New Fitness Functions in Binary Harris Hawks Optimization for Gene

Selection in Microarray Datasets

Ruba Abu Khurma

, Pedro A. Castillo

, Ahmad Sharieh

and Ibrahim Aljarah

King Abdullah II School for Information Technology,

The University of Jordan, Amman, Jordan

Department of Computer Architecture and Computer Technology, ETSIIT and CITIC,

University of Granada, Granada, Spain

Keywords:

Swarm Intelligence, Harris Hawks Optimization, Gene Selection, Microarray Technology.

Abstract:

Gene selection (GS) is a challenging problem in medical applications. This is because of the availability of a

large number of genes and a limited number of patient’s samples in microarray datasets. Selecting the most

relevant genes is a necessary pre-processing step for building reliable cancer classiﬁcation systems. This paper

proposes two new ﬁtness functions in Binary Harris Hawks Optimization (BHHO) for GS. The main objective

is to select a small number of genes and achieve high classiﬁcation accuracy. The ﬁrst ﬁtness function balances

between the classiﬁcation performance and the number of genes. This is done by using a weight that increases

linearly throughout the optimization process. The second ﬁtness function is applied across two-stages. The

ﬁrst stage optimizes the classiﬁcation performance only while the second stage takes into consideration the

number of genes. K-nearest neighbor (K-nn) is used to evaluate the proposed approaches on ten microarray

data sets. The results show that the proposed ﬁtness functions can achieve better classiﬁcation results compared

with the ﬁtness function that takes into account only the classiﬁcation performance. Besides, they outperform

three other wrapper-based methods in most of the cases. The second ﬁtness function outperforms the ﬁrst

ﬁtness function across most of the datasets based on classiﬁcation accuracy and the number of genes.

1 INTRODUCTION

Microarray technology is a major application in

medicine and bioinformatics. In recent years, gene

expression datasets have been used for the diagnosis

of many diseases such as cancer disease. The gene

expression data sets cause a challenging problem for

data mining tasks (e.g classiﬁcation). This is because

they are coded by a large number of genes and a lim-

ited number of instances that represent the clinical pa-

tient status (Alomari et al., 2018). The large dimen-

sionality problem, also known as the curse of dimen-

sionality problem has many negative consequences

on the classiﬁcation system. The existence of irrel-

evant and redundant genes reduces the effectiveness

of the generalization process, complicates the learned

model, increases the learning time, makes the identi-

ﬁcation of a disease a difﬁcult task and increases the

cost of the biological classiﬁcation system due to in-

creasing the demand for specialized resources.

Gene selection (GS) is a data mining method that

is used to simplify the large scale gene expression data

sets by retaining the most informative genes. These

are considered the key marker in the identiﬁcation of

a disease (Chuang et al., 2011). The noisy genes such

as irrelevant and redundant genes are discarded and

eliminated from the training process. This can sim-

plify the learning model, speed up the learning pro-

cess, and potentially increase the performance of dis-

ease identiﬁcation (Mohamad et al., 2011). The out-

put of the GS process is a compact gene expression

data that can be used in the testing stage to produce

the ﬁnal decision about the clinical status of a patient.

GS compromises the search and evaluation pro-

cesses. According to evaluation, the GS methods are

commonly classiﬁed into ﬁlter and wrapper methods

(Khurma et al., 2020). The ﬁlter methods (e.g In-

formation gain) use the intrinsic characteristics of the

dataset. Wrapper methods uses a learning algorithm

in GS process to perform an internal learning process.

The search algorithm examines the gene space to

ﬁnd the optimal subset of genes that contains the most

useful genes in the diagnosis of a disease. Tradition-

ally, the complete search methods generate the entire

gene space and exhaustively traverse all the gene sub-

sets. This leads to an exponential running time, which

makes GS an Np-hard problem.

Meta-heuristic algorithms (MH) are stochastic

Khurma, R., Castillo, P., Sharieh, A. and Aljarah, I.

New Fitness Functions in Binary Harris Hawks Optimization for Gene Selection in Microarray Datasets.

DOI: 10.5220/0010021601390146

In Proceedings of the 12th International Joint Conference on Computational Intelligence (IJCCI 2020), pages 139-146

ISBN: 978-989-758-475-6

 2020 by SCITEPRESS – Science and Technology Publications, Lda. All r ights reserved

139

search methods that have been widely used to miti-

gate the GS process (Khurma. et al., 2020). They

initialize random solutions at the beginning of the

search and iteratively evaluate and update them until a

stopping criterion is satisﬁed. MH algorithms include

the Swarm Intelligence (SI) algorithm (Khurma et al.,

2020).

