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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">31371</article-id>
<article-id pub-id-type="doi">10.32604/cmc.2023.031371</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Malicious URL Classification Using Artificial Fish Swarm Optimization and Deep Learning</article-title>
<alt-title alt-title-type="left-running-head">Malicious URL Classification Using Artificial Fish Swarm Optimization and Deep Learning</alt-title>
<alt-title alt-title-type="right-running-head">Malicious URL Classification Using Artificial Fish Swarm Optimization and Deep Learning</alt-title>
</title-group>
<contrib-group content-type="authors">
<contrib id="author-1" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Hilal</surname><given-names>Anwer Mustafa</given-names></name><xref ref-type="aff" rid="aff-1">1</xref>
<xref ref-type="aff" rid="aff-2">2</xref><email>A.hilal@psau.edu.sa</email></contrib>
<contrib id="author-2" contrib-type="author">
<name name-style="western"><surname>Abdalla Hashim</surname><given-names>Aisha Hassan</given-names></name><xref ref-type="aff" rid="aff-1">1</xref></contrib>
<contrib id="author-3" contrib-type="author">
<name name-style="western"><surname>Mohamed</surname><given-names>Heba G.</given-names></name><xref ref-type="aff" rid="aff-3">3</xref></contrib>
<contrib id="author-4" contrib-type="author">
<name name-style="western"><surname>Nour</surname><given-names>Mohamed K.</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>Asiri</surname><given-names>Mashael M.</given-names></name><xref ref-type="aff" rid="aff-5">5</xref></contrib>
<contrib id="author-6" contrib-type="author">
<name name-style="western"><surname>Al-Sharafi</surname><given-names>Ali M.</given-names></name><xref ref-type="aff" rid="aff-6">6</xref></contrib>
<contrib id="author-7" contrib-type="author">
<name name-style="western"><surname>Othman</surname><given-names>Mahmoud</given-names></name><xref ref-type="aff" rid="aff-7">7</xref></contrib>
<contrib id="author-8" contrib-type="author">
<name name-style="western"><surname>Motwakel</surname><given-names>Abdelwahed</given-names></name><xref ref-type="aff" rid="aff-2">2</xref></contrib>
<aff id="aff-1"><label>1</label><institution>Department of Electrical and Computer Engineering, International Islamic University Malaysia 53100 Kuala Lumpur</institution>, <country>Malaysia</country></aff>
<aff id="aff-2"><label>2</label><institution>Department of Computer and Self Development, Preparatory Year Deanship, Prince Sattam bin Abdulaziz University</institution>, <addr-line>AlKharj</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-3"><label>3</label><institution>Department of Electrical Engineering, College of Engineering, Princess Nourah Bint Abdulrahman University</institution>, <addr-line>P.O. Box 84428, Riyadh, 11671</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-4"><label>4</label><institution>Department of Computer Sciences, College of Computing and Information System, Umm Al-Qura University</institution>, <country>Saudi Arabia</country></aff>
<aff id="aff-5"><label>5</label><institution>Department of Computer Science, College of Science &#x0026; Art at Mahayil, King Khalid University</institution>, <country>Saudi Arabia</country></aff>
<aff id="aff-6"><label>6</label><institution>Department of Computer Science, College of Computers and Information Technology, University of Bisha</institution>, <country>Saudi Arabia</country></aff>
<aff id="aff-7"><label>7</label><institution>Department of Computer Science, Faculty of Computers and Information Technology, Future University in Egypt</institution>, <addr-line>New Cairo, 11835</addr-line>, <country>Egypt</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Anwer Mustafa Hilal. Email: <email>A.hilal@psau.edu.sa</email></corresp>
</author-notes>
<pub-date pub-type="epub" date-type="pub" iso-8601-date="2022-08-16"><day>16</day>
<month>08</month>
<year>2022</year></pub-date>
<volume>74</volume>
<issue>1</issue>
<fpage>607</fpage>
<lpage>621</lpage>
<history>
<date date-type="received"><day>15</day><month>4</month><year>2022</year></date>
<date date-type="accepted"><day>24</day><month>6</month><year>2022</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Hilal et al.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Hilal 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_31371.pdf"></self-uri>
<abstract>
<p>Cybersecurity-related solutions have become familiar since it ensures security and privacy against cyberattacks in this digital era. Malicious Uniform Resource Locators (URLs) can be embedded in email or Twitter and used to lure vulnerable internet users to implement malicious data in their systems. This may result in compromised security of the systems, scams, and other such cyberattacks. These attacks hijack huge quantities of the available data, incurring heavy financial loss. At the same time, Machine Learning (ML) and Deep Learning (DL) models paved the way for designing models that can detect malicious URLs accurately and classify them. With this motivation, the current article develops an Artificial Fish Swarm Algorithm (AFSA) with Deep Learning Enabled Malicious URL Detection and Classification (AFSADL-MURLC) model. The presented AFSADL-MURLC model intends to differentiate the malicious URLs from genuine URLs. To attain this, AFSADL-MURLC model initially carries out data preprocessing and makes use of glove-based word embedding technique. In addition, the created vector model is then passed onto Gated Recurrent Unit (GRU) classification to recognize the malicious URLs. Finally, AFSA is applied to the proposed model to enhance the efficiency of GRU model. The proposed AFSADL-MURLC technique was experimentally validated using benchmark dataset sourced from Kaggle repository. The simulation results confirmed the supremacy of the proposed AFSADL-MURLC model over recent approaches under distinct measures.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Malicious URL</kwd>
<kwd>cybersecurity</kwd>
<kwd>deep learning</kwd>
<kwd>machine learning</kwd>
<kwd>metaheuristics</kwd>
<kwd>gated recurrent unit</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1"><label>1</label><title>Introduction</title>
