 0.767 0.733 0.737 3502 3486 3487.6
BDE 0.693 0.663 0.683 3530 3478 3521.9
BGA 0.727 0.707 0.717 3528 3428 3501.7
EBGWO (Ours)
1.000 0.987 0.997 534 333 426.7
DLBCL
BGWO1
0.987 0.961 0.971 3706 2826 3343.4
BGWO2
1.000
0.948 0.986 1700 1002 1408.3
BPSO 0.919 0.891 0.901 2703 2672 2675.1
BDE 0.885 0.869 0.882 2732 2687 2721.4
BGA 0.906 0.883 0.896 2709 2699 2685.1
EBGWO (Ours)
0.931 0.889 0.903 913 524 649.8
Leukemia
BGWO1
0.861 0.833 0.849 5065 3897 4428.5
BGWO2
0.889 0.847 0.874 2141 1618 1805.5
BPSO 0.828 0.809 0.814 3516 3505 3514.9
BDE 0.782 0.751 0.784 3537 3527 3531.2
BGA 0.801 0.782 0.792 3501 3461 3481.8
EBGWO (Ours)
0.935 0.903 0.919 220 103 143.4
Colon
BGWO1
0.887 0.855 0.865 1316 1096 1189.4
BGWO2
0.919 0.871 0.900 622 351 455.2
BPSO 0.849 0.829 0.839 986 931 936.5
BDE 0.810 0.780 0.794 995 955 965.3
BGA 0.881 0.875 0.878 990 984 987.3
EBGWO (Ours)
0.985 0.970 0.977 1148 781 1005.5
Lung Cancer
BGWO1
0.966 0.941 0.951 7598 6621 7211
BGWO2
0.975 0.956 0.966 2672 2167 2413.2
BPSO 0.936 0.931 0.935 6196 6179 6180.7
BDE 0.931 0.921 0.924 6256 6218 6226.8
BGA 0.952 0.939 0.945 6235 6214 6218.2
Values in bold represent the best result and values in italic denote the worst in each column, respectively.
An Excited Binary Grey Wolf Optimizer for Feature Selection in Highly Dimensional Datasets
131

iii) 𝑀𝑖𝑛_𝐴𝑐𝑐 Minimum Accuracy value
obtained when a given algorithm is repeated
for 10 independent runs.
iv) 𝐴𝑣𝑔_𝐴𝑐𝑐: Is the average of all the accuracy
values obtained when a given algorithm is
repeated for 10 independent runs.
v) 𝑀𝑎𝑥_𝑁𝑓𝑒𝑎𝑡: Is the Maximum number of
features reported by a given algorithm
during the 10 independent runs.
vi) 𝑀𝑖𝑛_𝑁𝑓𝑒𝑎𝑡: Is the Minimum number of
features reported by a given algorithm
during the 10 independent runs.
vii) 𝐴𝑣𝑔_𝑁𝑓𝑒𝑎𝑡 Is the average of all the
number of features reported by a given
algorithm during the 10 independent runs.
viii) Dataset: Captures the datasets utilized for
experimentation as articulated in Table 1.
It is important to point out that the best result
achieved in each column for all the considered gene
expression datasets is highlighted in bold while the
worst is italicized.
Concerning the classification accuracy, as
presented in Table 3, the proposed EBGWO
algorithm outperformed all the competing when the
fitness function (refer to Equation 24) was adopted.
Concerning the selection of the informative subset
of genes, again the proposed EBGWO identified
subsets with the least number of features to achieve
the highest classification accuracy for all the seven
highly dimensional microarray datasets considered in
this paper.
6 CONCLUSION AND FUTURE
WORKS
An excited grey wolf optimizer (EGWO) is proposed
in this paper. In the proposed algorithm, the concept
of the complete current response of a direct current
(DC) excited resistor capacitor (RC) circuit are
innovatively utilized to make the non-linear control
strategy of parameter 𝑎 of the GWO adaptive. Since
this scheme allocates a large proportion of the number
of iterations to global exploration compared to local
exploitation, the convergence speed of the proposed
EGWO algorithm is enhanced while minimizing the
local minima trapping effect. Moreover, since the
proposed scheme assigns each wolf a value of
parameter 𝑎 that is proportional its fitness values in
both the search space and the current iteration
(generation), diversity and the quality of the solutions
is improved as well.
To overcome premature converge (a limitation of
existing versions of GWO algorithms) and still
maintain the social hierarchy of the pack, a new
position-updated equation utilizing the fitness values
of vectors 𝑋
⃗

, 𝑋
⃗

and 𝑋
⃗

is proposed in determining
new candidate individuals.
As a feature selector, EBGWO is compared with
five metaheuristic algorithms i.e. BGWO1, BGWO2,
BPSO, BDE and BGA that are in existence. The
obtained experimental results revealed that EBGWO
yielded the best performance and overtook the other
algorithms. EBGWO not only attained the highest
classification accuracy, but also selected subsets with
the least number of informative features (genes). In
conclusion, the proposed EBGWO is successful, and
more appropriate to be used as a feature selector in
highly dimensional datasets. For further works, a
chaotic map can be adopted to fine-tune the
parameters of the EBGWO. Utilizing EBGWO as a
hybrid filter-wrapper for feature selection seeking to
evaluate the generality of the selected attributes will
be another valuable contribution. Moreover, EGWO
will be applied to other optimization areas, such as
training neural network, knapsack, and numerical
problems.
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