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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">23657</article-id>
<article-id pub-id-type="doi">10.32604/cmc.2022.023657</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Design of QoS Aware Routing Protocol for IoT Assisted Clustered WSN</article-title>
<alt-title alt-title-type="left-running-head">Design of QoS Aware Routing Protocol for IoT Assisted Clustered WSN</alt-title>
<alt-title alt-title-type="right-running-head">Design of QoS Aware Routing Protocol for IoT Assisted Clustered WSN</alt-title>
</title-group>
<contrib-group content-type="authors">
<contrib id="author-1" contrib-type="author">
<name name-style="western"><surname>Dutta</surname><given-names>Ashit Kumar</given-names></name><xref ref-type="aff" rid="aff-1">1</xref>
</contrib>
<contrib id="author-2" contrib-type="author">
<name name-style="western"><surname>Srinivasan</surname><given-names>S.</given-names></name><xref ref-type="aff" rid="aff-2">2</xref>
</contrib>
<contrib id="author-3" contrib-type="author">
<name name-style="western"><surname>Rao</surname><given-names>Bobbili Prasada</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>Hemalatha</surname><given-names>B.</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>Pustokhina</surname><given-names>Irina V.</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>Pustokhin</surname><given-names>Denis A.</given-names></name><xref ref-type="aff" rid="aff-6">6</xref>
</contrib>
<contrib id="author-7" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Joshi</surname><given-names>Gyanendra Prasad</given-names></name><xref ref-type="aff" rid="aff-7">7</xref><email>joshi@sejong.ac.kr</email>
</contrib>
<aff id="aff-1"><label>1</label><institution>Department of Computer Science and Information Systems, College of Applied Sciences, Almaarefa University</institution>, <addr-line>Riyadh, 13713</addr-line>, <country>Kingdom of Saudi Arabia</country></aff>
<aff id="aff-2"><label>2</label><institution>Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences</institution>, <addr-line>Saveetha Nagar, Thandalam, Chennai, 602105</addr-line>, <country>India</country></aff>
<aff id="aff-3"><label>3</label><institution>Department of Electrical and Electronics Engineering, Vignan&#x0027;s Institute of Information Technology</institution>, <addr-line>Visakhapatnam, 530049</addr-line>, <country>India</country></aff>
<aff id="aff-4"><label>4</label><institution>Department of Electronics and Communication Engineering, Thirumalai Engineering College</institution>, <addr-line>Kancheepuram, 631551</addr-line>, <country>India</country></aff>
<aff id="aff-5"><label>5</label><institution>Department of Entrepreneurship and Logistics, Plekhanov Russian University of Economics</institution>, <addr-line>117997, Moscow</addr-line>, <country>Russia</country></aff>
<aff id="aff-6"><label>6</label><institution>Department of Logistics, State University of Management</institution>, <addr-line>109542, Moscow</addr-line>, <country>Russia</country></aff>
<aff id="aff-7"><label>7</label><institution>Department of Computer Science and Engineering, Sejong University</institution>, <addr-line>Seoul, 05006</addr-line>, <country>Korea</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Gyanendra Prasad Joshi. Email: <email>joshi@sejong.ac.kr</email></corresp>
</author-notes>
<pub-date pub-type="epub" date-type="pub" iso-8601-date="2021-11-29"><day>29</day>
<month>11</month>
<year>2021</year></pub-date>
<volume>71</volume>
<issue>2</issue>
<fpage>3785</fpage>
<lpage>3801</lpage>
<history>
<date date-type="received"><day>15</day><month>9</month><year>2021</year></date>
<date date-type="accepted"><day>20</day><month>10</month><year>2021</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2022 Dutta et al.</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Dutta 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_23657.pdf"></self-uri>
<abstract>
<p>In current days, the domain of Internet of Things (IoT) and Wireless Sensor Networks (WSN) are combined for enhancing the sensor related data transmission in the forthcoming networking applications. Clustering and routing techniques are treated as the effective methods highly used to attain reduced energy consumption and lengthen the lifetime of the WSN assisted IoT networks. In this view, this paper presents an Ensemble of Metaheuristic Optimization based QoS aware Clustering with Multihop Routing (EMO-QoSCMR) Protocol for IoT assisted WSN. The proposed EMO-QoSCMR protocol aims to achieve QoS parameters such as energy, throughput, delay, and lifetime. The proposed model involves two stage processes namely clustering and routing. Firstly, the EMO-QoSCMR protocol involves cross-entropy rain optimization algorithm based clustering (CEROAC) technique to select an optimal set of cluster heads (CHs) and construct clusters. Besides, oppositional chaos game optimization based routing (OCGOR) technique is employed for the optimal set of routes in the IoT assisted WSN. The proposed model derives a fitness function based on the parameters involved in the IoT nodes such as residual energy, distance to sink node, etc. The proposed EMO-QoSCMR technique has resulted to an enhanced NAN of 64 nodes whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS methods have resulted in a lesser NAN of 2, 10, 42, and 51 rounds. The performance of the presented protocol has been evaluated interms of energy efficiency and network lifetime.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Internet of things</kwd>