<p>The advent of advanced intelligence technologies has brought a tremendous impact upon growth and development of marketplaces through multiple applications [<xref ref-type="bibr" rid="ref-1">1</xref>]. In modern era, it is absolutely essential for an institution to have online presence so that it can nurture itself into a prosperous and successful enterprise. As a result, internet and World Wide Web (WWW) have become a part of day-to-day operations in institutions and companies across the globe [<xref ref-type="bibr" rid="ref-2">2</xref>]. Unfortunately, the technical developments have also brought security problems along with it and these security issues are mainly targeted at scamming the final users. Such types of attacks contain prohibited websites that deal with forged goods and fraudulent activities are performed by means of cheating the end users through exchange of sensitive information. This information is accessed inappropriately with an intention to steal cash or identification of the users. At times, it is also done to establish the worst piece of code and malwares in user&#x2019;s appliances [<xref ref-type="bibr" rid="ref-3">3</xref>]. This is a common modality followed by different forms of attacks and in several circumstances, it is highly challenging to develop powerful software that can find cyber-security crimes [<xref ref-type="bibr" rid="ref-4">4</xref>]. Conventional security management technologies have evolved in the recent times due to exponential rise of security threats that occur through accelerated developments in information and communication technologies. It is important to note that only seasoned security experts can resolve this security issues and overcome the challenges faced due to cyberattacks. The increasing number of compromised URLs is the most important factor observed in such cyber-attack methodologies [<xref ref-type="bibr" rid="ref-5">5</xref>,<xref ref-type="bibr" rid="ref-6">6</xref>]. Uniform Resource Locators (URLs) indicates that the reports are universally available and it can be accessed across the globe through World Wide Web.</p>
<p>In general, malicious URLs can be identified with the help of Machine Learning (ML) technique through two steps as detailed herewith. At first, a suitable feature indication is obtained from the URL, and secondly, based on the feature identified, ML-related prediction methods are provided training to find out the malicious URLs [<xref ref-type="bibr" rid="ref-7">7</xref>,<xref ref-type="bibr" rid="ref-8">8</xref>]. The first step discussed above i.e., attaining the feature indication in which fruitful information regarding the URL is saved in a vector so that the ML methods can be implied to it. Several kinds of features have been assumed earlier such as content features, lexical features, popular features, and host-based features [<xref ref-type="bibr" rid="ref-9">9</xref>,<xref ref-type="bibr" rid="ref-10">10</xref>]. However, lexical features are the most widely used features as they have proved to yield superior outcomes and are comparatively simple to attain [<xref ref-type="bibr" rid="ref-11">11</xref>]. Lexical features briefly depict the lexical properties attained from URL string. These features involve statistic properties namely, URL length, total number of dots, and many more [<xref ref-type="bibr" rid="ref-12">12</xref>]. Moreover, Bag-of-Words (BoW) features are frequently utilized. BoWs represent either whether a specific string or word is displayed in the URL. Subsequently, each and every peculiar word in the training dataset is considered as a feature [<xref ref-type="bibr" rid="ref-13">13</xref>]. In second stage, such features are employed to train the prediction methods like support vector machines (SVMs). Further, such methodologies can also be reviewed as unclear blacklists [<xref ref-type="bibr" rid="ref-14">14</xref>].</p>
<p>In literature [<xref ref-type="bibr" rid="ref-15">15</xref>], a malicious URL recognition and detection system was proposed on the basis of Attention mechanism with Convolution Neural Network (CNN) and Long Short-Term Memory Network (Attention-Based CNN-LSTM). In relation to the weight from attention model, the local features, generated earlier, are fed as input to the LSTM network. Followed by, these features are successively pooled to compute the global feature of the URLs. At last, the URL is classified and detected by SoftMax function with global feature. In the study conducted earlier [<xref ref-type="bibr" rid="ref-16">16</xref>], an algorithm was suggested which employs AndroAnalyzer, a model that applies both deep learning systems and static analysis. In this study, the analysis was conducted on original datasets comprising 7,622 applications. Further tests were also carried out on ML technique by comparing them with Deep Learning (DL) technique based on the feature vectors obtained.</p>
<p>Afzal&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-17">17</xref>] presented a hybrid DL technique termed &#x2018;URLdeepDetect&#x2019; to analyze the time-of-click for URLs and a classifier to detect malicious URLs. URLdeepDetect analyzes both semantic and lexical characteristics of a URL by employing different technologies that involve semantic vector methodologies and URL encryption to differentiate a URL as benign or malicious. Srinivasan&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-18">18</xref>] developed DeepURLDetect (DURLD), in which raw URL is encoded with character-level embedding. In order to capture a variety of data in URL, the study employed a hidden layer in DL architecture. This is done so to extract the features from character level embedding. Afterwards, a non-linear activation function was applied to determine the possibilities of a URL being benign or malicious. Mondal&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-19">19</xref>] designed a novel concept based on ML technique. The suggested model made use of different classifiers, for instance ensemble learning, to forecast the class probability of URLs. Further, it also employed a threshold to filter the decision of different classifications. In this study, the decisions were grouped to denote their respective class probabilities and signify the class labels with maximum class probability to conclude the decision upon unlabelled URL.</p>
<p>The current article develops an Artificial Fish Swarm Algorithm (AFSA) with Deep Learning Enabled Malicious URL Detection and Classification (AFSADL-MURLC) model. The aim of the presented AFSADL-MURLC model is to properly identify the existence of malicious URLs. To attain this, AFSADL-MURLC model initially pre-processes the data and makes use of Glove-based word embedding technique. Then, the created vector model is passed onto Gated Recurrent Unit (GRU) classification model to recognize the malicious URLs. Finally, in order to improve the efficacy of GRU model, AFSA is applied. The proposed AFSADL-MURLC technique was experimentally validated using benchmark dataset from Kaggle repository.</p>
<p>Rest of the paper is organized as follows. Section 2 introduces the proposed model and Section 3 offers information on experimental validation. At last, Section 4 concludes the paper.</p>
