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<front>
<journal-meta>
<journal-id journal-id-type="pmc">CMC</journal-id>
<journal-id journal-id-type="nlm-ta">CMC</journal-id>
<journal-id journal-id-type="publisher-id">CMC</journal-id>
<journal-title-group>
<journal-title>Computers, Materials &#x0026; Continua</journal-title>
</journal-title-group>
<issn pub-type="epub">1546-2226</issn>
<issn pub-type="ppub">1546-2218</issn>
<publisher>
<publisher-name>Tech Science Press</publisher-name>
<publisher-loc>USA</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">33513</article-id>
<article-id pub-id-type="doi">10.32604/cmc.2023.033513</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Voting Classifier and Metaheuristic Optimization for Network Intrusion&#x00A0;Detection</article-title>
<alt-title alt-title-type="left-running-head">Voting Classifier and Metaheuristic Optimization for Network Intrusion Detection</alt-title>
<alt-title alt-title-type="right-running-head">Voting Classifier and Metaheuristic Optimization for Network Intrusion Detection</alt-title>
</title-group>
<contrib-group content-type="authors">
<contrib id="author-1" contrib-type="author">
<name name-style="western"><surname>Khafaga</surname><given-names>Doaa Sami</given-names>
</name><xref ref-type="aff" rid="aff-1">1</xref></contrib>
<contrib id="author-2" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Karim</surname><given-names>Faten Khalid</given-names>
</name><xref ref-type="aff" rid="aff-1">1</xref><email>fkdiaaldin@pnu.edu.sa</email></contrib>
<contrib id="author-3" contrib-type="author">
<name name-style="western"><surname>Abdelhamid</surname><given-names>Abdelaziz A.</given-names>
</name><xref ref-type="aff" rid="aff-2">2</xref>
<xref ref-type="aff" rid="aff-3">3</xref></contrib>
<contrib id="author-4" contrib-type="author">
<name name-style="western"><surname>El-kenawy</surname><given-names>El-Sayed M.</given-names>
</name><xref ref-type="aff" rid="aff-4">4</xref></contrib>
<contrib id="author-5" contrib-type="author">
<name name-style="western"><surname>Alkahtani</surname><given-names>Hend K.</given-names>
</name><xref ref-type="aff" rid="aff-1">1</xref></contrib>
<contrib id="author-6" contrib-type="author">
<name name-style="western"><surname>Khodadadi</surname><given-names>Nima</given-names>
</name><xref ref-type="aff" rid="aff-5">5</xref></contrib>
<contrib id="author-7" contrib-type="author">
<name name-style="western"><surname>Hadwan</surname><given-names>Mohammed</given-names>
</name><xref ref-type="aff" rid="aff-6">6</xref></contrib>
<contrib id="author-8" contrib-type="author">
<name name-style="western"><surname>Ibrahim</surname><given-names>Abdelhameed</given-names>
</name><xref ref-type="aff" rid="aff-7">7</xref></contrib>
<aff id="aff-1"><label>1</label><institution>Department of Computer Sciences, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428</institution>, <addr-line>Riyadh, 11671</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-2"><label>2</label><institution>Department of Computer Science, Faculty of Computer and Information Sciences, Ain Shams University</institution>, <addr-line>Cairo, 11566</addr-line>, <country>Egypt</country></aff>
<aff id="aff-3"><label>3</label><institution>Department of Computer Science, College of Computing and Information Technology, Shaqra University</institution>, <addr-line>11961</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-4"><label>4</label><institution>Department of Communications and Electronics, Delta Higher Institute of Engineering and Technology</institution>, <addr-line>Mansoura, 35111</addr-line>, <country>Egypt</country></aff>
<aff id="aff-5"><label>5</label><institution>The Department of Civil and Environmental Engineering, Florida International University</institution>, <addr-line></addr-line><addr-line>Miami, FL</addr-line>, <country>USA</country></aff>
<aff id="aff-6"><label>6</label><institution>Department of Information Technology, College of Computer, Qassim University</institution>, <addr-line>Buraydah, 51452</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-7"><label>7</label><institution>Computer Engineering and Control Systems Department, Faculty of Engineering, Mansoura University</institution>, <addr-line>Mansoura, 35516</addr-line>, <country>Egypt</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Faten Khalid Karim. Email: <email>fkdiaaldin@pnu.edu.sa</email></corresp>
</author-notes>
<pub-date pub-type="epub" date-type="pub" iso-8601-date="2022-10-28"><day>28</day>
<month>10</month>
<year>2022</year></pub-date>
<volume>74</volume>
<issue>2</issue>
<fpage>3183</fpage>
<lpage>3198</lpage>
<history>
<date date-type="received">
<day>19</day>
<month>6</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>11</day>
<month>8</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Khafaga et al.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Khafaga et al.</copyright-holder>
<license xlink:href="https://creativecommons.org/licenses/by/4.0/">
<license-p>This work is licensed under a <ext-link ext-link-type="uri" xlink:type="simple" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</ext-link>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
</license>
</permissions>
<self-uri content-type="pdf" xlink:href="TSP_CMC_33513.pdf"></self-uri>
<abstract>