<kwd>wireless sensor networks</kwd>
<kwd>clustering</kwd>
<kwd>routing</kwd>
<kwd>metaheuristics</kwd>
<kwd>cluster head selection</kwd>
<kwd>QoS parameters</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1"><label>1</label><title>Introduction</title>
<p>Internet of Things (IoT) is globally suggested to use in various applications for interlinking various networks. In recent days IoTs are used in various heterogeneous networks such as medical networks, vehicular networks, mobile networks as well as sensor networks [<xref ref-type="bibr" rid="ref-1">1</xref>]. In particular, the sensor network or WSN can improve the distributed intelligence and communication protocols for smart devices and various other equipment, which is combined to form a novel futuristic internet solution in IoT. The WSNs are emerging as an advanced platform that is useful in lots of applications like healthcare, environmental monitoring, intelligence surveillance, smart cities, military, etc. In these applications, small sensors act as nodes to collect and transmit the information to a base station or sink node [<xref ref-type="bibr" rid="ref-2">2</xref>]. An individual sensor node is a self-operating device which is connected wirelessly and is spatially distributed. So every individual node can simultaneously sense, process, and interact with one another. The price of IoT systems has decreased dramatically, opening up a number of possibilities to boost potential innovation and deployments [<xref ref-type="bibr" rid="ref-3">3</xref>]. Researchers have been exploring the Wireless Sensor Networks technology (WSNs) for over a decade and, along with numerous routing methods, different techniques have been proposed by the researchers with regard to reducing the packet and frame size of medium access control (MAC) and physical layers. Various other unsophisticated processes, energy combination with applied fusion techniques, time, placement, and safety mechanisms have been made aware of. They enrich fundamental infrastructures, high-level abstractions that are assisted by operating system designs, and large-scale management systems to handle data generated in an appropriate way [<xref ref-type="bibr" rid="ref-4">4</xref>]. The energy control of the IoT networks is now becoming self-sufficient. <?A3B2 "fig1",5,"anchor"?><xref ref-type="fig" rid="fig-1">Fig. 1</xref> illustrates the overview of WSN.</p>
<fig id="fig-1"><label>Figure 1</label><caption><title>Overview of WSN</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_23657-fig-1.png"/></fig>
<p>WSN provides extremely flexible control and monitoring at an efficient cost since they are infrastructure-less and autonomous [<xref ref-type="bibr" rid="ref-5">5</xref>]. The costs of a single node are efficient as the node in WSN are constrained based on the memory, processing, energy, as well as transmission resource. Since energy is one of the key problems, where IoT serves as a compromising region which links billions of WSNs. In MANET the networks node are free to transfer everywhere in the network. The importance and functioning of the present system in industry are occasionally converted to the consistent solution render with IoT. Although IoT assures opportunity to establish the reliable system, energy utilization seem to be a key constraint in IoT network.</p>
<p>In general, the dynamic nature of the WSN environments is because of the absence/presence of the hurdle, exhaustion of sensor battery, mobility of the sensor, sink nodes, and unstable weather situations between the nodes in the network. Because of the fact, that there is a continuous variation in the routes among the nodes, that require reacting and tracing via efficient routing protocols [<xref ref-type="bibr" rid="ref-6">6</xref>]. Thus, carrying out the network routings is one of the key challenges due to the nonstatic node that arbitrarily moves in the predefined searching area. Secure node multi-casting routing approach improves the security by electing the route according to the less amount of communications as well generate a bandwidth minimum multi-cast trees. This would resist each threat involving wormhole attacks. For IoT applications, the message is distributed to some nodes via multi-cast transmission. The