</sec>
<sec id="s2"><label>2</label><title>The Proposed Model</title>
<p>In this study, a novel AFSADL-MURLC model has been proposed to properly differentiate the malicious URLs from genuine URLs. The proposed AFSADL-MURLC model primarily performs data pre-processing and makes use of Glove-based word embedding technique. Besides, the created vector model is then passed onto GRU classification model to recognize the malicious URLs. Finally, in order to improve the efficacy of GRU model, AFSA is applied. <xref ref-type="fig" rid="fig-1">Fig. 1</xref> depicts the block diagram of AFSADL-MURLC technique.</p>
<sec id="s2_1"><label>2.1</label><title>Pre-processing</title>
<p>In the first step, the tokenization of URLs is performed. Basic tokenizer can be used in this regard and it already exists in The Natural Language Toolkit (NLTK). Further, basic tokenizer is essentially maintained in python to work with programs that contain approaches compared with human language data. NLTK contains numerous libraries which are utilized on string as well as character to determine the semantic meaning behind these elements. Amongst the individuals&#x2019; library, tokenizer library can be used for parsing the URL to distinct tokens. It can create an array for storing the token followed by parsing. The tokens of all the URLs are attached one by one from the array which are later distributed to vector method.</p>
<fig id="fig-1"><label>Figure 1</label><caption><title>Overall block diagram of AFSADL-MURLC technique</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31371-fig-1.png"/></fig>
</sec>
<sec id="s2_2"><label>2.2</label><title>Word Embedding</title>
<p>Global Vector (GloVe) [<xref ref-type="bibr" rid="ref-20">20</xref>], for word representation, is an unsupervised technique to derive word embedding from textual input. To start with, <inline-formula id="ieqn-1"><mml:math id="mml-ieqn-1"><mml:mi>A</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>A</mml:mi></mml:math></inline-formula> term-based co-occurrence matrix is considered to obtain the representation. Co-occurrence matrixes are generally used in the exploration of semantic relationships amid terms. As an example, higher cosine similarity is represented between words like &#x2018;mother&#x2019; and &#x2018;women&#x2019; or &#x2018;queen&#x2019; and &#x2018;king&#x2019;. The algorithm learns from a huge Gigaword and Wikipedia corpus in an unsupervised manner. For <inline-formula id="ieqn-2"><mml:math id="mml-ieqn-2"><mml:mi>i</mml:mi></mml:math></inline-formula>-th word with vector representation <inline-formula id="ieqn-3"><mml:math id="mml-ieqn-3"><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, the objective function is represented by
<disp-formula id="eqn-1"><label>(1)</label><mml:math id="mml-eqn-1" display="block"><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mover><mml:mi>w</mml:mi><mml:mo>&#x007E;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mfrac></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-1">Eq. (1)</xref>, <inline-formula id="ieqn-4"><mml:math id="mml-ieqn-4"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> is the probability of the instances occurring together and <inline-formula id="ieqn-5"><mml:math id="mml-ieqn-5"><mml:mspace width="thickmathspace" /><mml:mi>i</mml:mi></mml:math></inline-formula> and <italic>k</italic> denote the words with similar contexts. The algorithm utilizes <inline-formula id="ieqn-6"><mml:math id="mml-ieqn-6"><mml:mi>c</mml:mi><mml:mi>o</mml:mi></mml:math></inline-formula>-occurrence probability as a feature by capturing the contextual word and statistics.</p>
</sec>
<sec id="s2_3"><label>2.3</label><title>GRU Based Classification</title>
<p>At the time of classification process, the created vector model is passed onto GRU classification model to recognize the malicious URLs. GRU model holds <inline-formula id="ieqn-7"><mml:math id="mml-ieqn-7"><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> current activation, prior activation <inline-formula id="ieqn-8"><mml:math id="mml-ieqn-8"><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and recent input <inline-formula id="ieqn-9"><mml:math id="mml-ieqn-9"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. Recurrent Neural Network (RNN) has the ability to learn long-term patterns and are better in comparison with feed forward Deep Neural Network (DNN) [<xref ref-type="bibr" rid="ref-21">21</xref>], since feed-forward DNN is developed in a way such that the input context features are continuously different. The hidden activation of RNN is expressed as follows using <xref ref-type="disp-formula" rid="eqn-1">Eq. (1)</xref>:
<disp-formula id="eqn-2"><label>(2)</label><mml:math id="mml-eqn-2" display="block"><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>&#x03C6;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>W</mml:mi><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:msup><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:msup><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msup><mml:mi>b</mml:mi><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>But a simplified RNN is hard to train using recurrent connectivity on the hidden state due to exploding or vanishing gradient problems. LSTM model addresses these difficulties by introducing cell state, input, forget and output gates to control the flow of data over a period of time. The basic principle of LSTM is that the memory cells maintain their state over a period of time. So, GRU is proposed as an alternate structure to LSTM model. GRU model is an established model in terms of efficiency than LSTM in some tasks. Following is the equation applied to the model.</p>
<p><disp-formula id="eqn-3"><label>(3)</label><mml:math id="mml-eqn-3" display="block"><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>&#x03B4;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>W</mml:mi><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msup><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msup><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msup><mml:mi>b</mml:mi><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-4"><label>(4)</label><mml:math id="mml-eqn-4" display="block"><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>&#x03B4;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>W</mml:mi><mml:mrow><mml:mi>z</mml:mi></mml:mrow></mml:msup><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>z</mml:mi></mml:mrow></mml:msup><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msup><mml:mi>b</mml:mi><mml:mrow><mml:mi>z</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-5"><label>(5)</label><mml:math