<p>Managing physical objects in the network&#x2019;s periphery is made possible by the Internet of Things (IoT), revolutionizing human life. Open attacks and unauthorized access are possible with these IoT devices, which exchange data to enable remote access. These attacks are often detected using intrusion detection methodologies, although these systems&#x2019; effectiveness and accuracy are subpar. This paper proposes a new voting classifier composed of an ensemble of machine learning models trained and optimized using metaheuristic optimization. The employed metaheuristic optimizer is a new version of the whale optimization algorithm (WOA), which is guided by the dipper throated optimizer (DTO) to improve the exploration process ofthe traditional WOA optimizer. The proposed voting classifier categorizes the network intrusions robustly and efficiently. To assess the proposed approach, a dataset created from IoT devices is employed to record the efficiency of the proposed algorithm for binary attack categorization. The dataset records are balanced using the locality-sensitive hashing (LSH) and Synthetic Minority Oversampling Technique (SMOTE). The evaluation of the achieved results is performed in terms of statistical analysis and visual plots to prove the proposed approach&#x2019;s effectiveness, stability, and significance. The achieved results confirmed the superiority of the proposed algorithm for the task of network intrusion detection.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Voting classifier</kwd>
<kwd>whale optimization algorithm</kwd>
<kwd>dipper throated optimization</kwd>
<kwd>intrusion detection</kwd>
<kwd>internet-of-things</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label>
<title>Introduction</title>
<p>Growth and flexibility in every area have been seen in the Internet of Things (IoT) during the last several years [<xref ref-type="bibr" rid="ref-1">1</xref>&#x2013;<xref ref-type="bibr" rid="ref-5">5</xref>]. The IoT in real-life is depicted in <xref ref-type="fig" rid="fig-1">Fig. 1</xref>. An increasing number of intelligent systems are based on IoT, and securing these systems is a significant challenge [<xref ref-type="bibr" rid="ref-6">6</xref>&#x2013;<xref ref-type="bibr" rid="ref-10">10</xref>]. In the current literature, cyber attack detection strategies for smart systems have been shown to be of great value. In the past, an IoT device breached by an attacker led to a power outage, affecting 225000 people [<xref ref-type="bibr" rid="ref-11">11</xref>] because the security mechanism was of insufficient quality. Interdependence among devices, limited variety, and more are only some of the characteristics of IoT technology [<xref ref-type="bibr" rid="ref-12">12</xref>]. We can better protect our smart systems by fully comprehending their functionalities. Since IoT devices communicate data with one another and with one other, the interdependence of these gadgets necessitates fewer human decisions and requires less human engagement. For example, an imaginative home scenario where the thermostat measures the temperature in the house and compares it to a preset threshold. When the thermostat detects a deviation from the preset temperature range, it attempts to restore equilibrium to the surrounding air. When it comes to maintaining a comfortable temperature, the smart plug is checked. When the AC is disconnected, the windows are automatically opened to maintain a stable temperature and allow for ventilation. Intruders can access a building by hacking into an IoT device and opening a door or window if the system is not adequately secured.</p>
<fig id="fig-1">
<label>Figure 1</label>
<caption>
<title>The domain of the internet of things (IoT) in real life</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_33513-fig-1.png"/>
</fig>
<p>Code injection and Man in the Middle (MitM) attacks [<xref ref-type="bibr" rid="ref-13">13</xref>] are two examples of attacks that might exploit an IoT device. Adversaries use code injection to modify data on IoT devices. These attacks employ techniques similar to listening for and intercepting communications between two nodes. An attacker can control a node in this scenario. Using an ensemble-based voting classifier for intrusion detection, this article examines how well it protects individual IoT devices while securing the network&#x2019;s dependency. The typical machine learning (ML) method was merged with the ensemble-based voting classifier, which then cast votes on each prediction to arrive at a final prediction. Soft voting and hard voting are two examples of voting. Section 3 contains a complete mathematical description of the suggested algorithm [<xref ref-type="bibr" rid="ref-14">14</xref>]. A real-world IoT network dataset named Ton-IoT is used to evaluate the performance of the technique proposed in this paper [<xref ref-type="bibr" rid="ref-15">15</xref>].</p>
<p>This paper includes the following: 1) A novel attack categorization model based on an ensemble has been suggested. Assessment of the presented method for IoT datasets 3) A comparison between the proposed and existing approaches is examined using various criteria. The rest of the document is structured as follows: Section 2 provides background information and an in-depth examination of IoT-related activities and dangers. Section 3 explores the solution under consideration. Data selection and pre-processing are discussed in Section 4. Section 5 wraps up the project and suggests some possible future avenues of exploration.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>Literature Review</title>