multi-cast routing protocols establish multicast routes to send data packets among source and destination. For example, applications in IoT with multi-cast transmissions update the price in a market on electronic shelf labels. Literature divides the routing protocol into geographic and non-geographic based protocols. In the event of nongeographic-based solution, the requested packet is flooded from the multi-cast source to each destination node, while, in geographic based multi-cast routing, the node knows the position by a GPS device [<xref ref-type="bibr" rid="ref-7">7</xref>]. Multi-channel routing reduces the congestion and interference to improve the data rate and reduce the energy utilization which ensures multiple QoS limitations. Alternatively, the network topology from adoptive to dynamic assists better efficiency in multi-media communications of IoT. It is necessary to effective multi-cast routing protocol for addressing the need for multi-media communication in a high dynamic IoT environment.</p>
<p>Shende et al. [<xref ref-type="bibr" rid="ref-8">8</xref>] proposes an energy aware multipath routing protocol depending on the optimization, CrowWhale-ETR, i.e., the incorporation of WOA &#x0026; CSA depending on the objective function developed by the trust factor and energy of the node. At first, the energy and trust of the node are calculated to establish the route i.e., optimally selected by a CWOA approach. These optimally selected paths are utilized to transmit the information, where the trust and energy of a single node are upgraded after the single communication, thus the secured node could be elected, and that enhances the secured transmission in the network. Tandon et al. [<xref ref-type="bibr" rid="ref-9">9</xref>] propose a Bio-inspired cross-layer routing (BiHCLR) protocol to achieve effectively and energy preserving routing in WSN assisted IoT. Initially, the deployed sensor nodes are arranged in the form of a grid as per the grid-based routing strategy. Then to enable energy preservation in BiHCLR, the fuzzy logic approach is executed to select the Cluster Head (CH) for every cell of the grid. Then a hybrid bio-inspired algorithm is used to select the routing path. The hybrid algorithm combines moth search and Salp Swarm optimization techniques.</p>
<p>Chouhan et al. [<xref ref-type="bibr" rid="ref-10">10</xref>] present the multipath routing protocol with the presented optimization algorithm, called TSGWO method in the IoT enabled WSN system. With the multipath routing protocol, the multi-path is developed using multi-path source nodes to many destinations. The multi-path source node packet is forward to multiple destinations at the same time. Initially, the node in IoT enabled WSN system is inspired together and perform the CH election with FGSA approach, and later the multi-path routing method is made based on the presented TSGWO algorithm where the routing paths are elected by taking into account the fitness variables such as trust factors and QoS parameters.</p>
<p>In Sunitha et al. [<xref ref-type="bibr" rid="ref-11">11</xref>], very much efficient and robust Evolutionary computing enabled WSN routing protocols are improved to energy efficacy and QoS. This presented method encompasses 2 major features NCAMND mines/exploits the network parameters or dynamic node for identifying malicious node, and EC-DDFP models learn through network or node connectivity and accessibility data to attain a dual disjoint path without shared component for ensuring energy effective routing and QoS centric. Jazebi et al. [<xref ref-type="bibr" rid="ref-12">12</xref>] proposed a routing system for IoT with SFLA method. RISA employs SFLA for finding content based paths among the source node and destination node. RISA could decrease power utilization as well as enhance the lifetime of network with a suitable data aggregation system.</p>
<p>Jaiswal et al. [<xref ref-type="bibr" rid="ref-13">13</xref>] propose a GWO based CH election method for WSN consider different aspects such as node degree, energy levels of the node, intracluster distance, priority factor, and sink distance. Also, this study addresses the routing via QoS aware relay nodes election for a reliable and effective intercluster routing from CH to BS. In Hajiee et al. [<xref ref-type="bibr" rid="ref-14">14</xref>], an ETOR approach is presented based on a new hybrid FF. The method has 2 major phases: one is for selecting a secured node according to the tolerance constant and another is for selecting an opportunistic node from the secured node to implement routing. ETOR employs the multipath route techniques using an intracluster and intercluster multihop transmission method. Furthermore, the secure and optimal routes are elected according to a new hybrid FF.</p>
