Multi-Objective Bees Algorithm for Feature Selection

Natalia Hartono

1,2 a

Department of Mechanical Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, U.K.

Department of Industrial Engineering, University of Pelita Harapan, MH Thamrin Boulevard 1100, Tangerang, Indonesia

Keywords: Bees Algorithm, Classification, Feature Selection, Machine Learning, Multi-objective.

Abstract: In machine learning, there are enormous features that can affect learning performance. The problem is that

not all the features are relevant or important. Feature selection is a vital first step in finding a smaller number

of relevant features. The feature selection problem is categorised as an NP-hard problem, where the possible

solution exponentially surges when the number of n-dimensional features increases. Previous research in

feature selection has shifted from single-objective to multi-objective because there are two conflicting

objectives: minimising the number of features and minimising classification errors. Bees Algorithm (BA) is

one of the most popular metaheuristics for solving complex problems. However, none of the previous studies

used BA in feature selection using a multi-objective approach. This paper aims to present the first study using

the Multi-objective Bees Algorithm (MOBA) as a wrapper approach in feature selection. The MOBA

developed for this study using basic combinatorial BA with combinatorial of swap, insertion and reversion as

local operators with Non-Dominated Sorting and Crowding Distance to find the Pareto Optimal Solutions.

The performance evaluation using nine Machine Learning classifiers shows that MOBA performs well in

classification. Future work will improve the MOBA and use larger datasets.

1 INTRODUCTION

The main issue in machine learning and data mining

is that there are immense features that are often

redundant and unrelated that lead to poor

performance of classification accuracy (Hammami et

al., 2019; Al-Tashi et al., 2020a; Jha and Saha, 2021).

The curse of dimensionality is a term coined by

Gheyas and Smith (2010) to describe a large number

of features (dimension) that leads to a large search

space size even though not all of the features are

relevant. To handle this problem, the researcher uses

feature selection. Researchers emphasise the benefit

of feature selections: reducing redundant data,

improving accuracy, and reducing the complexity of

the algorithm, thus increasing the algorithm training

speed (Xue et al., 2015; Hancer et al., 2018; Al-Tashi

et al., 2020a). Feature selection is known as an NP-

complete problem (Gheyas and Smith, 2010).

Albrecht (2006) provide the mathematical proof of

NP-complete of this feature selection problem. The

possible feature subsets are 2

with n features, which

is unrealistic to find the best subset using an

https://orcid.org/0000-0003-2314-1394

exhaustive search (Gheyas and Smith, 2010; Hancer

et al., 2018).

There are four known methods for feature

selection: filter method, wrapper method, hybrid

method, and embedded method (Jha and Saha, 2021).

The most widely used methods are the filter and

wrapper method. The difference between the filter

and wrapper lies in evaluating feature subsets, where

the wrapper uses classifiers in the evaluation process

(Al-Tashi et al., 2020a). Xue et al. (2015) point out

that the wrappers method is slower than filters but

yields better classification performance. Similarly,

other researchers also noted that the wrapper yields

more promising results than the filter approach

(Jimenez et al., 2017; Hancer et al., 2018; Hammami

et al., 2019). In addition, in their multi-objective

feature selection systematic literature review, Al-

Tashi et al. (2020a) reports that 84% of the articles

use the wrapper method, whereas 13% and 2% use the

filter method and hybrid method, respectively.

Adding to that, they also identify that the wrapper

method is exceptionally preferred by the researchers

because of the better performance compared to the

filter method.

358

Hartono, N.

Multi-Objective Bees Algorithm for Feature Selection.

DOI: 10.5220/0010754200003113

In Proceedings of the 1st International Conference on Emerging Issues in Technology, Engineering and Science (ICE-TES 2021), pages 358-369

ISBN: 978-989-758-601-9

Initial research for feature selection uses a single-

objective (SO) approach; however, the multi-

objective (MO) approach has gained attention in

recent years due to the ability to yield trade-off

solutions between two objectives (Wang et al., 2020).

In the literature review, the researcher has argued that

feature selection has at least two conflicting

objectives, for example, minimising the error rate of

classification and minimising the number of features

(Vignolo et al., 2013; Kozodoi et al., 2019; Al-Tashi

et al., 2020b). The MO approach is different from SO

because the best solution for one objective may not be

the best solution for the other objectives. The MO

approach gives different solutions that give trade-off

that balance between the objectives. Xue et al. (2015)

also compare the single-objective and multi-objective

approaches and concludes that multi-objective is

preferred over single-objective.

As explained earlier, it is impractical to search for

all possible solutions to find the best solution; the use

of metaheuristic in feature selection has attracted the

attention of researchers. Metaheuristics are well-

known for their ability to find a near-optimal solution

in a shorter computational time, and they have been

used in numerous studies. For example, Genetic

Algorithm and Particle Swarm Optimisation and its

MO version Non-dominated Sorting Genetic

Algorithm (NSGA-II) and MO-PSO are popular

metaheuristics used in feature selection. Regarding

the metaheuristic technique, one of the population-

based metaheuristics with a robust solution in the

continuous and combinatorial domain is Bees

Algorithm (BA). BA, inspired by the foraging activity

of honeybees to find nectar sources, was introduced

by Pham et al. (2005) and gained popularity due to its

ability to solve complex problems in faster

computational time and wide application in

engineering, business, bioinformatics (Yuce et al.,

2013; Hussein et al., 2017).