SI algorithms are inspired by the natural behavior

of creatures such as a ﬂock of birds, swarm of wolves,

school of ﬁsh. Swarm-based systems share informa-

tion between the individuals of a swarm to survive.

Common examples of SI algorithms include Parti-

cle Swarm Optimization (PSO) (Emary et al., 2016),

Grey Wolves Optimization (GWO) (Zawbaa et al.,

2018), Bat Algorithm (BA) (Al-Betar et al., 2020),

and Cuckoo Search (CS) (Moghadasian and Hosseini,

2014).

The search process in SI algorithms has mainly

two phases: exploration and exploitation. In explo-

ration, the individuals search globally in the gene

search space to ﬁnd the most promising region that

may include the optimal solution. In exploitation, the

individuals search locally in the found region to ap-

proach to the optimal solution.

Many SI algorithms have been proposed and mod-

iﬁed in the literature to increase the performance of

GS process for classiﬁcation of diseases. In (Tran

et al., 2014), the Binary Particle Swarm optimization

algorithm (BPSO) was modiﬁed by adopting the re-

set strategy to allow the stagnated best solution to

jump from local minima. The BPSO was modiﬁed

by Boolean algebra operation in (Emary et al., 2016).

The BPSO was modiﬁed using the binary quantum

operator in (Xi et al., 2016). The new model called

BQPSO applied a sampling around the personal best,

then used the average of the sampled points to update

the current solution. A hybrid model called GWO-

ALO integrated the GWO and Ant Lion Optimiza-

tion (ALO) in (Zawbaa et al., 2018). The main ob-

jective was to exploit the global search ability of the

GWO and the local search performance of the ALO.

A model compromised of the CS algorithm, Mutual

Information (MI), entropy ﬁlters, and artiﬁcial neu-

ral network (ANN) was proposed in (Moghadasian

and Hosseini, 2014). In (Al-Betar et al., 2020), a

hybrid ﬁlter/wrapper, called rMRMR-MBA was pro-

posed based on robust Minimum Redundancy Max-

imum Relevancy (rMRMR) ﬁlter and a modiﬁed bat

algorithm (MBA) using TRIZ optimisation operators.

Harris Hawks Optimization (HHO) is a new SI

algorithm proposed in 2019 (Heidari et al., 2019).

The HHO simulates the hunting behavior of Harris’

hawks in nature. The extensive experimental com-

parisons in (Heidari et al., 2019) showed that HHO

outperformed well-regarded optimization algorithms

when they were investigated on unconstrained, uni-

modal, multi-modal, and composition problems. A

wide range of applications adopted the HHO algo-

rithm (Thaher et al., 2020). However, HHO has never

been used in the medical and bioinformatics applica-

tions. This paper investigates for the ﬁrst time the

performance of the HHO algorithm in solving the GS

problem. The accuracy and the size of the selected

gene subsets are used as evaluation measurements.

The stability of the clinical classiﬁcation system is de-

termined by noticing the standard deviation of the av-

erage accuracy results across 30 runs of the algorithm.

This paper aims to develop a new ﬁtness function

in HHO for GS in microarray data sets. The over-

all goal is to enhance the classiﬁcation performance

of cancer diseases. The expectation is to determine

the smallest subset of relevant genes that can increase

the classiﬁcation performance. To achieve this goal,

this paper proposes two new ﬁtness functions in HHO

for solving the GS problem. The new ﬁtness func-

tions will be evaluated on ten benchmark microarray

data sets with different numbers of genes and sam-

ples. Speciﬁcally, we will investigate:

• The performance of HHO with a ﬁtness function

that considers the classiﬁcation performance only.

• The performance of HHO with a ﬁtness function

that considers the classiﬁcation performance and

number of genes simultaneously.

• The performance of HHO with a two-stage ﬁtness

function that considers the classiﬁcation perfor-

mance ﬁrst then takes into account the number of

selected genes.

The remainder of the paper is organized as fol-

lows: Harris Hawks Optimization is presented in Sec-

tion 2. Section 3 describes the HHO for GS. Section

4 describes the two proposed BHHO based GS ap-

proaches with new ﬁtness functions. Section 5 de-

scribes the experimental design. Section 6 presents

the experimental results with discussions. Compar-

isons with wrapper-based GS methods are provided

in Section 7. Finally, Section 8 provides conclusions

and future work.

2 HARRIS HAWKS

OPTIMIZATION

HHO has two phases of exploration and four phases

of exploitation.