id="mml-eqn-5" display="block"><mml:msub><mml:mrow><mml:mover><mml:mi>h</mml:mi><mml:mo>&#x007E;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>&#x03C6;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>W</mml:mi><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:msup><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2299;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:msup><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msup><mml:mi>b</mml:mi><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-6"><label>(6)</label><mml:math id="mml-eqn-6" display="block"><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2299;</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2299;</mml:mo><mml:msub><mml:mrow><mml:mover><mml:mi>h</mml:mi><mml:mo>&#x007E;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p>In the above equation, hidden activation, reset and update gate values at <italic>t</italic> time are correspondingly represented by <inline-formula id="ieqn-10"><mml:math id="mml-ieqn-10"><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mspace width="thinmathspace" /><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-11"><mml:math id="mml-ieqn-11"><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. The weights used for recurrent hidden and input layer are represented by <inline-formula id="ieqn-12"><mml:math id="mml-ieqn-12"><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:math></inline-formula> and <inline-formula id="ieqn-13"><mml:math id="mml-ieqn-13"><mml:msup><mml:mi>W</mml:mi><mml:mrow><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:math></inline-formula>, correspondingly. The bias is denoted as <inline-formula id="ieqn-14"><mml:math id="mml-ieqn-14"><mml:msup><mml:mi>b</mml:mi><mml:mrow><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:math></inline-formula>. Tangent and sigmoid activation functions are denoted through <inline-formula id="ieqn-15"><mml:math id="mml-ieqn-15"><mml:mi>&#x03C6;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mo>&#x22C5;</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula id="ieqn-16"><mml:math id="mml-ieqn-16"><mml:mspace width="thickmathspace" /><mml:mi>&#x03B4;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mo>&#x22C5;</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> respectively. There is no single memory cell in GRU compared to LSTM. Further, GRU does not have an output gate whereas it combines both forget and input gates into <inline-formula id="ieqn-17"><mml:math id="mml-ieqn-17"><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> update gate to create a balance between update activation <inline-formula id="ieqn-18"><mml:math id="mml-ieqn-18"><mml:msub><mml:mrow><mml:mover><mml:mi>h</mml:mi><mml:mo>&#x007E;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and prior activation <inline-formula id="ieqn-19"><mml:math id="mml-ieqn-19"><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> as demonstrated in <xref ref-type="disp-formula" rid="eqn-6">Eq. (6)</xref>. In <xref ref-type="disp-formula" rid="eqn-5">Eqs. (5)</xref> &#x0026; <xref ref-type="disp-formula" rid="eqn-6">(6)</xref> element-wise multiplication is represented through <inline-formula id="ieqn-20"><mml:math id="mml-ieqn-20"><mml:mo>&#x2299;</mml:mo></mml:math></inline-formula> term. The reset gate <inline-formula id="ieqn-21"><mml:math id="mml-ieqn-21"><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> decides whether to forget the prior activation or not (as illustrated in <xref ref-type="disp-formula" rid="eqn-5">Eq. (5)</xref>). <xref ref-type="fig" rid="fig-2">Fig. 2</xref> demonstrates the structure of GRU.</p>
<fig id="fig-2"><label>Figure 2</label><caption><title>Architecture of GRU</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31371-fig-2.png"/></fig>
</sec>
<sec id="s2_4"><label>2.4</label><title>AFSA Based Hyperparameter Optimization</title>
<p>In this final stage, AFSA is applied to improve the efficacy of GRU model by optimal-tuning of the hyperparameters [<xref ref-type="bibr" rid="ref-22">22</xref>&#x2013;<xref ref-type="bibr" rid="ref-24">24</xref>]. AFSA approach is a swarm intelligence technique that is developed based on the behaviour of animals [<xref ref-type="bibr" rid="ref-25">25</xref>]. Especially, the technique has its inspiration from animal behaviours such as clustering, collision, and foraging of fish followed by collective support in a fish swarm to realize a global optimal point. Here, <italic>Step</italic> is determined based on the maximum distance passed in Artificial Fish (AF) technique, <italic>Visual</italic> is defined by the apparent distance passed through AF, <inline-formula id="ieqn-22"><mml:math id="mml-ieqn-22"><mml:mi>T</mml:mi><mml:mi>r</mml:mi><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo></mml:mrow></mml:msub></mml:math></inline-formula><italic>The number</italic> represents the retry amount and <inline-formula id="ieqn-23"><mml:math id="mml-ieqn-23"><mml:mi>&#x03B7;</mml:mi></mml:math></inline-formula> represents the factor of crowd amount. Here, <inline-formula id="ieqn-24"><mml:math id="mml-ieqn-24"><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> represents the location of single AF as described by the resultant vector, and <inline-formula id="ieqn-25"><mml:math id="mml-ieqn-25"><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula> represents the distance between AF <italic>i</italic> and <italic>j</italic>. Random, prey, swarm and follow are the behavioral functions of the AF.</p>
<p>Consider that a fish observes the food with the help of its eyes, <inline-formula id="ieqn-26"><mml:math id="mml-ieqn-26"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> is the current location and <inline-formula id="ieqn-27"><mml:math id="mml-ieqn-27"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> represents the arbitrarily-elected location within [0,1],
<disp-formula id="eqn-7"><label>(7)</label><mml:math id="mml-eqn-7" display="block"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mtext mathvariant="italic">Visual</mml:mtext></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mrow><mml:mo>&#x223C;</mml:mo></mml:mrow><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-8">Eq. (8)</xref>, the arbitrary value are represented by <italic>rand</italic>. If <inline-formula id="ieqn-28"><mml:math id="mml-ieqn-28"><mml:msub><mml:mi>Y</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x003E;</mml:mo><mml:msub><mml:mi>Y</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, the fish moves in this direction. If not, a novel position <inline-formula id="ieqn-29"><mml:math id="mml-ieqn-29"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> is arbitrarily selected to judge whether it fulfills the moving conditions as given below.