BA was used to solve SO feature selection. From

2007 to 2021, sixteen previous research articles are

used single-objective BA for feature selection. The

first research of single objective BA for feature

selection is in semiconductor manufacturing by Pham

et al. (2007), and the latest research in liver disease

case study by Ramlie et al. (2020). However, to date,

there is no single research using multi-objective BA

for feature selection. Hancer et al. (2018) also point

out in their study that multi-objective research for

feature selection is still in its early stages. Similar to

that, Kozodoi et al. (2019) said that the literature on

MOFS is lacking. Al-Tashi et al. (2020) supported

this view in their systematic literature review of

multi-objective feature selection (MOFS); they

provide 38 articles from 2012 to 2019. Further

literature search to find new articles until April 2021

shows that no previous studies use MOBA; thus,

MOBA’s potential for MOFS has not been

investigated. The previous studies in MOFS and the

research position of this study are depicted in Table

Initially, BA’s development is in the continuous

domain and yields good results because of the balance

between local and global search architecture;

however, in the combinatorial domain, the approach

is different due to different neighbourhood concepts;

thus, it needs a different approach in the local search

operator (Koc, 2010). Koc (2010) developed the

combinatorial BA using simple-swap and insertion as

local search operator with application in a single

machine scheduling problem. Ismail et al. (2020)

improve the local search operator using swap,

reverse, and insertion with the Travelling Salesman

Problem (TSP). The results show that the best local

search operator uses a combination of those three

operators (swap, reverse and insertion) rather than

using single operators. This version developed by

Ismail et al. (2020) is called basic combinatorial BA.

The second application of basic combinatorial BA in

Vehicle Routing Problem by Ismail et al. (2021).

Zeybek et al. (2021) improved the combinatorial BA

called VPBA-II using the Vantage Point (VP)

strategy proposed by Zeybek and Koc (2015). The

VPBA-II put the Vantage Point Tree (VPT) in the

initial solution and global search while keeping the

same local search operator with previous research by

Ismail et al. (2020). The difference between the basic

combinatorial BA and VPBA-II lies in the initial

solution and global search architecture, where the

former uses random permutation while the VPBA-II

uses VPT.

The current work is the first study using the Multi-

objective Bees Algorithm (MOBA) for feature

selection. The aim is to use a wrapper method using

MOBA for better classification with Pareto Optimal

Solutions that reduces the number of features while

minimising the error rate of classification. As

aforementioned, the wrapper method and multi-

objective approach produce better results, and this

study employs this approach in the development of

BA. In addition, the MOBA uses the same local

operators as basic combinatorial BA. As Al-Tashi et

al. (2020a) point out, the MOFS is gaining traction in

machine learning and data mining research due to its

enormous number of features. They suggest that the

area of MOFS still has a wide improvement

possibility in the future regarding improvement

accuracy, reduced computational time, the search

Multi-Objective Bees Algorithm for Feature Selection

359

Table 1: Previous Research and Research Position.

mechanism, the number of objectives, and

evaluation measure. Therefore, the contribution of

this study is two-fold. First, the current work is the

first study using MOBA for feature selection.

Secondly, this study used more than three Machine

Learning classifiers to measure the feature subsets'

performance.

2 METHODS (AND MATERIALS)

As explained earlier, the objective of MOBA for

feature selection in this study comprises of two

objectives: minimise the number of features and

minimise the error rate of classification.

Author Search Technique Evaluation Dataset

Xue et al. (2012) NSBPSO & CMDBPSO Filter UCI

Vignolo et al. (2013) MOGA Wrapper Essex Face Database

Mukhopadhyay and Maulik (2013) NSGA-II Wrapper Medical Dataset

Xue et al. (2013a) NSGA-II and SPEA2 Filter UCI

Xue et al. (2013b) MOPSO Wrapper UCI

Xia et al. (2014) MOUFSA Wrapper UCI

de la Hoz et al. (2014) NSGA-II Wrapper NSL-KDD

Tan et al. (2014) MmGA Wrapper UCI

Khan and Baig (2015) NSGA-II Wrapper UCI

Wang et al. (2015) MECY-FS Filter UCI

Han and Ren (2015) MO-MIFS & NSGA-II Wrapper (Own) Real

Kundu and Mitra (2015) NSGA-II Wrapper UCI

Kimovski et al. (2015) MOEA Wrapper BCI (Own)

Yong et al. (2016) MOPSO Wrapper UCI

Sahoo and Chandra (2017) MOGWO Wrapper (Own) Real

Mlakar et al. (2017) MODE Wrapper CK, MMI, JAFFE

Zhu et al. (2017) I-NSGA-III Wrapper NSL-KDD

Peimankar et al. (2017) MOPSO Wrapper DGA

Jiménez et al. (2017) ENORA Wrapper Kaggle

Sohrabi and Tajik (2017) NSGA-II & MOPSO Wrapper (Own) Real

Deniz et al. (2017) MOGA Wrapper UCI

Zhang et al. (2017) MOPSO Wrapper MULAN

Das and Das (2017) MOEA/D Wrapper UCI

Kizilos et al. (2018) MO-TLBO Wrapper UCI

Amoozegar and Minaei-Bidgoli (2018) MO-PSO Filter UCI

Hancer et al. (2018) MO-ABC Wrapper UCI

Dashtban et al. (2018) MO-Bat Wrapper Cancer Dataset

Lai (2018) MOSSO Hybrid Medical Dataset

Cheng et al. (2018) MOFSRank Wrapper LETOR

Kozodoi et al. (2019) NSGA-II Wrapper Credit Scoring (Kaggle)