<p>Shafiq et al. [<xref ref-type="bibr" rid="ref-15">15</xref>] introduce the RCBRP algorithm for identifying the routing path where lesser energy is expended for enhancing the lifetime of the network. The system is proposed in 6 phases for exploring transmission. Also, proposed the 2 approaches: i) routing and energy effective clustering approach and ii) power utilization and distance measurement approach. The system consumes lesser energy and balances the load by clustering the smart device. Ruan et al. [<xref ref-type="bibr" rid="ref-16">16</xref>] proposed a PUDCRP approach. In the PUDCRP algorithm, the distribution of the cluster would alter vigorously while few nodes get fail. The PSO algorithms are employed for determining the areas where the candidate CH node is placed. The adoptive clustering approach depending on node distribution makes the cluster distribution highly reasonable that balances the power utilization of the system efficiently. Though several clustering and routing techniques are available in the literature, only few works have focused on QoS aware clustering and routing process. Therefore, it is needed to design effective QoS aware clustering with routing techniques for IoT assisted WSN.</p>
<p>This paper presents an Ensemble of Metaheuristic Optimization based QoS aware Clustering with Multihop Routing (EMO-QoSCMR) Protocol for IoT assisted WSN. The proposed EMO-QoSCMR protocol aims to achieve QoS parameters such as energy, throughput, delay, and lifetime. The proposed model involves two stage processes namely clustering and routing. Firstly, the EMO-QoSCMR protocol involves cross-entropy rain optimization algorithm based clustering (CEROAC) technique to select an optimal set of cluster heads (CHs) and construct clusters. Besides, oppositional chaos game optimization based routing (OCGOR) technique is employed for the optimal set of routes in the IoT assisted WSN. The proposed model derives a fitness function based on the parameters involved in the IoT nodes. The performance of the presented protocol has been evaluated interms of energy efficiency and network lifetime.</p>
</sec>
<sec id="s2"><label>2</label><title>The Proposed EMO-QoSCMR Technique</title>
<p>In this study, the EMO-QoSCMR protocol is designed to accomplish QoS in WSN by accomplishing energy efficiency and maximizing network lifetime. The EMO-QoSCMR protocol involves a two stage process namely CEROAC based clustering and OCGOR based routing. The detailed operations of these modules are given in the following.</p>
<sec id="s2_1"><label>2.1</label><title>Process Involved in CEROAC Based Clustering</title>
<p>At this stage, the CEROAC technique is derived to select the CHs and organize clusters. In ROA, the rain behaviours are inspired as it is determined in the traditional subsection. All the solutions to a problem can be referred to as raindrops. Based on this issue, few points in the answer space is determined in an arbitrary manner as raindrop falls on the ground. The main feature of a drop of rain is the radius. The radius of all the raindrops might be constrained as time passes and it is improved as raindrops are connected to alternative drops. Once the primary answer population is made, the radius of all droplets is assigned in a random fashion to a constraint range. In addition, every droplet validates the neighbourhood according to the size. Individual droplet which isn&#x0027;t yet connected just verify the end limits of the position that has covered. To solve the issue in dimension space, all the droplets are composed of n variables. Therefore, in the first phase, the minimum and maximum limits of the parameter are validated as the limit is calculated by the radius of the droplets [<xref ref-type="bibr" rid="ref-17">17</xref>]. Followed by, two endpoints of the parameter are tested and it is continued until attaining the last parameter. Next, the cost of initial droplets is updated by shifting in a downward direction. It is implemented for all the droplets, as well as the cost, and place of all the droplets would be allocated. The radius of droplets would be altered in two manners:</p>
<p>Once 2 droplets using radius r<sub>1</sub> &#x0026; r<sub>2</sub>, they are closer to one another with the general field and they connect to develop large droplets of radius R:
<disp-formula id="eqn-1"><label>(1)</label><mml:math id="mml-eqn-1" display="block"><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msubsup><mml:mi>r</mml:mi><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>r</mml:mi><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:msubsup></mml:mrow><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></disp-formula>
</p>
<p>Let <italic>n</italic> be the amount of parameters for each droplet. Once a droplet using radius r<sub>1</sub> isn&#x0027;t moved, according to the soil features, which is shown as <inline-formula id="ieqn-1"><mml:math id="mml-ieqn-1"><mml:mi>&#x03B1;</mml:mi></mml:math></inline-formula>, water is observed with the soil.