<p>By automating the working environment to decrease human participation and increase system efficiency, the Internet of Things (IoT) is a new technology [<xref ref-type="bibr" rid="ref-16">16</xref>]. As IoT technology continues to advance, new forms of cyberattacks are being developed daily. These networks are easy targets for cybercriminals because they lack adequate security measures. When an IoT device is hacked, attackers can control all of the other devices connected to that device [<xref ref-type="bibr" rid="ref-17">17</xref>]. Detecting an attacker&#x2019;s infiltration or malicious behavior on the network can help prevent these attacks from happening in the first place. Intrusion detection methods are crucial in spotting unwanted activity on networks like this. <xref ref-type="table" rid="table-1">Tab. 1</xref> summarizes the content of this chapter. Ensemble approaches, including Boosted Trees, Bagged Trees, Subspace Discriminant, and Boosted Trees, have been applied in [<xref ref-type="bibr" rid="ref-18">18</xref>] to offer routing protocol for low-power and lossy networks (RPL)-based network intrusion detection for IoT networks. Network intrusion detection systems (NIDS) are tested using the RPL-NIDS17 dataset. Authors in [<xref ref-type="bibr" rid="ref-19">19</xref>] presented an ensemble-based intrusion detection system to avoid harmful events in IoT networks, especially the botnet attack against hypertext transfer protocol (HTTP), message queuing telemetry transport (MQTT), and domain name space (DNS) protocols. An adaptive boost ensemble technique for attack detection was developed by combining three machine learning algorithms: decision tree (DT), na&#x00EF;ve Bayes (NB), and artificial neural network (ANN). An evaluation of the proposed technique was performed using the Network Information Management System (NIMS) botnet data sets.</p>
<table-wrap id="table-1">
<label>Table 1</label>
<caption>
<title>The models used in the literature for intrusion detection</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th>Paper</th>
<th>Model</th>
<th>Evaluation metrics</th>
</tr>
</thead>
<tbody>
<tr>
<td>[<xref ref-type="bibr" rid="ref-15">15</xref>]</td>
<td>Lineat Regression (LR), Linear Discriminant Analysis (LDA), k-Nearest Neighbors (KNN), Random Forest (RF), Classification and Regression Trees (CART)</td>
<td>Accuracy, Precision<break/>Recall, F-measure</td>
</tr>
<tr>
<td>[<xref ref-type="bibr" rid="ref-18">18</xref>]</td>
<td>Ensemble learning</td>
<td>Accuracy, Receiver Operating Characteristic (ROC)</td>
</tr>
<tr>
<td>[<xref ref-type="bibr" rid="ref-19">19</xref>]</td>
<td>Adaptive boost</td>
<td>ROC, Detection rate, Accuracy, False positive rate, ROC</td>
</tr>
<tr>
<td>[<xref ref-type="bibr" rid="ref-20">20</xref>]</td>
<td>Ensemble voting</td>
<td>F-measure, Detection rate, Accuracy, Precision</td>
</tr>
<tr>
<td>[<xref ref-type="bibr" rid="ref-21">21</xref>]</td>
<td>XGBoost</td>
<td>Precision, Accuracy<break/>ROC, F-measure, Recall</td>
</tr>
<tr>
<td>[<xref ref-type="bibr" rid="ref-22">22</xref>]</td>
<td>XGBoost</td>
<td>Accuracy</td>
</tr>
<tr>
<td>[<xref ref-type="bibr" rid="ref-23">23</xref>]</td>
<td>Ensemble learning</td>
<td>Precision, Accuracy,<break/>F1-Measure, Recall</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>A two-stage intrusion detection system was proposed in [<xref ref-type="bibr" rid="ref-20">20</xref>]. It is hypothesized that a voting ensemble classifier may be developed by selecting optimum features and combining C4.5 and RF and Random Forest by Penalizing Attribute (RF-PA) machine learning methods. Evaluation measures Accuracy, Precision, Detection rate, and F-measure were used to assess the presented techniques. Authors in [<xref ref-type="bibr" rid="ref-21">21</xref>] proposed employing the XGBoost model for intrusion detection. Evaluation measures included accuracy, precision, recall, and the F1 measure for the test dataset. As an assessment metric for an intrusion detection system based on Extreme Gradient Boosting (XGBoost), the proposed method was put to a test dataset [<xref ref-type="bibr" rid="ref-22">22</xref>]. To guard against attacks on wifi, authors in [<xref ref-type="bibr" rid="ref-23">23</xref>] suggested an ensemble-based intrusion detection system based on a dataset and assessed using the evaluation metrics accuracy, precision, recall, and F1-measure. This system is essential to enable narrowband and broadband IoT applications. To detect infiltration in IoT networks, Authors in [<xref ref-type="bibr" rid="ref-24">24</xref>] evaluated eleven methods, including seven supervised and three unsupervised ones. Unsupervised algorithms that performed best were found to use XGBOOST and Expectation-Maximization (EM). The accuracy, area under the curve (AUC), and Matthews correlation coefficient (MCC), of 11 algorithms were evaluated.</p>
<p>As with intrusion detection, however, the assessment of datasets [<xref ref-type="bibr" rid="ref-25">25</xref>] plays a significant role. IoT 4.0 telemetry datasets were proposed in [<xref ref-type="bibr" rid="ref-15">15</xref>] by writers who used a variety of attack scenarios to create a whole new generation of data. An IoT device data collection containing actual sensor readings from seven IoT sensors. DT and RF beat ML and deep learning (DL) algorithms in evaluation criteria like accuracy, precision, recall, F-measure, etc. Results reveal that a single machine learning algorithm&#x2019;s performance changes when the data from sensors vary. The best attack detection performance on every sensor, thus, requires ensemble-based learning. As previously stated, designing an optimum intrusion detection system requires a realistic dataset near real-time scenarios [<xref ref-type="bibr" rid="ref-26">26</xref>,<xref ref-type="bibr" rid="ref-27">27</xref>]. For this study, many openly accessible datasets were compared and analyzed using various criteria such as different attack scenarios, data from IoT telemetry, and independent datasets for each type of IoT item. Several publicly accessible datasets may be used to construct and analyze an intrusion detection system (IDS), such as the Labeled Wireless Sensor Network Data Repository (LWSNDR). Data created for evaluating IDSs in IoT and Industrial internet of things (IIoT) networks is now publicly available through a new dataset [<xref ref-type="bibr" rid="ref-28">28</xref>&#x2013;<xref ref-type="bibr" rid="ref-31">31</xref>].</p>