González et al. (2019) NSGA-II Wrapper BCI (Own)

Sharma and Rani (2019) MOSHO & SSA Wrapper Cancer Dataset

Zhang et al. (2020) MOFSBDE Wrapper UCI

Nayak et al. (2020) FAEMODE Filter UCI

Al-Tashi et al. (2020) Grey Wolf Wrapper UCI

Wang et al. (2020) MO ABC Wrapper UCI

Rostami et al. (2020) MO PSO Wrapper Medical Dataset

Rodrigues et al. (2020) ABO Wrapper UCI

Rathee and Ratnoo (2020) NSGA-II + CHC Wrapper UCI

Khammasi and Krichen (2020) NSGAII and LR Wrapper NSL-KDD, UNSW-NB15, CIC-IDS2017

Kou et al. (2021) NSGA-II Wrapper (Own)

Karagoz et al. (2021) NSGA-II Wrapper MIR-Flickr and WMS

Jha and Saha (2021) MO PSO Filter UCI

Hu and Zhang (2021) PSOMOFS Wrapper UCI & Real (Own)

Hu et al. (2021) Grey Wolf Wrapper IEEE CEC3014

This paper MOBA Wrapper UCI

ICE-TES 2021 - International Conference on Emerging Issues in Technology, Engineering, and Science

360

The equation for multi-objective feature selection

as follows:

(

) = min(

(

)) (1)

where

(2)

and

2 = (ωtrain.Ftrain) + [(1 − ωtrain).Fval](3)

Fs denotes the Number of Feature Selected, ωtrain

denotes the weighting factor for training set in cross-

validation. For this study, the ωtrain set at 0.8. The

classification error on the training set is Ftrain, and

Fval is the classification error on the validating set.

The research steps for this study are depicted in

Figure 1, followed by the description of each step.

Figure 1: Research Steps in current work.

As depicted in Table 1, 89% of previous MOFS

studies use benchmark datasets, and only 11% use

their own datasets. The most widely used benchmark

datasets are the UCI Machine Learning Repository

(University of California). Due to the fact that

benchmark datasets are popular and concerning data

availability, this study uses the UCI Machine

Learning Repository, detailed in Table 2. The dataset

has a balanced distribution of classes.

Table 2: Benchmark Data Description.

Dataset

Number

Features

Number

Instances

Classes

Pima Indian

Diabetes

8 768 2

Breastcancer 9 699 2

Wine 13 178 3

Sonar 60 208 2

In this study, the MOBA for feature selection was

developed using the best local operator from basic

combinatorial BA. The combination of swap,

insertion and reserve introduced by Ismail et al.

(2020) was chosen for MOBA’s development. As a

wrapper-based method, the MOBA needs a classifier

to calculate the error of the classification. Al-Tashi et

al. (2020b) point out that the Artificial Neural

Network (ANN) is known as a superior classifier due

to its speed in classification. Moreover, Baptista et al.

(2013) suggest that one of the best ANN training

algorithms is Levenberg-Marquardt (LM)

backpropagation. The MOBA utilises ANN to

calculate the classification error, which in this study

uses LM backpropagation with 10 hidden layers and

a 0.8 learning rate. The MOBA parameter for this

study is as follows: 20 number of scout bees (n), 10

number of elite bees (nep), 5 number of best bees

(nsp), 1 number of elite sites (e) and 5 number of best

sites (m), maximum iteration 50. The MOBA

algorithm flowchart for this study is presented in

Figure 2.

The experiment runs 10 times using Matlab 2020a

in the University of Birmingham’s BEAR Cloud

service for each dataset. The results are Pareto

Optimal Solutions in the form of a feature subset that

balanced the two objectives. The performance

measurement for feature subsets generated by

MOBA, nine supervised Machine Learning (ML)

Techniques, is used to compare the accuracy of the

full features and the feature subsets. The ML

techniques are Medium Tree (MT), Linear

Discriminant (LD), Quadratic Discriminant (QD),

Gaussian Naive Bayes (GNB), Kernel Naive Bayes

(KNB), Linear Support Vector Machine (L-SVM),

Quadratic SVM (Q-SVM), Medium KNN (M-KNN),

and Cosine KNN (Co-KNN) with 10-fold cross-

validation.

Multi-Objective Bees Algorithm for Feature Selection

361

Figure 2: MOBA flowchart for this study.

3 RESULTS AND DISCUSSION

The benefit of using the MO approach is that

decision-makers will have more options to choose

from the Pareto Frontier. For example, figure 3

depicts the Pareto Optimal Solution from one of the

experiments performed on Wine Datasets. As can be

seen, the higher the number of features selected, the

lower the classification error. As a result, the

decision-maker could pick one subset for

classification calculations, saving time on the

experiments.

Table 3 provides the average results from 10 runs

for each dataset. It is apparent from this table that

MOBA is able to reduce the number of features by

more than 50%. The average ratio of selected features

ranges from 0.38 to 0.45. The average error of the

feature subset ranges from 0.05 to 0.17. Interestingly,

the bigger dataset shows lower errors.