<disp-formula id="eqn-8"><label>(8)</label><mml:math id="mml-eqn-8" display="block"><mml:msubsup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow></mml:mfrac><mml:mo>&#x00D7;</mml:mo><mml:mi>S</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>p</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mrow><mml:mo>&#x223C;</mml:mo></mml:mrow><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>Arbitrary motion can be generated using the following equation, if it does not <inline-formula id="ieqn-30"><mml:math id="mml-ieqn-30"><mml:mi>T</mml:mi><mml:mi>r</mml:mi><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo></mml:mrow></mml:msub></mml:math></inline-formula> <italic>Number</italic> times.
<disp-formula id="eqn-9"><label>(9)</label><mml:math id="mml-eqn-9" display="block"><mml:msubsup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:mrow><mml:mtext mathvariant="italic">Visual</mml:mtext></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mrow><mml:mo>&#x223C;</mml:mo></mml:mrow><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>To avoid over-crowding, <inline-formula id="ieqn-31"><mml:math id="mml-ieqn-31"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> i.e., an artificial present location is fixed. Then, the amount of fish in <inline-formula id="ieqn-32"><mml:math id="mml-ieqn-32"><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> company and <inline-formula id="ieqn-33"><mml:math id="mml-ieqn-33"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> center in the region (that is. <inline-formula id="ieqn-34"><mml:math id="mml-ieqn-34"><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x003C;</mml:mo><mml:mrow><mml:mtext mathvariant="italic">Visual</mml:mtext></mml:mrow></mml:math></inline-formula>) are determined. If <inline-formula id="ieqn-35"><mml:math id="mml-ieqn-35"><mml:msub><mml:mi>Y</mml:mi><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>&#x003C;</mml:mo><mml:mi>&#x03B7;</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:msub><mml:mi>Y</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, the location of the companion characterizes less crowd and optimal quantity of food. The fish moves towards its companion region centre as given below.
<disp-formula id="eqn-10"><label>(10)</label><mml:math id="mml-eqn-10" display="block"><mml:msubsup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow></mml:mfrac><mml:mo>&#x00D7;</mml:mo><mml:mi>S</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>p</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mrow><mml:mo>&#x223C;</mml:mo></mml:mrow><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>Otherwise, it begins to implement the behaviour of prey.</p>
<p>In <xref ref-type="disp-formula" rid="eqn-10">Eq. (10)</xref>, <inline-formula id="ieqn-36"><mml:math id="mml-ieqn-36"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> represents the present location of AF swarm. The swarm determines the main company <inline-formula id="ieqn-37"><mml:math id="mml-ieqn-37"><mml:msub><mml:mi>Y</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> as <inline-formula id="ieqn-38"><mml:math id="mml-ieqn-38"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> in the region i.e., <inline-formula id="ieqn-39"><mml:math id="mml-ieqn-39"><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x003C;</mml:mo><mml:mrow><mml:mtext mathvariant="italic">Visual</mml:mtext></mml:mrow></mml:math></inline-formula>). If <inline-formula id="ieqn-40"><mml:math id="mml-ieqn-40"><mml:msub><mml:mi>Y</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>&#x003C;</mml:mo><mml:mi>&#x03B7;</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:msub><mml:mi>Y</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, the location of the company characterizes a lesser crowd and optimal number of food. Later, the swarm moves to <inline-formula id="ieqn-41"><mml:math id="mml-ieqn-41"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>:
<disp-formula id="eqn-11"><label>(11)</label><mml:math id="mml-eqn-11" display="block"><mml:msubsup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow></mml:mfrac><mml:mo>&#x00D7;</mml:mo><mml:mi>S</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>p</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mrow><mml:mo>&#x223C;</mml:mo></mml:mrow><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>It allows AF to accomplish food and company through a large regional area.</p>
<p>With <inline-formula id="ieqn-42"><mml:math id="mml-ieqn-42"><mml:mi>D</mml:mi><mml:mspace width="thickmathspace" /><mml:mrow><mml:mtext>dimension</mml:mtext></mml:mrow></mml:math></inline-formula> searching space, the probable distance between two AFs is applied to limit <italic>Visual</italic> &#x0026; <italic>Step</italic> of AF. <inline-formula id="ieqn-43"><mml:math id="mml-ieqn-43"><mml:mi>M</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mi>D</mml:mi></mml:math></inline-formula> is defined in the following equation.