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2.1 Exploration Phase

In HHO, the Harris’ hawks perch randomly on some

locations and wait to detect a prey based on two

strategies. By considering equal chance q for each

perching strategy, they perch based on the positions

of other family members and the rabbit, which is

modeled in Eq. (1) for the condition of q < 0.5, or

perch on random tall trees , which is modeled in Eq.

(1) for condition of q ≥ 0.5.

X(t+1) =



rand

(t) − r

rand

(t) − 2r

X(t)

q ≥ 0.5

rabbit

(t) − X

(t)) − r

(LB + r

(UB − LB)) o.w

(1)

where X(t + 1) is the position vector of hawks in the

next iteration t, X

rabbit

(t) is the position of rabbit, X(t)

is the current position vector of hawks, r

, r

and q are random numbers inside (0,1), which are up-

dated in each iteration, LB and UB show the upper and

lower bounds of variables, X

rand

(t) is a randomly se-

lected hawk from the current population, and X

is the

average position of the current population of hawks.

The average position of hawks is attained using Eq.

(2):

(t) =

∑

i=1

(t) (2)

where X

(t) indicates the location of each hawk in it-

eration t and N denotes the total number of hawks. It

is possible to obtain the average location in different

ways, but we utilized the simplest rule.

2.2 Transition from Exploration to

Exploitation

The HHO algorithm can transfer from exploration to

exploitation then change between different exploita-

tive behaviors based on the escaping energy of the

prey. The escaping behavior of prey decreases the

energy of prey considerably. The energy of prey is

modeled as:

E = 2E

(1 −

) (3)

where E indicates the escaping energy of the prey,

T is the maximum number of iterations, and E

the initial state of its energy. In HHO, E

randomly

changes inside the interval (-1, 1) at each iteration.

2.3 Exploitation Phase

According to the escaping behaviors of the prey and

chasing strategies of the Harris’ hawks, four possible

strategies are proposed in the HHO to model the at-

tacking stage. The preys always try to escape from

threatening situations. Suppose that r is the chance

of prey in successfully escaping (r <0.5) or not suc-

cessfully escaping (r ≥0.5) before surprise pounce.

Whatever the prey does, the hawks will perform a

hard or soft besiege to catch the prey. In this regard,

when |E| ≥0.5, the soft besiege happens, and when

|E| <0.5, the hard besiege occurs.

• Soft besiege: when r ≥ 0.5 and |E| ≥ 0.5. This

behavior is modeled by the following rules:

X(t + 1) = ∆X(t)− E

rabbit

(t) − X (t)

(4)

∆X(t) = X

rabbit

(t) − X (t) (5)

where ∆X(t) is the difference between the posi-

tion vector of the rabbit and the current location in

iteration t, r

is a random number inside (0,1), and

J = 2(1−r

) represents the random jump strength

of the rabbit throughout the escaping procedure.

The J value changes randomly in each iteration to

simulate the nature of rabbit motions.

• Hard besiege: when r ≥0.5 and |E| <0.5. In this

situation, the current positions are updated using

Eq. (6):

X(t + 1) = X

rabbit

(t) − E

∆X(t)

(6)

• Soft besiege with progressive rapid dives: when

still |E| ≥0.5 but r <0.5. This procedure is more

intelligent than the previous case.

To mathematically model the escaping patterns of

the prey, the levy ﬂight (LF) concept is utilized in

the HHO algorithm. To perform a soft besiege,

the hawks can evaluate (decide) their next move

based on the following rule in Eq. (7):

Y = X

rabbit

(t) − E

rabbit

(t) − X (t)

(7)

Then, they compare the possible result of such a

movement to the previous dive to detect that will

it be a good dive or not. If it was not reasonable,

they also start to perform irregular, abrupt, and

rapid dives when approaching the rabbit based on

the LF-based patterns using the following rule:

Z = Y + S × LF(D) (8)

where D is the dimension of problem and S is a

random vector by size 1 × D and LF is the levy

ﬂight function, which is calculated using Eq. (9)

(Yang, 2010):

LF(x) = 0.01×

u × σ

, σ =

Γ(1 + β) × sin(

πβ

)

Γ(

1+β

) × β × 2

(

β−1

)

(9)

New Fitness Functions in Binary Harris Hawks Optimization for Gene Selection in Microarray Datasets

141

where u, v are random values inside (0,1), β is a

default constant set to 1.5. Hence, the ﬁnal strat-

egy for updating the positions of hawks in the soft

besiege phase can be performed by Eq. (10):

X(t + 1) =



Y i f F(Y ) < F(X(t))

Z i f F(Z) < F(X(t))

(10)

where Y and Z are obtained using Eqs.(7) and (8).