As described in the previous section, the selected

features trained using nine ML classifiers and Pima

Indian Diabetes, Breastcancer, Wine and Sonar

presented in Table 4, 5, 6, and 7, respectively. The

MOBA feature subsets and the accuracy of the Pima

Indian Diabetes Dataset can be seen in Table 4. It

shows that most of the feature subsets generated by

MOBA for this dataset yield the same or better

accuracy (in bold) with a smaller number of features

than the accuracy of full features for all nine ML

training. The interesting finding in Table 5 is that

accuracy using Medium Tree and Coarse KNN is

higher than using all features. What stands out in

Table 6 is that in the 9th run, the feature subsets with

eight features (ratio equal to 0.6154) yield 100%

classification accuracy when trained using QD. Table

7 shows that the classification accuracy in each

feature subset is all higher in Medium KNN. Thus,

overall results from four benchmark datasets indicate

that feature subsets generated by MOBA yield good

performance for classification.

Figure 3: Pareto Optimal Solution on Wine Dataset.

Table 3: Average Size of Selected Features (f1), Average

Error of the Selected Features (f2) and Average Ratio of

Selected Features.

Dataset

Total

Features

Mean

Ratio

Pima Indian

Diabetes

8 3.05 0.17 0.38

Breastcance

9 3.68 0.17 0.41

Wine 13 5.57 0.05 0.43

Sona

60 26.95 0.09 0.45

This study confirms previous studies that not all

the features are relevant for classification, and a

reduced dimensionality can achieve similar or higher

classification accuracy. Furthermore, results show

that MOBA performs well in classification accuracy.

ICE-TES 2021 - International Conference on Emerging Issues in Technology, Engineering, and Science

362

Table 4: MOBA result and classification accuracy on Pima Indian Diabetes Dataset.