<p>Using Telemetry data from several IoT/IIoT services, this dataset includes information on a wide range of attacks. Fridge sensor, Garage door, Global Positioning Sensor (GPS), Weather, Motion light sensor, and Thermostat are all included in the dataset&#x2019;s 7 IoT devices. The data recorded in these datasets differ; hence, the retrieved dataset is derived from various sources. Garage door IoT devices, for example, only deal with &#x2018;ON&#x2019; or &#x2018;OFF&#x2019;, signifying the door&#x2019;s status, as not all IoT devices deal with the same kind of data. Some devices also deal with real-valued numeric data in the same way. The typical ML algorithm&#x2019;s performance does not remain constant as the kind of data changes. For this reason, we proposed an accurate classifier that could handle data and operate optimally on most devices in IoT networks by using DT, KNN, RF, and Na&#x00EF;ve Bayes (NB) algorithms, which we have integrated. An IDS may be analyzed using the dataset listed in <xref ref-type="table" rid="table-2">Tab. 2</xref>. An IDS for IoT devices can use the Ton-IoT dataset, which is based on data from various/separate IoT devices, as shown in the table above.</p>
<table-wrap id="table-2">
<label>Table 2</label>
<caption>
<title>Dataset preprocessing using locality sensitive hashing (LSH)-synthetic minority oversampling technique (SMOTE) balancing</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th>Category</th>
<th>Total instances in dataset</th>
<th>Utilized instances</th>
<th style="background:#FFFFFF;">Using LSH-SMOTE</th>
</tr>
</thead>
<tbody>
<tr>
<td>Attack</td>
<td>33,337</td>
<td>33,337</td>
<td style="background:#FFFFFF;">1,33,348</td>
</tr>
<tr>
<td>Normal</td>
<td>4,31,981</td>
<td>1,33,348</td>
<td style="background:#FFFFFF;">1,33,348</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s3">
<label>3</label>
<title>Methodology</title>
<p>To detect attacks on RPL-based IoT networks, we proposed a new algorithm based on dipper throated optimization (DTO) and whale optimization algorithm (WOA) in this paper. We referred to as (DTO-Guided WOA). This algorithm is employed to optimize the parameters of the voting classifier based on three classifiers, namely, neural networks (NN), RF, and KNN. Data collection, processing, and detection are all covered in the design of the suggested technique. Sniffer and sensor systems comprise the data collecting system. A sniffer may be necessary to access IPv6 over low-power wireless personal area networks (6LoWPAN). A database of sensor events and packets that have been intercepted and routed may be accessed. The dataset&#x2019;s most essential properties are then identified using a feature selection technique. The detecting system includes an alarm/attack notification module. Regularly, it does traffic analysis to offer user interfaces with log data. The architecture of the proposed approach is depicted in <xref ref-type="fig" rid="fig-2">Fig. 2</xref>.</p>
<fig id="fig-2">
<label>Figure 2</label>
<caption>
<title>The architecture of the proposed network intrusion detection system</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_33513-fig-2.png"/>
</fig>
<sec id="s3_1">
<label>3.1</label>
<title>Dataset Collection</title>
<p>The proposed method is trained using the RPL-NIDS17 dataset [<xref ref-type="bibr" rid="ref-32">32</xref>]. This data set was generated with the help of the NetSim application. Simulating many sorts of network infrastructures is easy using NetSim. The Internet of Things network includes a gateway, sensor nodes, a wired node, and a router. Each attack is documented in great detail in a comma-separated values (CSV) file. It&#x2019;s possible to merge all of the CSV files into a single dataset 20 features may be tagged using this dataset&#x2019;s time, essential, and flow properties. Aside from the primary traffic patterns, hello flooding, and selective forwarding that may be used in routing attacks, include Sybil (blackhole), sinkhole, and clone intrusion detections. This dataset only contains 33,337 routing attacks and 431,981 pieces of regular traffic. Because of the imbalance, the data is skewed.</p>
</sec>
<sec id="s3_2">
<label>3.2</label>
<title>Dataset Preprocessing</title>
<p>The first step in getting ready is to clean up your data. Encrypting and de-duplicating the data is also part of this process. Even though computers can only read numeric data, the dataset comprises numeric and nominal data. As a result, the dataset&#x2019;s characters have been converted to numeric values for storage. After all of this, data scaling is employed to speed things up. The dataset contains a wide range of characteristics, both in size and unit. Data integrity may be maintained throughout the time when scaled [<xref ref-type="bibr" rid="ref-33">33</xref>&#x2013;<xref ref-type="bibr" rid="ref-40">40</xref>]. As part of data preparation, the amount of samples in the dataset is balanced such that each class has equal numbers of samples [<xref ref-type="bibr" rid="ref-41">41</xref>&#x2013;<xref ref-type="bibr" rid="ref-47">47</xref>]. The locality-sensitive hashing and synthetic minority oversampling techniques were used here to accomplish this aim. Before and after balancing, the number of samples in the dataset is shown in <xref ref-type="table" rid="table-2">Tab. 2</xref>.</p>

</sec>
<sec id="s3_3">
<label>3.3</label>
<title>Dipper Throated Optimization</title>
<p>Dipper throated optimization (DTO) is based on tracking the locations and speeds of swimming and flying birds to simulate the genuine process of seeking food. Swimming birds&#x2019; positions and speeds are updated using these equations.</p>