• Hard besiege with progressive rapid dives

When |E| <0.5 and r <0.5, the following rule is

performed in hard besiege condition:

X(t + 1) =



Y i f F(Y ) < F(X(t))

Z i f F(Z) < F(X(t))

(11)

where Y and Z are obtained using new rules in

Eqs.(12) and (13).

Y = X

rabbit

(t) − E

rabbit

(t) − X

(t)

(12)

Z = Y + S × LF(D) (13)

where X

(t) is obtained using Eq. (2).

The pseudocode of the proposed HHO algorithm

is reported in Algorithm 1.

3 HHO ALGORITHM FOR GENE

SELECTION

The HHO algorithm was ﬁrst used for solving the fea-

ture selection problem (FS) in (Thaher et al., 2020).

The methodology used for converting the continuous

HHO into binary is a two-step binarization method.

In this method, the solution is transformed into bi-

nary but the real operators are used without convert-

ing. The solutions are converted into binary using two

steps. The ﬁrst step is by using a transfer function

(TF) to convert the real solution R

into intermedi-

ate vector [0, 1]

. Each element in the vector contains

a probability of converting the corresponding feature

or gene into either ”0” or ”1”.The second step is per-

formed by using a speciﬁc binarization method.

This paper uses the S-shaped TF, which was used

ﬁrstly in (Kennedy and Eberhart, 1997) to convert the

continuous PSO into binary using Eq 14.

T (x

(t)) =

1 + e

−x

(t)

(14)

Algorithm 1: Pseudo-Code of HHO algorithm.

Inputs: The population size N and maximum num-

ber of iterations T

Outputs: The location of rabbit and its ﬁtness

value

Initialize the random population X

(i = 1, 2, . . . , N)

while (stopping condition is not met) do

Calculate the ﬁtness values of hawks

Set X

rabbit

as the location of rabbit (best loca-

tion)

for (each hawk (X

)) do

Update the initial energy E

and jump

strength J  E

=2rand()-1, J=2(1-rand())

Update the E using Eq. (3)

if (|E| ≥ 1) then  Exploration phase

Update the location vector using Eq. (1)

if (|E| < 1) then  Exploitation phase

if (r ≥0.5 and |E| ≥ 0.5 ) then  Soft

besiege

Update the location vector using Eq.

(4)

else if (r ≥0.5 and |E| < 0.5 ) then 

Hard besiege

Update the location vector using Eq.

(6)

else if (r <0.5 and |E| ≥ 0.5 ) then 

Soft besiege with progressive rapid dives

Update the location vector using Eq.

(10)

else if (r <0.5 and |E| < 0.5 ) then 

Hard besiege with progressive rapid dives

Update the location vector using Eq.

(11)

Return X

rabbit

4 PROPOSED BHHO BASED

GENE SELECTION

APPROACHES

This section describes the BHHO algorithm for GS

with three ﬁtness functions. The basic ﬁtness func-

tion concerns the overall classiﬁcation performance.

The other new ﬁtness functions are proposed to fur-

ther increase the classiﬁcation performance and mini-

mize the number of selected genes in HHO GS frame-

work.

4.1 Basic Fitness Function: Error Rate

The BHHO can be used to solve the GS problem us-

ing a single objective ﬁtness function. This ﬁtness

ECTA 2020 - 12th International Conference on Evolutionary Computation Theory and Applications

142

function utilizes the classiﬁcation performance only.

The main target is to maximize the classiﬁcation accu-

racy or minimize the error rate in classiﬁcation tasks.

Eq 15 shows the basic ﬁtness function which will be

used as a baseline for comparison with the new ﬁtness

functions.

Fitness

= ErrorRate (15)

Where ErrorRate is determined according to Equa-

tion 6:

ErrorRate =

FP + FN

T P + T N + FP + FN

(16)

Where T P, T N, FP and FN stand for true pos-

itives, true negatives, false positives and false nega-

tives, respectively.

4.2 New Fitness Function: Error Rate

and # Genes

Using the basic function in Eq 15, the BHHO may

select a gene subset that has irrelevant or redundant

genes. This is because the formula doesn’t take into

account minimizing the number of features, but focus

on the classiﬁcation performance only. This causes

to select gene subsets that increases the classiﬁca-

tion performance and discard the number of selected

genes. The problem of this approach is that the

BHHO may select a gene subset with a classiﬁca-

tion performance that may be achieved by a smaller

gene subset. To address this problem, a new multi-

objective ﬁtness function is proposed that aims to

maximize the classiﬁcation performance (minimize

the classiﬁcation error rate) and minimizes the num-

ber of genes. The formula of the new ﬁtness function

is shown in Eq 17.