Run f1 f2

Feature

subsets

Accuracy

MT LD QD GNB KNB

SVM

KNN

Coarse

KNN

1 0.2193 F3 62.9% 65.1% 64.7% 64.7% 64.6% 65.1% 60.0% 59.5% 65.0%

3 0.1569 F2, F4, F6 72.8% 76.6% 75.1% 76.0% 75.3% 76.2% 75.1% 71.9% 75.1%

2 0.2081 F1, F4 66.3% 67.1% 67.3% 67.3% 66.4% 65.1% 66.9% 64.2% 68.0%

5 0.1450

F1, F2, F5,

F6, F8

73.6% 76.3% 75.4% 75.1% 74.0% 76.4% 76.7% 75.7% 75.9%

1 0.1996 F8 64.8% 65.6% 66.4% 66.4% 65.6% 65.0% 44.1% 62.5% 64.6%

5 0.1531

F2, F3, F4,

F7, F8

71.6% 76.7% 74.7% 77.0% 75.1% 76.3% 76.6% 72.8% 74.5%

3 0.1599 F1, F2, F7 72.3% 76.2% 75.4% 75.7% 76.0% 76.3% 75.5% 75.4% 76.0%

2 0.1929 F4, F8 65.5% 65.1% 66.1% 64.5% 67.3% 65.1% 64.5% 64.2% 67.2%

2 0.1934 F1, F8 66.5% 66.3% 65.8% 66.9% 66.9% 65.1% 64.6% 65.9% 66.8%

3 0.1512 F2, F7, F8 70.7% 75.3% 74.9% 75.1% 75.3% 74.3% 75.4% 73.4% 76.4%

6 0.1463

F1, F2, F4,

F6, F7, F8

73.2% 77.3% 74.7% 76.3% 77.5% 77.1% 76.0% 75.7% 75.0%

4 0.1470

F2, F6, F7,

73.3% 77.5% 76.4% 77.9% 77.3% 77.5% 77.7% 75.5% 77.6%

1 0.1997 F8 64.8% 65.6% 66.4% 66.4% 65.6% 65.0% 44.1% 62.5% 64.6%

2 0.1701 F2, F4 71.9% 73.7% 74.7% 74.6% 74.6% 74.2% 71.1% 71.0% 74.7%

5 0.1488

F1, F2, F4,

F6, F7, F8

72.9% 76.8% 75.1% 75.8% 77.1% 77.2% 77.0% 75.7% 76.0%

3 0.1531 F2, F6, F8 73.7% 76.8% 76.2% 77.0% 76.8% 76.7% 76.3% 74.7% 76.3%

2 0.2045 F1, F4 66.3% 67.1% 67.3% 67.3% 66.4% 65.1% 66.9% 64.2% 68.0%

3 0.1540 F2, F5, F8 73.4% 73.3% 75.3% 73.2% 70.4% 74.1% 76.0% 72.7% 76.7%

5 0.1449

F2, F3, F5,

F6, F8

73.8% 77.3% 75.1% 76.2% 73.2% 77.2% 77.0% 75.5% 75.8%

4 0.1497

F2, F5, F7,

70.3% 75.3% 74.1% 74.7% 72.7% 75.7% 76.7% 74.7% 75.9%

1 0.2201 F3 62.9% 65.1% 64.7% 64.7% 64.6% 65.1% 63.2% 59.5% 65.0%

4 0.1512

F2, F3, F6,

73.6% 76.7% 75.9% 77.2% 75.8% 76.6% 77.7% 75.8% 76.0%

3 0.1768 F5, F6, F8 70.3% 68.0% 69.7% 69.0% 70.6% 68.2% 69.7% 71.5% 68.0%

2 0.1950 F1, F8 66.5% 66.3% 65.8% 66.9% 66.9% 65.1% 64.6% 65.9% 66.8%

1 0.2162 F7 64.8% 65.6% 66.4% 66.4% 65.6% 65.1% 41.9% 62.5% 64.6%

4 0.1533

F1, F2, F7,

70.2% 75.8% 75.7% 74.7% 74.7% 75.7% 76.2% 76.4% 75.4%

3 0.1889 F5, F7, F8 66.5% 65.9% 67.6% 67.8% 69.3% 65.1% 67.3% 66.5% 68.5%

2 0.1893 F5, F6 66.1% 67.2% 68.8% 67.6% 67.4% 65.1% 55.6% 67.3% 65.1%

2 0.1936 F4, F8 65.5% 65.1% 66.1% 64.5% 67.3% 65.1% 64.5% 64.2% 67.2%

4 0.1503

F2, F4, F6,

74.0% 76.7% 75.4% 76.8% 77.3% 77.2% 77.2% 75.5% 76.6%

3 0.1620 F2, F3, F7 69.5% 74.2% 74.3% 75.4% 74.7% 74.1% 74.9% 73.7% 74.3%

1 0.1696 F2 71.2% 74.7% 75.0% 75.0% 74.2% 74.6% 47.0% 70.2% 74.0%

5 0.1529

F1, F2, F3,

F6, F8

74.2% 77.0% 75.7% 75.7% 76.0% 76.8% 78.0% 75.5% 75.1%

3 0.1540 F2, F5, F6 72.1% 75.7% 74.9% 75.1% 71.1% 75.9% 75.5% 74.9% 75.0%

2 0.1584 F2, F6 72.8% 77.1% 76.0% 76.8% 75.5% 76.0% 74.2% 73.8% 75.0%

6 0.1443

F1, F2, F3,

F4, F6, F8

74.2% 77.0% 74.5% 76.2% 75.3% 76.4% 77.6% 77.1% 74.2%

5 0.1527

F1, F2, F5,

F6, F8

73.6% 76.3% 75.4% 75.1% 74.0% 76.4% 76.7% 75.7% 75.9%

3 0.1555 F2, F3, F8 72.1% 74.2% 75.3% 74.6% 74.6% 75.0% 77.0% 74.2% 74.3%

All

features

8 - F1-F8 74.2% 77.5% 73.4% 75.3% 73.0% 77.1% 76.7% 72.9% 73.8%

Multi-Objective Bees Algorithm for Feature Selection

363

Table 5: MOBA result and classification accuracy on Breastcancer Dataset.