<disp-formula id="eqn-12"><label>(12)</label><mml:math id="mml-eqn-12" display="block"><mml:mi>M</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:msqrt><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mo movablelimits="true" form="prefix">max</mml:mo></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mo movablelimits="true" form="prefix">min</mml:mo></mml:mrow></mml:msub><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>&#x00D7;</mml:mo><mml:mi>D</mml:mi></mml:msqrt></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-12">Eq. (12)</xref>, the lower and upper limits of the optimization range are represented by <inline-formula id="ieqn-44"><mml:math id="mml-ieqn-44"><mml:mspace width="thickmathspace" /><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mo movablelimits="true" form="prefix">min</mml:mo></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-45"><mml:math id="mml-ieqn-45"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mo movablelimits="true" form="prefix">max</mml:mo></mml:mrow></mml:msub></mml:math></inline-formula> correspondingly and the dimension of the search space is represented by <italic>D</italic>.</p>
</sec>
</sec>
<sec id="s3"><label>3</label><title>Experimental Validation</title>
<p>In this section, the proposed AFSADL-MURLC model was experimentally validated using a benchmark dataset sourced from Kaggle repository (available at <uri xlink:href="https://www.kaggle.com/datasets/siddharthkumar25/malicious-and-benign-urls">https://www.kaggle.com/datasets/siddharthkumar25/malicious-and-benign-urls</uri>). In this study, the authors used 5,000 samples under benign category and 5,000 samples under malicious category.</p>
<p>The confusion matrices generated by the proposed AFSADL-MURLC model on identification of malicious URLs are given in <xref ref-type="fig" rid="fig-3">Fig. 3</xref>. For 80&#x0025; of training (TR) data, the proposed AFSADL-MURLC model recognized 3,924 samples under benign class and 3,936 samples under malicious class. In line with this, for 20&#x0025; of testing (TS) data, AFSADL-MURLC technique recognized 990 samples under benign class and 985 samples under malicious class. Along with that, for 70&#x0025; of TR data, the presented AFSADL-MURLC approach recognized 3,475 samples under benign class and 3,500 samples under malicious class. At last, on 30&#x0025; of TS data, the proposed AFSADL-MURLC system recognized 1,510 samples under benign class and 1,478 samples under malicious class.</p>
<fig id="fig-3"><label>Figure 3</label><caption><title>Confusion matrices generated by AFSADL-MURLC technique for (a) 80&#x0025; of TRS, (b) 20&#x0025; of TS set, (c) 70&#x0025; of TRS, and (d) 30&#x0025; of TS set</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31371-fig-3.png"/></fig>
<p><xref ref-type="table" rid="table-1">Tab. 1</xref> and <xref ref-type="fig" rid="fig-4">Fig. 4</xref> report the overall classification outcomes accomplished by the proposed AFSADL-MURLC model with 80&#x0025; of TR and 20&#x0025; of TS datasets. For 80&#x0025; of TR data, the presented AFSADL-MURLC model recognized the instances under benign class with <inline-formula id="ieqn-46"><mml:math id="mml-ieqn-46"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-47"><mml:math id="mml-ieqn-47"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-48"><mml:math id="mml-ieqn-48"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula>, and AUC values such as 98.25&#x0025;, 98.27&#x0025;, 98.22&#x0025;, 98.25&#x0025;, and 98.25&#x0025; respectively. At the same time, for 80&#x0025; of TR data, the proposed AFSADL-MURLC methodology recognized the instances under malicious class with <inline-formula id="ieqn-49"><mml:math id="mml-ieqn-49"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-50"><mml:math id="mml-ieqn-50"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-51"><mml:math id="mml-ieqn-51"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula>, and AUC values such as 98.25&#x0025;, 98.23&#x0025;, 98.28&#x0025;, 98.25&#x0025;, and 98.25&#x0025; correspondingly. Moreover, on 20&#x0025; of TS data, the presented AFSADL-MURLC algorithm recognized the instances under benign class with <inline-formula id="ieqn-52"><mml:math id="mml-ieqn-52"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-53"><mml:math id="mml-ieqn-53"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-54"><mml:math id="mml-ieqn-54"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula>, and AUC values such as 98.75&#x0025;, 99&#x0025;, 98.51&#x0025;, 98.75&#x0025;, and 98.75&#x0025; correspondingly.</p>
<table-wrap id="table-1"><label>Table 1</label><caption><title>Results of the analysis of AFSADL-MURLC technique under different measures on 80&#x0025; of TRS and 20&#x0025; of TSS</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 align="left">Labels</th>
<th align="left">Accuracy</th>
<th align="left">Precision</th>
<th align="left">Recall</th>
<th align="left">F-Score</th>
<th align="left">AUC Score</th>
</tr>
</thead>
<tbody>
<tr>
<td align="center" colspan="6">Training set (80&#x0025;)</td>
</tr>
<tr>
<td align="left">Benign</td>
<td align="left">98.25</td>
<td align="left">98.27</td>
<td align="left">98.22</td>
<td align="left">98.25</td>
<td align="left">98.25</td>
</tr>
<tr>
<td align="left">Malicious</td>
<td align="left">98.25</td>
<td align="left">98.23</td>
<td align="left">98.28</td>
<td align="left">98.25</td>
<td align="left">98.25</td>
</tr>
<tr>
<td align="center" colspan="6">Testing set (20&#x0025;)</td>
</tr>
<tr>
<td align="left">Benign</td>
<td align="left">98.75</td>
<td align="left">99.00</td>
<td align="left">98.51</td>
<td align="left">98.75</td>
<td align="left">98.75</td>
</tr>
<tr>
<td align="left">Malicious</td>
<td align="left">98.75</td>
<td align="left">98.50</td>
<td align="left">98.99</td>
<td align="left">98.75</td>
<td align="left">98.75</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="fig-4"><label>Figure 4</label><caption><title>Results of the analysis of AFSADL-MURLC technique on 80&#x0025; of TRS and 20&#x0025; of TSS</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31371-fig-4.png"/></fig>