Fitness

= α

#Genes

#All Genes

+ (1 − α

) ×

ErrorRate

Error

(17)

Where

= α

max

(18)

Where α ∈ [0, 1]. t denotes the tth iteration in the

optimization process. #Genes represents the number

of selected genes. #AllGenes stands for the number

of all the available genes. ErrorRate is the classi-

ﬁcation error rate got by the selected gene subset.

Error

is the error rate got by using all the available

genes. α

max

is the predeﬁned maximum value of α

and α

max

∈ [0, 1]. T is the predeﬁned maximum num-

ber of iterations for the BHHO evolutionary process.

Using Eq 17, the relative importance of the num-

ber of genes and the classiﬁcation error rate is deter-

mined by the α

and (1 − α

) respectively. The er-

ror rate is always assumed more signiﬁcant than the

size of the genes subset. Thus, the (1 − α) is assigned

to value greater than the α

max

. α

increases linearly

throughout the optimization process of the BHHO.

This means that the error rate has greater importance

at the initial stages of the optimization process. The

linear increment of the α

causes to reduce the im-

portance of the error rate at the late stages. The op-

posite case occurs for the number of selected genes.

The size of a genes subset is given larger weights at

the latter stages. Another matter is that the number

of genes is much larger than the error rate. Thus, a

normalization step is required to balance these com-

ponents. This is done by dividing the size of genes

subset by the total number of genes. The result will

fall in the range (0,1]. Besides, the classiﬁcation er-

ror rate is divided by the error rate got by using all

available genes. This will transform the error rate to a

value in the range [0,1]. Normalizing the error rate is

a necessary step because in some microarray data sets,

the error rate changes in a small range throughout the

evolutionary process. Another issue is that

ErrorRate

Error0

may be larger than 1 at the begging of the optimiza-

tion process. This is normal because the error rate is

required to dominate the evolutionary process at the

initial stages. When α

increases to a relatively large

value, BHHO reduces the value of ErrorRate to be

smaller than the Error

4.3 New Fitness Function: A Two-stage

Approach

In the proposed Fitness

, using a linear increasing

weight can balance the error rate and the number of

selected genes. Thus, it can solve the problem of

selecting redundant and irrelevant genes in the gene

subset. However, there is still a problem that the

BHHO selects a small gene subset with low classi-

ﬁcation performance instead of selecting a large gene

subset with high classiﬁcation performance. To solve

this problem, Fitness

is proposed to perform GS in

two stages. This implies that the entire optimization

process is divided into two stages. In the ﬁrst stage,

the BHHO concerns optimizing the classiﬁcation per-

formance. In the second stage, the number of selected

genes is considered in the ﬁtness function. In the two-

stage ﬁtness function, the BHHO uses the solutions

found in the ﬁrst stage to perform further optimiza-

tion for the number of genes. This causes the BHHO

to start in the second stage with optimized solutions

that achieved suitable classiﬁcation performance in

the ﬁrst stage. The ﬁtness function used in this two-

stage GS approach is shown in Eq 19.

New Fitness Functions in Binary Harris Hawks Optimization for Gene Selection in Microarray Datasets

143

Fitness

(

ErrorRate, Stage1

α ×

#Genes

#All Genes

+ (1 − α) ×

ErrorRate

Error

, Stage2

(19)

Where α is constant values and αin[0, 1]. α shows

the relative importance of the number of features and

(1 − α) shows the relative importance of the classi-

ﬁcation error rate. ErrorRate, #Genes, #All Genes,

ErrorRate, Error

are the same as the ones used in

Fitness

. As the classiﬁcation performance is as-

sumed to be more important than the number of fea-

tures, α is set to be smaller than (1 − α).

5 EXPERIMENTAL DESIGN

All the experiments were executed on a personal

machine with AMD Athlon Dual-Core QL-60 CPU

at 1.90 GHz and memory of 2 GB running Win-

dows7 Ultimate 64 bit operating system. The op-

timization algorithms have been all implemented

in Python in the EvoloPy-FS framework (Khurma

et al., 2020). Ten microarray datasets taken

from http://csse.szu.edu.cn/staff/zhuzx/Datasets.html

are used to evaluate the performance of the proposed

approach. The selected benchmark data sets are com-

monly used in many studies and cover the example of

small, medium, and large dimensional data sets. Table

1 shows the characteristics of the selected datasets.

Table 1: Gene expression datasets characteristics.