Run f1 f2

Feature

subsets

Accuracy

MT LD QD GNB KNB

L-

SVM

Q-

SVM

M-

KNN

Co-

KNN

2 0.1839 F3, F4 68.9% 70.3% 71.3% 71.7% 70.3% 71.3% 67.8% 69.2% 70.3%

7 0.1560

F1, F3, F4,

F5, F6, F7,

67.5% 74.1% 72.0% 74.5% 70.6% 72.0% 75.5% 73.4% 70.3%

4 0.1614

F1, F4, F5,

73.1% 74.8% 72.0% 72.7% 71.7% 72.4% 74.5% 74.5% 70.3%

3 0.1770 F3, F6, F7 71.7% 71.7% 69.9% 70.3% 70.3% 70.3% 69.6% 70.3% 70.3%

1 0.2067 F8 70.3% 70.3% 70.3% 70.3% 70.3% 70.3% 70.3% 68.5% 70.3%

2 0.1758 F5, F6 75.2% 75.9% 71.0% 71.3% 70.3% 71.0% 76.2% 70.3% 70.3%

6 0.1496

F1, F5, F6,

F7, F8, F9

71.7% 73.8% 72.4% 71.7% 71.3% 71.0% 74.5% 75.2% 70.3%

5 0.1581

F1, F3, F4,

F5, F6

67.8% 73.1% 71.7% 73.4% 72.7% 72.0% 74.8% 73.4% 70.3%

2 0.1909 F3, F9 71.0% 67.5% 68.5% 69.2% 68.5% 70.3% 69.2% 67.5% 70.3%

5 0.1569

F4, F5, F6,

F7, F9

75.5% 75.2% 69.9% 72.7% 72.4% 72.0% 76.6% 72.0% 70.3%

3 0.1698 F3, F4, F6 71.3% 73.4% 72.7% 72.7% 73.1% 71.7% 75.9% 72.7% 70.6%

2 0.2006 F2, F8 71.0% 70.3% 68.9% 70.3% 70.3% 70.3% 70.3% 65.0% 70.3%

6 0.1421

F1, F3, F5,

F6, F7, F9

72.0% 73.4% 71.3% 71.7% 71.7% 71.0% 74.5% 73.8% 70.3%

5 0.1677

F4, F5, F6,

F7, F8

73.4% 74.8% 74.1% 73.8% 73.4% 72.0% 74.5% 73.8% 70.3%

3 0.1835 F1, F4, F9 67.1% 72.7% 69.9% 72.0% 72.0% 71.7% 67.5% 69.2% 70.3%

2 0.1833 F4, F5 69.6% 72.0% 72.0% 72.0% 71.7% 72.0% 69.9% 71.3% 70.3%

5 0.1608

F2, F4, F5,

F7, F9

72.4% 72.7% 69.2% 70.6% 71.3% 72.0% 73.4% 72.7% 70.3%

3 0.1657 F3, F5, F6 76.2% 75.5% 70.3% 71.7% 71.0% 71.3% 76.2% 74.5% 70.3%

2 0.1862 F1, F6 72.7% 72.4% 69.2% 72.0% 71.0% 70.3% 72.0% 72.4% 70.3%

6 0.1534

F1, F2, F3,

F5, F6, F8

71.0% 75.2% 72.4% 71.3% 71.3% 71.3% 76.2% 72.0% 70.3%

4 0.1630

F2, F4, F5,

73.8% 74.5% 73.8% 72.7% 73.4% 72.0% 75.2% 74.8% 70.3%

3 0.1774 F4, F6, F7 73.8% 75.2% 74.5% 73.1% 73.1% 71.7% 75.2% 74.1% 70.3%

1 0.2085 F7 70.3% 70.3% 70.3% 70.3% 70.3% 70.3% 70.3% 70.3% 70.3%

6 0.1540

F2, F4, F5,

F7, F8, F9

73.1% 72.4% 70.6% 71.0% 71.7% 72.0% 71.7% 73.1% 70.3%

2 0.1709 F4, F6 74.8% 74.1% 73.4% 72.7% 73.4% 71.7% 75.5% 74.8% 71.7%

4 0.1649

F4, F6, F7,

73.4% 74.8% 73.8% 73.8% 72.0% 71.7% 74.8% 74.5% 70.3%

1 0.2079 F8 70.3% 70.3% 70.3% 70.3% 70.3% 70.3% 70.3% 68.5% 70.3%

5 0.1566

F1, F3, F5,

F6, F9

72.0% 74.1% 71.7% 71.7% 72.7% 70.3% 75.5% 71.3% 70.3%

3 0.1773 F2, F5, F6 74.1% 75.9% 71.3% 71.7% 70.3% 71.3% 76.2% 75.2% 70.3%

4 0.1723

F2, F3, F4,

72.0% 71.0% 72.4% 72.0% 70.3% 72.0% 72.7% 68.2% 70.3%

3 0.1738 F1, F4, F7 74.8% 72.4% 71.7% 71.7% 70.6% 71.7% 74.5% 74.1% 70.3%

5 0.1488

F3, F5, F6,

F7, F8

72.0% 75.9% 72.4% 70.6% 72.0% 71.3% 75.2% 73.4% 70.3%

4 0.1630

F2, F4, F6,

73.1% 73.8% 71.3% 73.1% 72.0% 71.7% 74.5% 72.7% 70.3%

2 0.1824 F3, F4 68.9% 70.3% 71.3% 71.7% 70.3% 71.3% 67.8% 69.2% 70.3%

6 0.1506

F3, F4, F5,

F6, F7, F9

70.3% 73.8% 69.9% 73.1% 72.7% 72.0% 76.6% 73.1% 70.3%

5 0.1659

F3, F4, F5,

F6, F8

71.7% 74.5% 73.1% 73.1% 72.4% 72.0% 75.5% 72.7% 70.3%

4 0.1748

F4, F5, F7,

72.4% 72.4% 69.6% 70.6% 71.7% 72.0% 73.8% 70.3% 70.3%

All

features

F1 - F9 65.4% 74.1% 69.2% 72.0% 72.0% 72.0% 72.4% 72.7% 70.3%

ICE-TES 2021 - International Conference on Emerging Issues in Technology, Engineering, and Science

364

Table 6: MOBA result and classification accuracy on Wine Dataset.