<p><disp-formula id="eqn-1"><label>(1)</label><mml:math id="mml-eqn-1" display="block"><mml:mi>B</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>B</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>.</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>.</mml:mo><mml:mi>B</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>B</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:math></disp-formula>where <inline-formula id="ieqn-1"><mml:math id="mml-ieqn-1"><mml:mi>B</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> and <inline-formula id="ieqn-2"><mml:math id="mml-ieqn-2"><mml:mi>B</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are the normal location and best location of the bird at iteration <italic>t</italic>, and <inline-formula id="ieqn-3"><mml:math id="mml-ieqn-3"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-4"><mml:math id="mml-ieqn-4"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> are adaptive values whose values are changed during the optimization process based on the iteration number and random values. The flying bird&#x2019;s location is updated using the following equation.</p>
<p><disp-formula id="eqn-2"><label>(2)</label><mml:math id="mml-eqn-2" display="block"><mml:mi>B</mml:mi><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mi>B</mml:mi><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>B</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>B</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>B</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">G</mml:mi><mml:mi mathvariant="italic">b</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">t</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>B</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p><disp-formula id="eqn-3"><label>(3)</label><mml:math id="mml-eqn-3" display="block"><mml:mi>B</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>B</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>B</mml:mi><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>where <inline-formula id="ieqn-5"><mml:math id="mml-ieqn-5"><mml:mi>B</mml:mi><mml:mi>S</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> is the updated speed of each bird, <inline-formula id="ieqn-6"><mml:math id="mml-ieqn-6"><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> is a random number in [0; 1], <inline-formula id="ieqn-7"><mml:math id="mml-ieqn-7"><mml:mi>B</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">G</mml:mi><mml:mi mathvariant="italic">b</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">t</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> is the global best location, and <inline-formula id="ieqn-8"><mml:math id="mml-ieqn-8"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> is a weight value, <inline-formula id="ieqn-9"><mml:math id="mml-ieqn-9"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-10"><mml:math id="mml-ieqn-10"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> are constants.</p>
</sec>
<sec id="s3_4">
<label>3.4</label>
<title>Whale Optimization</title>
<p>Humpback whales forage for food using WOA, a novel metaheuristic algorithm described in [<xref ref-type="bibr" rid="ref-29">29</xref>]. Whales searching for tiny fish near the surface swim in a circle and make bubbles along a route that looks like a &#x201C;9,&#x201D; as illustrated in <xref ref-type="fig" rid="fig-3">Fig. 3</xref>. In the first phase of the algorithm, the encircling prey and the spiral bubble-net attack approach were depicted; in the second phase, the system searched for prey randomly (exploration phase). In the following sections, we will go through some details of the mathematical model of each phase. Random numbers will be generated using a uniform distribution, as shown in the formulae.</p>
<fig id="fig-3">
<label>Figure 3</label>
<caption>
<title>The hunting process of grey wolf optimization</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_33513-fig-3.png"/>
</fig>
<sec id="s3_4_1">
<label>3.4.1</label>
<title>Exploitation Phase</title>
<p>Humpback whales initially encircle their prey to catch it. <xref ref-type="disp-formula" rid="eqn-4">Eqs. (4)</xref> and <xref ref-type="disp-formula" rid="eqn-5">(5)</xref> can be used to represent this behavior quantitatively.</p>
<p><disp-formula id="eqn-4"><label>(4)</label><mml:math id="mml-eqn-4" display="block"><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:mi>C</mml:mi><mml:mspace width="thinmathspace" /><mml:mo>.</mml:mo><mml:mspace width="thinmathspace" /><mml:mover><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mover><mml:mi>X</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p><disp-formula id="eqn-5"><label>(5)</label><mml:math id="mml-eqn-5" display="block"><mml:mrow><mml:mover><mml:mi>X</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mover><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mover><mml:mi>A</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mspace width="thinmathspace" /><mml:mo>.</mml:mo><mml:mspace width="thinmathspace" /><mml:mi>D</mml:mi></mml:math></disp-formula></p>
<p>In this case, <italic>t</italic> is the current iteration, <inline-formula id="ieqn-11"><mml:math id="mml-ieqn-11"><mml:mover><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo>&#x2192;</mml:mo></mml:mover></mml:math></inline-formula> represents the best solution found thus far, <inline-formula id="ieqn-12"><mml:math id="mml-ieqn-12"><mml:mrow><mml:mover><mml:mi>X</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> is the position vector, and |. | denotes the absolute value. The coefficient vectors A and C are also determined as in <xref ref-type="disp-formula" rid="eqn-3">Eqs. (3)</xref> and <xref ref-type="disp-formula" rid="eqn-4">(4)</xref>:</p>