NO Datasets # Genes # Samples # classes

1 Breast 24,481 97 2

2 MLL 12,582 72 3

3 Colon 2000 62 2

4 ALL-AML 7129 72 2

5 ALL-AML-3C 7129 72 3

6 ALL-AML-4C 7129 72 4

7 CNS 7129 60 2

8 Ovarian 15,154 253 2

9 SRBCT 2308 83 4

10 Lymphoma 4026 62 3

The maximum number of iterations and the pop-

ulation size were set to 100 and 10 respectively. In

this work, the K-nn classiﬁer (K = 5) is used to as-

sess the goodness of each solution in the wrapper GS

approach. Each data set is randomly divided into two

parts; 80% for training and 20% for testing. To ob-

tain statistically signiﬁcant results, this division was

repeated 30 independent times. Therefore, the ﬁnal

statistical results represent the average over 30 inde-

pendent runs. As the maximum iteration is 100, in

the two-stage approach, the ﬁrst 50 iterations are the

ﬁrst stage and the last 50 iterations are the second

stage. We assume the number of genes is important

in GS but much less important than classiﬁcation ac-

curacy. Therefore, α

max

= 0.2 in Eq 17 and α = 0.2 in

Eq 19 in the second stage of the two-stage approach.

BGWO, BCS, and BBA were used for comparison

with the proposed approaches. The parameters set-

tings of them as follows: in GWO α value is [2,0].

In BA, Qmin Frequency minimum is 0, Qmax Fre-

quency maximum is 2, A Loudness is 0.5, r Pulse rate

is 0.5. In CS, pa value is 0.25 and β is 3/2.

The proposed evaluation measures are classiﬁca-

tion accuracy and number of selected genes.

6 RESULTS AND DISCUSSIONS

The experimental results of the three approaches on

ten datasets are shown in Table 2. In the table, “All”

means that all of the available genes are used for clas-

siﬁcation. BHHO-Er stands for the BHHO based GS

approach with Eq 15 as the ﬁtness function. BHHO-

ErNo and BHHO-2Stage represent the two proposed

GS approaches with Eq 17 and Eq 19 as ﬁtness func-

tions, respectively. “#A” and “#G” show the average

test accuracy and the size of the gene subsets selected

by each algorithm in 30 runs respectively. “Std-Acc”

represents the standard deviation of the 30 test accu-

racy achieved by each algorithm.

6.1 Results of BHHO with Basic Fitness

Function

Inspecting Table 2, it can be seen that the BHHO-

Er algorithm can select gene subsets with a sufﬁcient

number of genes and high classiﬁcation performance.

In comparison with the results of BHHO with all the

gene subsets, BHHO-Er achieves higher classiﬁcation

accuracy in almost all microarray data sets. Regard-

ing the number of selected genes, it appears that the

BHHO-Er minimized the number of selected genes to

half of the original number of genes. The 5K-nn clas-

siﬁer with BHHO-Er obtained a classiﬁcation accu-

racy similar to using all genes across only one data set

which is the Breast data set. The results suggest that

BHHO-Er can efﬁciently select a subset of relevant

genes that contains around half of the original genes

and increase the classiﬁcation performance. For ex-

ample, in the ALL-AML4c data set, with all the 7,129

genes, 5K-nn could achieve a classiﬁcation accuracy

of 81.425% while with 3,427 genes, it can increase

the classiﬁcation accuracy to 83.569%. All the stan-

dard deviation values shown by “StdAcc” are smaller

than 0.05 which indicates the stability of the proposed

approach.

ECTA 2020 - 12th International Conference on Evolutionary Computation Theory and Applications

144

Table 2: Experimental results.