Run f1 f2 Feature subsets

Accurac

MT LD QD GNB KNB L-SVM Q-SVM

M-

KNN

Co-KNN

2 0.071 F1, F12 88.2% 89.3% 88.2% 88.2% 88.8% 89.3% 87.6% 88.8% 85.4%

7 0.022

F2, F3, F5, F6,

F10, F11, F13

89.9% 94.4% 95.5% 94.9% 94.9% 96.1% 94.4% 93.8% 88.8%

5 0.053

F3, F5, F6, F7,

F11

91.0% 86.0% 93.3% 88.8% 90.4% 87.1% 93.3% 87.6% 77.5%

4 0.062 F2, F4, F6, F10 88.2% 88.8% 93.8% 88.2% 93.8% 89.9% 91.6% 90.4% 79.2%

7 0.015

F1, F6, F7, F9,

F11, F12, F13

90.4% 93.8% 98.9% 94.9% 94.9% 95.5% 96.1% 94.9% 69.1%

5 0.025

F2, F6, F7,

F10, F13

92.7% 96.1% 97.2% 94.4% 97.2% 94.9% 97.2% 95.5% 78.7%

6 0.019

F2, F5, F7,

F10, F12, F13

91.6% 94.9% 96.6% 94.9% 95.5% 95.5% 96.1% 95.5% 82.6%

4 0.028

F7, F8, F10,

F13

93.3% 93.8% 95.5% 93.8% 94.4% 93.8% 97.2% 93.8% 78.7%

7 0.015

F1, F3, F4, F6,

F7, F12, F13

91.6% 96.1% 97.8% 94.4% 95.5% 97.2% 95.5% 96.1% 77.0%

6 0.027

F1, F3, F6, F7,

F9, F13

89.3% 95.5% 98.3% 93.8% 93.3% 93.3% 94.9% 94.9% 80.9%

4 0.111 F2, F6, F9, F13 85.4% 87.1% 87.1% 87.1% 89.3% 87.1% 87.1% 88.8% 71.9%

8 0.015

F1, F2, F3, F6,

F7, F8, F11,

F13

90.4% 95.5% 98.9% 94.9% 94.9% 94.9% 96.6% 94.9% 86.5%

5 0.031

F1, F2, F4,

F12, F13

92.7% 93.3% 93.3% 93.8% 96.1% 94.4% 94.4% 96.1% 84.8%

3 0.125 F7, F8, F12 75.3% 82.6% 86.5% 82.6% 83.1% 83.1% 83.7% 83.1% 56.2%

4 0.036 F1, F7, F8, F10 92.7% 92.1% 96.6% 93.3% 94.4% 92.1% 94.9% 93.8% 78.7%

9 0.016

F1, F4, F6, F7,

F8, F10, F11,

F12, F13

88.8% 96.6% 97.8% 97.2% 96.6% 97.2% 97.2% 96.1% 80.3%

6 0.026

F2, F5, F10,

F11, F12, F13

89.3% 93.8% 94.9% 95.5% 96.1% 94.9% 95.5% 95.5% 89.3%

2 0.080 F1, F12 88.2% 89.3% 88.2% 88.2% 88.8% 89.3% 87.6% 88.8% 85.4%

7 0.015

F2, F3, F5, F6,

F10, F11, F13

89.9% 94.4% 95.5% 94.9% 94.9% 96.1% 94.4% 93.8% 88.8%

5 0.054

F3, F5, F6, F7,

F11

91.0% 86.0% 93.3% 88.8% 90.4% 87.1% 93.3% 87.6% 77.5%

4 0.050 F2, F4, F6, F10 88.2% 88.8% 93.8% 88.2% 93.8% 89.9% 91.6% 90.4% 79.2%

6 0.018

F1, F3, F7, F8,

F10, F12

92.1% 95.5% 97.2% 93.3% 94.9% 95.5% 95.5% 93.8% 89.3%

9 0.002

F1, F3, F4, F5,

F6, F7, F8,

F10, F13

91.6% 98.3% 98.3% 97.8% 97.8% 97.8% 97.2% 97.2% 83.7%

5 0.035

F2, F6, F7,

F10, F13

92.7% 96.1% 97.2% 94.4% 97.2% 94.9% 97.2% 95.5% 78.7%

4 0.074

F1, F7, F10,

F13

92.1% 96.6% 96.6% 96.1% 97.2% 94.9% 97.2% 96.1% 83.7%

8 0.013

F1, F3, F5, F8,

F9, F11, F12,

F13

89.3% 96.1% 97.8% 96.6% 96.6% 94.9% 97.2% 94.9% 88.8%

5 0.030

F1, F3, F6,

F12, F13

91.6% 94.9% 93.3% 93.3% 94.9% 93.8% 92.1% 94.9% 82.0%

6 0.022

F4, F6, F8, F9,

F10, F13

93.8% 91.0% 94.9% 93.8% 95.5% 92.7% 91.6% 91.6% 78.1%

5 0.026

F2, F6, F10,

F12, F13

93.3% 94.9% 95.5% 93.8% 95.5% 96.1% 94.9% 95.5% 80.3%

8 0.000

F1, F3, F4, F7,

F9, F11, F12,

F13

91.0% 97.2% 100.0% 97.2% 97.8% 98.9% 98.9% 97.8% 82.0%

7 0.018

F1, F4, F5, F9,

F10, F11, F13

91.6% 95.5% 97.2% 98.3% 97.8% 96.1% 95.5% 94.9% 86.5%

3 0.111 F3, F11, F12 77.0% 75.3% 80.9% 78.1% 77.5% 72.5% 80.9% 77.5% 77.0%

4 0.031

F1, F3, F11,

F12

91.6% 93.3% 95.5% 92.1% 95.5% 95.5% 95.5% 93.8% 91.0%

9 0.006

F2, F3, F4, F8,

F9, F10, F11,

F12, F13

90.4% 98.3% 97.2% 97.2% 97.2% 98.9% 98.3% 94.9% 91.0%

6 0.016

F2, F7, F9,

F10, F11, F13

92.7% 96.1% 97.2% 95.5% 96.6% 96.1% 96.6% 95.5% 80.3%

All

Features

13 - F1 - F13 88.8% 98.9% 99.4% 97.2% 96.6% 98.3% 96.6% 97.2% 83.7%

Multi-Objective Bees Algorithm for Feature Selection

365

Table 7: MOBA result and classification accuracy on Sonar Dataset.