<p><xref ref-type="table" rid="table-2">Tab. 2</xref> and <xref ref-type="fig" rid="fig-5">Fig. 5</xref> demonstrates the overall classification results attained by AFSADL-MURLC technique with 70&#x0025; of TR and 30&#x0025; of TS datasets. For 80&#x0025; of TR data, AFSADL-MURLC model recognized the instances under benign class with <inline-formula id="ieqn-55"><mml:math id="mml-ieqn-55"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-56"><mml:math id="mml-ieqn-56"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-57"><mml:math id="mml-ieqn-57"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula>, and AUC values such as 99.64&#x0025;, 99.57&#x0025;, 99.71&#x0025;, 99.64&#x0025;, and 99.64&#x0025; correspondingly. Besides, for 80&#x0025; of TR data, the proposed AFSADL-MURLC approach recognized the instances under malicious class with <inline-formula id="ieqn-58"><mml:math id="mml-ieqn-58"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-59"><mml:math id="mml-ieqn-59"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-60"><mml:math id="mml-ieqn-60"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula>, and AUC values such as 99.64&#x0025;, 99.72&#x0025;, 99.57&#x0025;, 99.64&#x0025;, and 99.64&#x0025; respectively. Furthermore, on 20&#x0025; of TS data, the proposed AFSADL-MURLC technique recognized the instances under benign class with <inline-formula id="ieqn-61"><mml:math id="mml-ieqn-61"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-62"><mml:math id="mml-ieqn-62"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-63"><mml:math id="mml-ieqn-63"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula>, and AUC values such as 99.60&#x0025;, 99.54&#x0025;, 99.67&#x0025;, 99.60&#x0025;, and 99.60&#x0025; correspondingly.</p>
<table-wrap id="table-2"><label>Table 2</label><caption><title>Results of the analysis of AFSADL-MURLC technique under different measures on 70&#x0025; of TRS and 30&#x0025; of TSS</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 align="left">Labels</th>
<th align="left">Accuracy</th>
<th align="left">Precision</th>
<th align="left">Recall</th>
<th align="left">F-Score</th>
<th align="left">AUC Score</th>
</tr>
</thead>
<tbody>
<tr>
<td align="center" colspan="6">Training set (70&#x0025;)</td>
</tr>
<tr>
<td align="left">Benign</td>
<td align="left">99.64</td>
<td align="left">99.57</td>
<td align="left">99.71</td>
<td align="left">99.64</td>
<td align="left">99.64</td>
</tr>
<tr>
<td align="left">Malicious</td>
<td align="left">99.64</td>
<td align="left">99.72</td>
<td align="left">99.57</td>
<td align="left">99.64</td>
<td align="left">99.64</td>
</tr>
<tr>
<td align="center" colspan="6">Testing set (30&#x0025;)</td>
</tr>
<tr>
<td align="left">Benign</td>
<td align="left">99.60</td>
<td align="left">99.54</td>
<td align="left">99.67</td>
<td align="left">99.60</td>
<td align="left">99.60</td>
</tr>
<tr>
<td align="left">Malicious</td>
<td align="left">99.60</td>
<td align="left">99.66</td>
<td align="left">99.53</td>
<td align="left">99.60</td>
<td align="left">99.60</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="fig-5"><label>Figure 5</label><caption><title>Results of the analysis of AFSADL-MURLC technique on 70&#x0025; of TRS and 30&#x0025; of TSS</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31371-fig-5.png"/></fig>
<p>Training Accuracy (TA) and Validation Accuracy (VA) values, attained by the proposed AFSADL-MURLC model on test dataset, are demonstrated in <xref ref-type="fig" rid="fig-6">Fig. 6</xref>. The experimental outcomes imply that the proposed AFSADL-MURLC model gained the maximum TA and VA values. To be specific, VA seemed to be higher than TA.</p>
<fig id="fig-6"><label>Figure 6</label><caption><title>TA and VA analyses results of AFSADL-MURLC technique</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31371-fig-6.png"/></fig>
<p>Training Loss (TL) and Validation Loss (VL) values, achieved by the presented AFSADL-MURLC model on test dataset, are portrayed in <xref ref-type="fig" rid="fig-7">Fig. 7</xref>. The experimental outcomes infer that AFSADL-MURLC model achieved the least TL and VL values. To be specific, VL seemed to be lower than TL.</p>
<fig id="fig-7"><label>Figure 7</label><caption><title>TL and VL analyses results of AFSADL-MURLC technique</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31371-fig-7.png"/></fig>
<p><xref ref-type="table" rid="table-3">Tab. 3</xref> provides the results for comprehensive comparative analysis achieved by the proposed AFSADL-MURLC model and other existing models. <xref ref-type="fig" rid="fig-8">Fig. 8</xref> showcases the comparative investigation results attained by AFSADL-MURLC model and other existing models in terms of <inline-formula id="ieqn-64"><mml:math id="mml-ieqn-64"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. The figure indicates that Na&#x00EF;ve Bayes (NB) model achieved the least <inline-formula id="ieqn-65"><mml:math id="mml-ieqn-65"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 95.37&#x0025;. Besides, Multilayer Perceptron (MLP) and LSTM models attained slightly enhanced <inline-formula id="ieqn-66"><mml:math id="mml-ieqn-66"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values such as 97.94&#x0025; and 98.08&#x0025; respectively. In addition, Lloyd&#x2019;s and Random Forest (RF) models demonstrated reasonable <inline-formula id="ieqn-67"><mml:math id="mml-ieqn-67"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values such as 99.23&#x0025; and 99.03&#x0025; respectively. However, the proposed AFSADL-MURLC model accomplished superior outcomes with a maximum <inline-formula id="ieqn-68"><mml:math id="mml-ieqn-68"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.60&#x0025;.</p>


<table-wrap id="table-3"><label>Table 3</label><caption><title>Comparative analysis results of AFSADL-MURLC technique and other existing approaches</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Methods</th>
<th align="left">Accuracy</th>
<th align="left">F-Score</th>
<th align="left">Precision</th>
<th align="left">Recall</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">RF Algorithm</td>
<td align="left">99.03</td>
<td align="left">98.84</td>
<td align="left">98.80</td>
<td align="left">98.24</td>
</tr>
<tr>
<td align="left">MLP Algorithm</td>
<td align="left">97.94</td>
<td align="left">98.19</td>
<td align="left">99.17</td>
<td align="left">97.70</td>
</tr>
<tr>
<td align="left">NB Model</td>
<td align="left">95.37</td>
<td align="left">95.29</td>
<td align="left">99.01</td>
<td align="left">92.04</td>
</tr>
<tr>
<td align="left">LSTM Model</td>
<td align="left">98.08</td>
<td align="left">98.02</td>
<td align="left">98.90</td>
<td align="left">97.51</td>
</tr>
<tr>
<td align="left">Lloyd&#x2019;s Algorithm</td>
<td align="left">99.23</td>