Algorithm

Dataset

Breast MLL Colon ALL-AML ALL-AML3c

All #A 75.800 94.000 78.500 85.100 82.211

#G 24,481 12,582 2000 7129 7129

BHHO-Er #A 75.800 94.420 79.256 85.742 83.006

#G 12,175.217 8,052.48 1,031.111 3,831.838 2,176.441

#A-Std 2.111E-17 1.755E-3 52.800E-5 1.359E-3 4.251E-2

BHHO-ErNo #A 75.800 95.341 79.391 85.822 83.140

#G 6,242.655 7,839.554 853.333 2,815.955 1,792.734

#A-Std 2.111E-17 1.536E-3 50.211E-5 1.729E-3 4.671E-2

BHHO-2Stage #A 75.800 95.958 79.455 85.963 83.620

#G 5,451.103 4,936.015 811.111 2,560.499 1,866.121

#A-Std 2.111E-17 2.189E-3 44.369E-5 1.952E-5 5.008E-2

ALL-AML4c CNS Ovarian SRBCT Lymphoma

All #A 81.425 66.456 91.623 87.623 98.315

#G 7,129 7,129 15,154 2308 1026

BHHO-Er #A 83.569 67.889 94.569 87.612 98.450

#G 3,427 3,389.840 7,631.773 1,129.443 504.087

#A-Std 1.430E-2 4.223E-2 1.456E-2 2.854E-2 17.857E-5

BHHO-ErNo #A 84.001 68.201 95.226 87.655 98.596

#G 3,427.012 2,691.198 7,248.359 1,104.516 493.910

#A-Std 1.375E-2 4.985E-2 1.369E-2 2.159E-2 7.589E-5

BHHO-2Stage #A 84.250 68.025 95.631 87.598 98.629

#G 2,828.685 2,644.859 5,720.635 1,114.0716 503.106

#A-Std 1.231E-2 5.079E-2 1.175E-2 2.006E-2 8.438E-5

6.2 Results of BHHO with New Fitness

Function: Error Rate and #Genes

Based on the results in Table 2, the selected gene sub-

sets in most of the cases contains fewer than half of

the original number of genes. The highest reduc-

tion rate was achieved on the Breast data set, which

is around 75% of the original genes. In comparison

with the accuracy obtained by all the gene sets, the

BHHO-ErNo got a higher classiﬁcation rate across

all the data sets except the Breast data set. BHHO-

ErNo can search in the gene space and obtain gene

subsets with a smaller size than those obtained by the

BHHO-Er across all the data sets. The reduction rate

across four data sets is more than 16%. The highest

reduction rates were around 49% on the Breast data

set and 27% on the ALL-AML data set. Regarding the

standard deviation results, there is no clear difference

between the BHHO-Er and the BHHO-ErNo. This

supports the idea that adding the number of genes to

the formula of ﬁtness function as in Eq 17 helps the

BHHO to search in the gene space for smaller size

gene subsets. The removal of the irrelevant and redun-

dant genes can simplify the generated learning model

and achieve better classiﬁcation results on testing.

6.3 Results of BHHO with New

Two-Stage Fitness Function

Based on Table 2, the results of BHHO-2Stage shows

that the size of the selected gene subsets using this ap-

proach reached to around 60% of the number of origi-

nal genes in many cases. The Breast data set achieved

the highest reduction rate of around 78%. The gener-

ated gene subsets by BHHO-2Stage achieved higher

classiﬁcation performance compared with using all

genes across all the data sets except the Breast data

set. By comparing BHHO-2Stage with BHHO-Er,

BHHO-2Stage can generate smaller size gene subsets

than BHHO-Er. In comparison with the BHHO-Er,

the reduction of the average size is more than 20% in

six of ten data sets and it is around 55% in the Breast

data set. With smaller gene subsets, BHHO-2Stage

achieves better or same classiﬁcation performance as

“BPSO-Er” in almost all data sets. The standard de-

viation values in the two approaches are very close.

7 COMPARISONS WITH OTHER

WRAPPER-BASED GS

METHODS

To show the performance of the proposed ﬁtness func-

tions, we compare the best-proposed approach, which

is BHHO-2Stage with three well-known wrapper-

based GS methods. These are BGWO, BBA, and

BCS. We will apply theses GS approaches with a 2

stage ﬁtness function. Taking the Breast data set as an

example, BGWO selects 9,559 genes with a classiﬁ-

cation performance 72.44%, BCS selects 7,360 genes

with classiﬁcation performance 74.84%, and BBA se-

lects 6,289 genes with a classiﬁcation performance of

64.23%. The average number of genes in BHHO-

2Stage is 5,451.103 with classiﬁcation performance

75.800. These results show the superiority of the

New Fitness Functions in Binary Harris Hawks Optimization for Gene Selection in Microarray Datasets

145

BHHO-2Stage approach to other well-known GS ap-

proaches using the same ﬁtness function.

8 CONCLUSIONS

This paper presents a new GS method based on the

BHHO algorithm and KNN classiﬁer. Two new ﬁt-

ness functions are proposed. The ﬁrst ﬁtness function

combines the classiﬁcation performance and the size

of the genes subset in one formula. A linear weight

is used to balance these components together. The

second one is a two-stage ﬁtness function. This fo-

cuses on optimizing the classiﬁcation performance in

the ﬁrst stage and optimizing the number of genes in

the second stage. The new two ﬁtness functions were

compared with a common ﬁtness function that uses

the classiﬁcation performance only in a BHHO based-

wrapper GS approach. The results show that BHHO

with the ﬁtness function that uses the classiﬁcation

performance only can improve the classiﬁcation per-

formance using all genes. In almost all the data sets,

BHHO with either of the two proposed ﬁtness func-

tions could achieve higher classiﬁcation performance.