<p><disp-formula id="eqn-6"><label>(6)</label><mml:math id="mml-eqn-6" display="block"><mml:mrow><mml:mover><mml:mi>A</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mrow><mml:mover><mml:mi>a</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mo>.</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mover><mml:mi>a</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math></disp-formula></p>
<p><disp-formula id="eqn-7"><label>(7)</label><mml:math id="mml-eqn-7" display="block"><mml:mrow><mml:mover><mml:mi>C</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mn>2.</mml:mn><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math></disp-formula></p>
<p>In the exploration and exploitation stages, &#x2018;a&#x2019; declines linearly from 2 to 0, and r is produced randomly with uniform distribution in the interval [0,1]. Search agents (whales) update their locations based on the best-known solution&#x2019;s position (prey), according to <xref ref-type="disp-formula" rid="eqn-5">Eq. (5)</xref>. Predators can only be located in the vicinity of a whale by altering the values of A and C vectors. According to <xref ref-type="disp-formula" rid="eqn-8">Eq. (8)</xref>, t is the iteration number, and the value in <xref ref-type="disp-formula" rid="eqn-6">Eq. (6)</xref> is decreased to produce the shrinking encircling behavior.</p>
<p><disp-formula id="eqn-8"><label>(8)</label><mml:math id="mml-eqn-8" display="block"><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>t</mml:mi><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mn>2</mml:mn><mml:mrow><mml:mi>M</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mrow><mml:mi mathvariant="italic">I</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">s</mml:mi></mml:mrow></mml:mrow></mml:mfrac></mml:mstyle></mml:math></disp-formula></p>
<p>Search agent (X) and best known search agent (X<sup>&#x002A;</sup>) distances are obtained as shown in <xref ref-type="fig" rid="fig-3">Fig. 3</xref>; then the spiral in <xref ref-type="disp-formula" rid="eqn-9">Eq. (9)</xref> is used to produce the neighbour search agent&#x2019;s position.</p>

<p><disp-formula id="eqn-9"><label>(9)</label><mml:math id="mml-eqn-9" display="block"><mml:mrow><mml:mover><mml:mi>X</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mover><mml:mi>D</mml:mi><mml:mo>&#x0060;</mml:mo></mml:mover></mml:mrow><mml:mo>.</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msup><mml:mo>.</mml:mo><mml:mi>C</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mi>l</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mover><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p><disp-formula id="eqn-10"><label>(10)</label><mml:math id="mml-eqn-10" display="block"><mml:mrow><mml:mover><mml:mi>D</mml:mi><mml:mo>&#x0060;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:mover><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mover><mml:mi>X</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:math></disp-formula>where <italic>l</italic> is a random number within the range [&#x2212;1, 1], the logarithmic spiral&#x2019;s constant is denoted by b. In <xref ref-type="disp-formula" rid="eqn-11">Eq. (11)</xref>, we suppose there is a 50% chance that the optimization process will pick between the spiral-shaped approach and shrinking encircling when p is some random value in the range [0,1].</p>
<p><disp-formula id="eqn-11"><label>(11)</label><mml:math id="mml-eqn-11" display="block"><mml:mrow><mml:mover><mml:mi>X</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="right" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:mover><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mover><mml:mi>A</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mo>.</mml:mo><mml:mi>D</mml:mi><mml:mo>,</mml:mo></mml:mtd><mml:mtd><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mo>&#x003C;</mml:mo><mml:mn>0.5</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mover><mml:mi>D</mml:mi><mml:mo>&#x0060;</mml:mo></mml:mover></mml:mrow><mml:mo>.</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msup><mml:mo>.</mml:mo><mml:mi>C</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mi>l</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mover><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mtd><mml:mtd><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mn>0.5</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula></p>
</sec>
<sec id="s3_4_2">
<label>3.4.2</label>
<title>Exploration Phase</title>
<p>Instead of adjusting the search agents&#x2019; placement based on the position of the best one found thus far, a random search agent is used to direct the search in WOA. Since A is used to compel the search agent to wander far away from the best-known search agent, random values larger than 1 or less than &#x2212;1 are employed. <inline-formula id="ieqn-13"><mml:math id="mml-ieqn-13"><mml:msub><mml:mrow><mml:mover><mml:mi>X</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> is a randomly selected whale from the present population in <xref ref-type="disp-formula" rid="eqn-12">Eq. (12)</xref>, which mathematically models this procedure.</p>
<p><disp-formula id="eqn-12"><label>(12)</label><mml:math id="mml-eqn-12" display="block"><mml:mrow><mml:mover><mml:mi>D</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mover><mml:mi>X</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mover><mml:mi>A</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mo>.</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mover><mml:mi>C</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mo>.</mml:mo><mml:msub><mml:mrow><mml:mover><mml:mi>X</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mover><mml:mi>X</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>