<td align="left">96.70</td>
<td align="left">96.90</td>
<td align="left">95.51</td>
</tr>
<tr>
<td align="left">AFSADL-MURLC</td>
<td align="left">99.60</td>
<td align="left">99.60</td>
<td align="left">99.60</td>
<td align="left">99.60</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="fig-8"><label>Figure 8</label><caption><title><inline-formula id="ieqn-84"><mml:math id="mml-ieqn-84"><mml:mi>A</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis results of AFSADL-MURLC technique and other existing approaches</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31371-fig-8.png"/></fig>
<p><xref ref-type="fig" rid="fig-9">Fig. 9</xref> illustrates the comparative analysis results attained by the proposed AFSADL-MURLC technique and other existing models with respect to <inline-formula id="ieqn-69"><mml:math id="mml-ieqn-69"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula>. The figure infers that NB technique produced the least <inline-formula id="ieqn-70"><mml:math id="mml-ieqn-70"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 95.29&#x0025;. Also, MLP and LSTM systems achieved somewhat higher <inline-formula id="ieqn-71"><mml:math id="mml-ieqn-71"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> values such as 98.19&#x0025; and 98.02&#x0025; respectively. Next, Lloyd&#x2019;s and RF models demonstrated reasonable <inline-formula id="ieqn-72"><mml:math id="mml-ieqn-72"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> values such as 96.70&#x0025; and 98.84&#x0025; respectively. Eventually, the proposed AFSADL-MURLC technique accomplished superior outcomes with a high <inline-formula id="ieqn-73"><mml:math id="mml-ieqn-73"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 99.60&#x0025;.</p>
<fig id="fig-9"><label>Figure 9</label><caption><title><inline-formula id="ieqn-85"><mml:math id="mml-ieqn-85"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> analysis results of AFSADL-MURLC technique and other existing methods</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31371-fig-9.png"/></fig>
<p><xref ref-type="fig" rid="fig-10">Fig. 10</xref> portrays the comparative investigation results of AFSADL-MURLC approach and other existing models in terms of <inline-formula id="ieqn-74"><mml:math id="mml-ieqn-74"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. The figure indicates that NB algorithm produced the least <inline-formula id="ieqn-75"><mml:math id="mml-ieqn-75"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.01&#x0025;. In addition, MLP and LSTM methods achieved slightly increased <inline-formula id="ieqn-76"><mml:math id="mml-ieqn-76"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values such as 99.17&#x0025; and 98.90&#x0025; respectively. Followed by, Lloyd&#x2019;s and RF models demonstrated reasonable <inline-formula id="ieqn-77"><mml:math id="mml-ieqn-77"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values such as 96.90&#x0025; and 98.80&#x0025; respectively. Finally, the proposed AFSADL-MURLC methodology accomplished superior outcome with a high <inline-formula id="ieqn-78"><mml:math id="mml-ieqn-78"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.60&#x0025;.</p>

<fig id="fig-10"><label>Figure 10</label><caption><title><inline-formula id="ieqn-86"><mml:math id="mml-ieqn-86"><mml:mi>P</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis results of AFSADL-MURLC technique and other existing methods</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31371-fig-10.png"/></fig>
<p><xref ref-type="fig" rid="fig-11">Fig. 11</xref> demonstrates the comparative examination results accomplished by the proposed AFSADL-MURLC algorithm and other existing models with respect to <inline-formula id="ieqn-79"><mml:math id="mml-ieqn-79"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. The figure implies that NB system resulted in less <inline-formula id="ieqn-80"><mml:math id="mml-ieqn-80"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 98.24&#x0025;. Moreover, MLP and LSTM methods achieved somewhat superior <inline-formula id="ieqn-81"><mml:math id="mml-ieqn-81"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values such as 97.70&#x0025; and 97.51&#x0025; correspondingly. In addition, Lloyd&#x2019;s and RF approaches demonstrated reasonable <inline-formula id="ieqn-82"><mml:math id="mml-ieqn-82"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values such as 95.51&#x0025; and 98.24&#x0025; correspondingly. At last, the proposed AFSADL-MURLC system accomplished superior outcome with a maximum <inline-formula id="ieqn-83"><mml:math id="mml-ieqn-83"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.60&#x0025;. Thus, the current study establishes that AFSADL-MURLC model has the ability to achieve maximum performance over other methods.</p>
<fig id="fig-11"><label>Figure 11</label><caption><title><inline-formula id="ieqn-87"><mml:math id="mml-ieqn-87"><mml:mi>R</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis results of AFSADL-MURLC technique and other existing approaches</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31371-fig-11.png"/></fig>
</sec>
<sec id="s4"><label>4</label><title>Conclusion</title>
<p>In this study, a novel AFSADL-MURLC model has been developed to properly identify the existence of malicious URLs. The proposed AFSADL-MURLC model primarily performs data preprocessing and makes use of Glove-based word embedding technique. Besides, the created vector model is passed onto GRU classification model to recognize the malicious URLs. Finally, in order to improve the efficacy of GRU model, AFSA is applied to it. The proposed AFSADL-MURLC model was experimentally validated using benchmark dataset sourced from Kaggle repository. The simulation results confirmed the supremacy of AFSADL-MURLC model over recent approaches under distinct measures. In future, hybrid DL and metaheuristic algorithms can be designed to improve the performance in terms of malicious URL detection and classification.</p>
</sec>
</body>
<back>
<fn-group>
<fn fn-type="other"><p><bold>Funding Statement:</bold> The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through Large Groups Project under grant number (45/43). Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2022R140), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. The authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: 22UQU4310373DSR21.</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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