Besides, they could achieve a fewer number of genes

than BHHO with overall classiﬁcation performance as

the ﬁtness function. BHHO with the two-stage ﬁtness

function outperforms the linearly changing weights

ﬁtness function in most problems based on the clas-

siﬁcation performance and the number of genes se-

lected. BHHO with the proposed ﬁtness functions can

successfully reduce the number of genes and achieve

higher classiﬁcation performance. In the future, we

will investigate a BHHO-based evolutionary multi-

objective GS approach to explore the Pareto front of

non-dominated solutions.

ACKNOWLEDGMENTS

This work is supported by the Ministerio espa

nol de

Econom

ıa y Competitividad under project TIN2017-

85727-C4-2-P (UGR-DeepBio).

REFERENCES

Al-Betar, M. A., Alomari, O. A., and Abu-Romman, S. M.

(2020). A triz-inspired bat algorithm for gene selec-

tion in cancer classiﬁcation. Genomics, 112(1):114–

126.

Alomari, O. A., Khader, A. T., Al-Betar, M. A., and

Alyasseri, Z. A. A. (2018). A hybrid ﬁlter-wrapper

gene selection method for cancer classiﬁcation. In

2018 2nd International Conference on BioSignal

Analysis, Processing and Systems (ICBAPS), pages

113–118. IEEE.

Chuang, L.-Y., Yang, C.-S., Wu, K.-C., and Yang, C.-

H. (2011). Gene selection and classiﬁcation using

taguchi chaotic binary particle swarm optimization.

Expert Systems with Applications, 38(10):13367–

13377.

Emary, E., Zawbaa, H. M., and Hassanien, A. E. (2016).

Binary grey wolf optimization approaches for feature

selection. Neurocomputing, 172:371–381.

Heidari, A. A., Mirjalili, S., Faris, H., Aljarah, I., Mafarja,

M., and Chen, H. (2019). Harris hawks optimization:

Algorithm and applications. Future generation com-

puter systems, 97:849–872.

Kennedy, J. and Eberhart, R. C. (1997). A discrete bi-

nary version of the particle swarm algorithm. In 1997

IEEE International conference on systems, man, and

cybernetics. Computational cybernetics and simula-

tion, volume 5, pages 4104–4108. IEEE.

Khurma., R. A., Aljarah., I., and Sharieh., A. (2020). An

Efﬁcient Moth Flame Optimization Algorithm using

Chaotic Maps for Feature Selection in the Medical

Applications. In Proceedings of the 9th International

Conference on Pattern Recognition Applications and

Methods - Volume 1: ICPRAM,, pages 175–182. IN-

STICC, SciTePress.

Khurma, R. A., Aljarah, I., Sharieh, A., and Mirjalili, S.

(2020). Evolopy-fs: An open-source nature-inspired

optimization framework in python for feature selec-

tion. In Evolutionary Machine Learning Techniques,

pages 131–173. Springer.

Moghadasian, M. and Hosseini, S. P. (2014). Binary cuckoo

optimization algorithm for feature selection in high-

dimensional datasets. In International conference

on innovative engineering technologies (ICIET’2014),

pages 18–21.

Mohamad, M. S., Omatu, S., Deris, S., and Yoshioka, M.

(2011). A modiﬁed binary particle swarm optimiza-

tion for selecting the small subset of informative genes

from gene expression data. IEEE Transactions on in-

formation Technology in Biomedicine, 15(6):813–822.

Thaher, T., Heidari, A. A., Mafarja, M., Dong, J. S., and

Mirjalili, S. (2020). Binary harris hawks optimizer for

high-dimensional, low sample size feature selection.

In Evolutionary Machine Learning Techniques, pages

251–272. Springer.

Tran, B., Xue, B., and Zhang, M. (2014). Improved pso

for feature selection on high-dimensional datasets. In

Asia-Paciﬁc Conference on Simulated Evolution and

Learning, pages 503–515. Springer.

Xi, M., Sun, J., Liu, L., Fan, F., and Wu, X. (2016). Can-

cer feature selection and classiﬁcation using a binary

quantum-behaved particle swarm optimization and

support vector machine. Computational and mathe-

matical Methods in Medicine, 2016.

Yang, X.-S. (2010). Nature-inspired metaheuristic algo-

rithms. Luniver press.

Zawbaa, H. M., Emary, E., Grosan, C., and Snasel,

V. (2018). Large-dimensionality small-instance set

feature selection: A hybrid bio-inspired heuristic

approach. Swarm and Evolutionary Computation,

42:29–42.

ECTA 2020 - 12th International Conference on Evolutionary Computation Theory and Applications

146