<fig id="fig-6">
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_33513-inline-1.png"/></fig>
</p>
</sec>
</sec>
<sec id="s3_5">
<label>3.5</label>
<title>The Proposed Optimization Algorithm</title>
<p>The proposed DTO-Guided WOA employed in optimizing the voting classifiers parameter is listed in Algorithm 1. This algorithm is used to optimize the parameters of the classifiers and the voting ensemble to boost the overall classification accuracy of the network attacks.</p>
</sec>
</sec>
<sec id="s4">
<label>4</label>
<title>Experimental Results</title>
<p>The tests are conducted on a Windows 11 laptop with a 2.33 GHz Intel Core i5 and 16 GB of random access memory (RAM). MATLAB R2020a was used to build and evaluate the suggested framework. Text Analytics Toolbox MATLAB is used for preparing the dataset. An evaluation and comparison of the proposed approach&#x2019;s performance are carried out here.</p>
<p>The achieved results based on the proposed feature selection approach are presented in <xref ref-type="table" rid="table-3">Tab. 3</xref>, with 95.1% accuracy. In addition, a comparison between the performance of the majority voting and the proposed voting algorithm is presented in <xref ref-type="table" rid="table-4">Tabs. 4</xref>&#x2013;<xref ref-type="table" rid="table-6">6</xref>. In these tables, the performance of the proposed voting algorithm is much better than the traditional majority voting. The achieved AUC is (0.99) using the proposed approach, whereas the AUC value using the traditional voting is (0.974). In addition, the proposed approach&#x2019;s mean square error (MSE) is (2.50E-08), which reflects the superiority of the proposed approach when compared to the traditional voting algorithm.</p>
<table-wrap id="table-3">
<label>Table 3</label>
<caption>
<title>Evaluation results of the results achieved with/without data preprocessing</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th>Metric</th>
<th>NN</th>
<th>KNN</th>
<th>Random Forest</th>
</tr>
</thead>
<tbody>
<tr>
<td>AUC without SMOTE</td>
<td>0.813</td>
<td>0.861</td>
<td><bold>0.893</bold></td>
</tr>
<tr>
<td>MSE without SMOTE</td>
<td>0.052373</td>
<td>0.04932</td>
<td><bold>0.032853</bold></td>
</tr>
<tr>
<td>AUC with SMOTE</td>
<td>0.861</td>
<td>0.917</td>
<td><bold>0.931</bold></td>
</tr>
<tr>
<td>MSE with SMOTE</td>
<td>0.006708</td>
<td>0.005852</td>
<td><bold>0.0035723</bold></td>
</tr>
<tr>
<td>AUC with LSH-SMOTE</td>
<td>0.897</td>
<td>0.936</td>
<td><bold>0.951</bold></td>
</tr>
<tr>
<td>MSE with LSH-SMOTE</td>
<td>0.000574</td>
<td>0.000395</td>
<td><bold>0.0001012</bold></td>
</tr>
</tbody>
</table>
</table-wrap><table-wrap id="table-4">
<label>Table 4</label>
<caption>
<title>Comparison between the results achieved by the majority voting and the proposed approach</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th>Metric</th>
<th>Majority voting</th>
<th>Voting (DTO _Guided WOA)</th>
</tr>
</thead>
<tbody>
<tr>
<td>AUC with LSH-SMOTE</td>
<td>0.974</td>
<td><bold>0.999975</bold></td>
</tr>
<tr>
<td>MSE with LSH-SMOTE</td>
<td>0.000005931</td>
<td><bold>2.50E-08</bold></td>
</tr>
</tbody>
</table>
</table-wrap><table-wrap id="table-5">
<label>Table 5</label>
<caption>
<title>Assessment of the voting approach using the proposed optimization algorithm and other algorithms</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th></th>
<th>AUC with LSH-SMOTE</th>
<th>MSE with LSH-SMOTE</th>
</tr>
</thead>
<tbody>
<tr>
<td><bold>Voting (DTO _Guided WOA)</bold></td>
<td><bold>0.999975</bold></td>
<td><bold>2.50E-08</bold></td>
</tr>
<tr>
<td>Voting particle swarm optimimizatiion (PSO)</td>
<td>0.9914</td>
<td>0.00000151</td>
</tr>
<tr>
<td>Voting genetic algorithm (GA)</td>
<td>0.989</td>
<td>0.000002721</td>
</tr>
<tr>
<td>Voting grey wolf optimization (GWO)</td>
<td>0.986</td>
<td>0.000003025</td>
</tr>
<tr>
<td>Voting whale optimization algorithm (WOA)</td>
<td>0.981</td>
<td>0.000004084</td>
</tr>
</tbody>
</table>
</table-wrap><table-wrap id="table-6">
<label>Table 6</label>
<caption>
<title>Statistical analysis of the results achieved by the proposed optimization algorithm and other algorithms</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th></th>
<th>Voting (DTO _Guided WOA)</th>
<th>Voting WOA</th>
<th>Voting GWO</th>
<th>Voting GA</th>
<th>Voting PSO</th>
</tr>
</thead>
<tbody>
<tr>
<td>Number of values</td>
<td>14</td>
<td><bold>14</bold></td>
<td>14</td>
<td>14</td>
<td>14</td>
</tr>
<tr>
<td>Minimum</td>
<td><bold>1</bold></td>
<td>0.971</td>
<td>0.976</td>
<td>0.979</td>
<td>0.9714</td>
</tr>
<tr>
<td>25% Percentile</td>
<td><bold>1</bold></td>
<td>0.981</td>
<td>0.986</td>
<td>0.989</td>
<td>0.9914</td>
</tr>
<tr>
<td>Median</td>
<td><bold>1</bold></td>
<td>0.981</td>
<td>0.986</td>
<td>0.989</td>
<td>0.9914</td>
</tr>
<tr>
<td>75% Percentile</td>
<td><bold>1</bold></td>
<td>0.981</td>
<td>0.986</td>
<td>0.989</td>
<td>0.9914</td>
</tr>
<tr>
<td>Maximum</td>
<td><bold>1</bold></td>
<td>0.991</td>
<td>0.996</td>
<td>0.999</td>
<td>0.9914</td>
</tr>
<tr>
<td>Range</td>
<td><bold>0</bold></td>
<td>0.02</td>
<td>0.02</td>
<td>0.02</td>
<td>0.02</td>
</tr>
<tr>
<td>Mean</td>
<td><bold>1</bold></td>
<td>0.981</td>
<td>0.986</td>
<td>0.989</td>
<td>0.9893</td>
</tr>
<tr>
<td>Std. Error of mean</td>
<td><bold>0</bold></td>
<td>0.001048</td>
<td>0.001048</td>
<td>0.001048</td>
<td>0.001547</td>
</tr>
<tr>
<td>Std. Deviation</td>
<td><bold>0</bold></td>
<td>0.003922</td>
<td>0.003922</td>
<td>0.003922</td>
<td>0.005789</td>
</tr>
<tr>
<td>Sum</td>
<td><bold>14</bold></td>
<td>13.73</td>
<td>13.8</td>
<td>13.85</td>