Run f1 f2

Accuracy

MT LD QD GNB KNB

L-

SVM

Q-

SVM

M-

KNN

Co-

KNN

24 0.099570351 74.5% 74.5% 80.8% 67.8% 77.4% 77.4% 82.7% 74.5% 70.2%

28 0.065141175 76.9% 76.4% 83.2% 66.3% 74.5% 75.0% 88.9% 75.5% 67.8%

26 0.082009824 75.0% 73.1% 73.1% 67.8% 76.9% 75.0% 86.1% 73.6% 65.4%

25 0.087133333 69.7% 74.0% 84.6% 66.3% 73.1% 75.5% 80.8% 75.0% 70.2%

26 0.119605592 69.2% 69.7% 80.3% 71.2% 78.4% 73.6% 88.9% 78.8% 67.8%

34 0.066256786 66.8% 76.4% 80.8% 63.5% 74.5% 75.0% 85.6% 72.6% 72.1%

27 0.067409799 76.0% 73.6% 79.8% 66.3% 79.8% 75.5% 81.3% 77.4% 70.2%

22 0.082342043 67.8% 76.0% 86.5% 68.3% 76.0% 79.8% 83.2% 73.1% 69.2%

30 0.061619488 72.1% 73.6% 77.9% 67.3% 74.5% 71.6% 79.3% 75.5% 69.7%

25 0.073323144 68.8% 72.1% 79.3% 64.9% 75.0% 75.5% 82.2% 78.4% 68.3%

28 0.069419249 77.4% 75.5% 80.8% 65.4% 73.1% 74.5% 81.7% 77.4% 70.2%

22 0.156447064 75.0% 74.5% 70.7% 63.9% 70.7% 72.6% 78.8% 74.0% 69.7%

32 0.073525597 74.0% 75.0% 78.4% 65.9% 72.1% 77.9% 85.6% 73.6% 74.0%

26 0.116298846 66.8% 73.1% 81.7% 67.8% 79.3% 76.9% 85.1% 77.4% 69.2%

28 0.081887471 75.5% 75.0% 81.7% 65.4% 74.0% 75.0% 84.1% 75.0% 70.7%

22 0.114538244 70.2% 72.6% 73.6% 65.9% 75.0% 75.5% 74.0% 76.4% 71.6%

31 0.062488966 72.6% 75.5% 82.2% 70.7% 76.0% 74.0% 84.1% 76.9% 71.6%

30 0.092796008 70.2% 72.1% 82.2% 67.3% 77.9% 76.0% 82.7% 73.1% 71.6%

26 0.095563806 73.1% 72.6% 81.7% 70.2% 74.0% 76.9% 86.5% 74.5% 66.8%

24 0.123323653 68.3% 73.1% 76.4% 72.1% 70.7% 73.6% 81.7% 73.1% 68.8%

33 0.07257117 69.2% 75.0% 82.7% 68.8% 77.4% 77.4% 85.1% 75.0% 68.8%

26 0.080773004 72.1% 73.1% 76.9% 65.4% 72.6% 76.9% 80.8% 73.1% 72.6%

25 0.108421803 70.7% 76.4% 76.4% 70.7% 76.0% 78.8% 84.1% 73.6% 66.3%

25 0.106049107 73.1% 76.4% 81.3% 66.8% 79.3% 76.9% 87.0% 77.4% 70.2%

32 0.069255874 72.6% 72.6% 76.0% 70.2% 76.4% 80.3% 86.1% 75.0% 68.3%

29 0.086057013 71.2% 72.6% 78.4% 67.3% 73.1% 74.5% 80.8% 68.3% 66.8%

26 0.098852021 76.9% 75.0% 81.7% 66.3% 75.5% 74.5% 80.8% 71.6% 70.2%

22 0.086423399 68.8% 70.7% 81.3% 67.8% 71.6% 72.1% 83.2% 76.0% 66.3%

38 0.06712303 69.7% 73.1% 82.2% 66.8% 78.8% 76.4% 87.5% 73.6% 69.2%

31 0.081604734 67.3% 75.0% 78.4% 67.3% 74.0% 75.5% 80.3% 77.9% 65.9%

32 0.074393338 73.6% 75.0% 80.3% 65.4% 72.6% 72.1% 84.1% 76.4% 72.6%

22 0.08962364 73.6% 70.2% 78.4% 66.3% 76.0% 70.2% 79.3% 76.9% 66.3%

30 0.062019176 72.1% 77.4% 79.3% 65.4% 75.5% 78.4% 83.7% 79.8% 69.2%

23 0.089152606 68.3% 70.2% 78.4% 65.4% 73.1% 73.6% 80.8% 74.0% 67.8%

25 0.083410711 75.5% 72.1% 76.9% 67.3% 74.0% 75.0% 80.8% 78.8% 73.1%

34 0.071585229 69.7% 74.5% 73.6% 66.8% 73.6% 75.0% 80.8% 75.0% 67.3%

27 0.076225531 62.5% 73.6% 75.5% 70.7% 75.5% 75.0% 79.3% 75.5% 65.9%

26 0.079361732 74.5% 77.4% 80.3% 64.9% 76.9% 80.3% 85.6% 74.0% 70.2%

All

features

60 - 72.6% 76.4% 74.5% 69.2% 76.4% 76.9% 87.0% 72.1% 72.1%

ICE-TES 2021 - International Conference on Emerging Issues in Technology, Engineering, and Science

366

4 CONCLUSIONS

The current work is a wrapper-based Multi-objective

Bees Algorithm (MOBA) for feature selection. The

study aim is to propose the first study of MOBA for

feature selection. The results of four benchmark

datasets confirm earlier research that feature selection

is required to reduce dimensionality and yield

equivalent or superior classification performance.

However, there are limitations and room for

improvement because this is the first MOBA study,

and some issues were not addressed. To begin with,

the optimal parameter for MOBA has not been

considered in this study. Second, the largest feature in

this study is 60 features; thus, this proposed algorithm

has not been tested on larger datasets.

Third, the development of MOBA using basic

combinatorial BA can be improved, for example,

adding the abandonment strategy, which is a strategy

in the standard (continues) BA. Fourth, this study has

not compared with other methods. Future works will

overcome these four limitations.

ACKNOWLEDGEMENTS

The author would like to acknowledge the generous

support from the Indonesia Endowment Fund for

Education (LPDP); Professor DT Pham; and

Industrial Engineering University of Pelita Harapan.

Thank you to the University of Birmingham for

providing flexible resources for intensive

computational work to the University’s research

community through BEAR Cloud Service.

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