<td>13.85</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="table" rid="table-7">Tabs. 7</xref> and <xref ref-type="table" rid="table-8">8</xref> show the findings of the analysis of variance (ANOVA) and Wilcoxon signed-rank tests, on the other hand. As can be seen from the tables, the proposed strategy is statistically significant, just like the different strategies. Therefore, the suggested method is suited to the task of selecting features. <xref ref-type="table" rid="table-7">Tab. 7</xref> shows the ANOVA test results for validating the proposed approach&#x2019;s stability and effectiveness. These tests stress the statistical significance and efficacy of the suggested method based on the hypotheses of these tests.</p>
<table-wrap id="table-7">
<label>Table 7</label>
<caption>
<title>One-way analysis of variance test</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th>Metric</th>
<th>SS</th>
<th>DF</th>
<th>MS</th>
<th>F (DFn, DFd)</th>
<th><italic>P</italic> value</th>
</tr>
</thead>
<tbody>
<tr>
<td>Treatment</td>
<td>0.002709</td>
<td>4</td>
<td>0.000677</td>
<td>F (4, 65) &#x003D; 42.50</td>
<td><italic>P</italic> &#x003C; 0.0001</td>
</tr>
<tr>
<td>Residual</td>
<td>0.001036</td>
<td>65</td>
<td>1.59E-05</td>
<td></td>
<td></td>
</tr>
<tr>
<td>Total</td>
<td>0.003745</td>
<td>69</td>
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
</table-wrap><table-wrap id="table-8">
<label>Table 8</label>
<caption>
<title>Wilcoxon signed rank test</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th></th>
<th>Voting (DTO _Guided WOA)</th>
<th>Voting WOA</th>
<th>Voting GWO</th>
<th>Voting GA</th>
<th>Voting PSO</th>
</tr>
</thead>
<tbody>
<tr>
<td>Theoretical median</td>
<td><bold>0</bold></td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr>
<td>Number of values</td>
<td><bold>14</bold></td>
<td>14</td>
<td>14</td>
<td>14</td>
<td>14</td>
</tr>
<tr>
<td>Actual median</td>
<td><bold>1</bold></td>
<td>0.981</td>
<td>0.986</td>
<td>0.989</td>
<td>0.9914</td>
</tr>
<tr>
<td>Discrepancy</td>
<td><bold>1</bold></td>
<td>0.981</td>
<td>0.986</td>
<td>0.989</td>
<td>0.9914</td>
</tr>
<tr>
<td>Significant (alpha &#x003D; 0.05)?</td>
<td><bold>Yes</bold></td>
<td>Yes</td>
<td>Yes</td>
<td>Yes</td>
<td>Yes</td>
</tr>
<tr>
<td>Exact or estimate?</td>
<td><bold>Exact</bold></td>
<td>Exact</td>
<td>Exact</td>
<td>Exact</td>
<td>Exact</td>
</tr>
<tr>
<td><italic>P</italic> value (two tailed)</td>
<td><bold>0.0001</bold></td>
<td>0.0001</td>
<td>0.0001</td>
<td>0.0001</td>
<td>0.0001</td>
</tr>
<tr>
<td>Sum of negative ranks</td>
<td><bold>0</bold></td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr>
<td>Sum of positive ranks</td>
<td><bold>105</bold></td>
<td>105</td>
<td>105</td>
<td>105</td>
<td>105</td>
</tr>
<tr>
<td>Sum of signed ranks (W)</td>
<td><bold>105</bold></td>
<td>105</td>
<td>105</td>
<td>105</td>
<td>105</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The attained outcomes are shown in <xref ref-type="fig" rid="fig-4">Fig. 4</xref> to demonstrate the approach&#x2019;s efficacy and superiority. It&#x2019;s easy to see that the proposed technique is highly accurate based on the data in this image because the residual error is so little. Quantile-by-quantile (QQ), heatmaps, ROCs, and histogram plots are utilized to demonstrate the suggested method&#x2019;s efficiency. Plots like this demonstrate how superior the recommended strategy is to the alternatives.</p>
<fig id="fig-4">
<label>Figure 4</label>
<caption>
<title>Visualization of the achieved results using the proposed methodology</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_33513-fig-4.png"/>
</fig>
<p>The accuracy of the achieved results using the proposed approach is presented in a histogram in <xref ref-type="fig" rid="fig-5">Fig. 5</xref>. As shown in this figure, the proposed approach achieves the best results compared to the other voting classifier approaches. These results prove the proposed approach&#x2019;s superiority in accurately detecting network attacks.</p>
<fig id="fig-5">
<label>Figure 5</label>
<caption>
<title>Histogram of the accuracy achieved by the proposed approach and other approaches</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_33513-fig-5.png"/>
</fig>
</sec>
<sec id="s5">
<label>5</label>
<title>Conclusions</title>
<p>This paper proposes a new optimization algorithm for optimizing the classifiers used in intrusion detection systems. The proposed algorithm is based on the dipper throated and whale optimization algorithms. The proposed algorithm is used in an architecture designed to detect network attacks in IoT environments. To validate the effectiveness of the proposed approach, several experiments were conducted to evaluate the stages of the proposed framework. Evaluation results showed the effectiveness of the proposed method. On the other hand, the comparison is conducted to show the superiority of the proposed approach. In addition, a statistical analysis is performed to prove the stability and significance of the proposed method for intrusion detection tasks. The recorded results confirm the findings and emphasize the significance of the proposed approach.</p>
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<p>Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2022R300), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.</p>
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<fn fn-type="other"><p><bold>Funding Statement:</bold> Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2022R300), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.</p>
</fn>
<fn fn-type="conflict"><p><bold>Conflicts of Interest:</bold> The authors declare that they have no conflicts of interest to report regarding the present study.</p>
</fn>
</fn-group>
<ref-list content-type="authoryear">
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