<disp-formula id="eqn-2"><label>(2)</label><mml:math id="mml-eqn-2" display="block"><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>&#x03B1;</mml:mi><mml:msubsup><mml:mi>r</mml:mi><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:msubsup></mml:mrow><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></disp-formula>
</p>
<p>Apparently, <inline-formula id="ieqn-2"><mml:math id="mml-ieqn-2"><mml:mi>&#x03B1;</mml:mi><mml:mspace width="thickmathspace" /></mml:math></inline-formula>demonstrates the amount of droplets which was absorbed in each iteration from zero to hundred percent. Moreover, it determines the minimum value for the droplet radius r<sub>min</sub>, whereas droplets with the least radius of that r<sub>min</sub> will be reduced.</p>
<p>As abovementioned, the population values can be decreased afterward few iterations, and maximal droplet is placed with a large area of analysis. By improving the analyses method, the local possible search of drop is proportionally maximized to the diameter of droplet. Hence, by increasing the amount of rounds, weak droplets get vanished or are linked to strong drops using the maximal area of analysis, and the primary population will be intensively decreased and discover the accurate answer (s). It is supposed that there are some variants between the recently proposed optimization method in ROA and the newly presented search models placed RFA approach, i.e., given below:
<list list-type="bullet">
<list-item><p>In ROA, the early population numbers are adapted afterward each iteration due to the link of neighbouring drop. It leads to enhance the search ability of a method and considerably reduce the optimization cost.</p></list-item>
<list-item><p>When the size of droplets is altered, the connecting of adjacent droplet or adsorption with the soils are carried out. Such performances modify the possible search of all the droplets and classify the droplet.</p></list-item>
<list-item><p>In RFA, and alternative searching methods, each population is made up of neighbour points and the droplets are improved one-step in an arbitrary manner. Likewise, all the populations identify the optimum path to the least points. When the path is established, it is moved in downwards iteratively using step, and the cost function is decreased in an individual iteration.</p></list-item>
</list></p>
<p>Based on the idealization and approximation of the models, the rain methods are described. In depth, tuning parameters of these methods such as basic raindrops radius, initial raindrops amount (population amount), etc. Followed by, the values are assigned to each droplet based on the cost function. Next, all the droplets are shifted in downwards direction. Therefore, nearer droplet is integrated with each other, that results in enhanced result. When droplets are ended at the lowest points, the radius begins to reduce gradually caused the precision of the answer to be improved. Subsequently, it is relevant for identifying an extremal point of the objective function.
<fig id="fig-7"><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_23657-fig-7.png"/></fig></p>
<p>In order to improve the performance of the ROA, CEROAC technique is derived by the inclusion of the CE concept. The CE approach for optimization could be determined in the following equation.
<disp-formula id="eqn-3"><label>(3)</label><mml:math id="mml-eqn-3" display="block"><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>S</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:munder><mml:mrow><mml:mo form="prefix">max</mml:mo></mml:mrow><mml:mrow><mml:mi>x</mml:mi><mml:mo>&#x2208;</mml:mo><mml:mi>X</mml:mi></mml:mrow></mml:munder><mml:mo>&#x2061;</mml:mo><mml:mi>S</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo></mml:math></disp-formula>
Whereas <inline-formula id="ieqn-8"><mml:math id="mml-ieqn-8"><mml:mrow><mml:msup><mml:mi>&#x03B3;</mml:mi><mml:mo>&#x2217;</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> represent the maximal on the provided set <italic>X</italic>, the <inline-formula id="ieqn-9"><mml:math id="mml-ieqn-9"><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> denotes the maximum <inline-formula id="ieqn-10"><mml:math id="mml-ieqn-10"><mml:mi>x</mml:mi><mml:mo>.</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>S</mml:mi></mml:math></inline-formula> indicates the efficiency metric. While evaluating sample <italic>X</italic> iteratively, a set of indicators function <inline-formula id="ieqn-11"><mml:math id="mml-ieqn-11"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mo fence="false" stretchy="false">{</mml:mo><mml:mrow><mml:mi>S</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mspace width="thinmathspace" /><mml:mo>&#x2265;</mml:mo><mml:mspace width="thinmathspace" /><mml:mi>&#x03B3;</mml:mi></mml:mrow><mml:mo fence="false" stretchy="false">}</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> are determine. <inline-formula id="ieqn-12"><mml:math id="mml-ieqn-12"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mo fence="false" stretchy="false">{</mml:mo><mml:mrow><mml:mi>S</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mspace width="thinmathspace" /><mml:mo>&#x2265;</mml:mo><mml:mspace width="thinmathspace" /><mml:mi>&#x03B3;</mml:mi></mml:mrow><mml:mo fence="false" stretchy="false">}</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> represent the <inline-formula id="ieqn-13"><mml:math id="mml-ieqn-13"><mml:mi>S</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> as above in the level <inline-formula id="ieqn-14"><mml:math id="mml-ieqn-14"><mml:mi>&#x03B3;</mml:mi></mml:math></inline-formula> for sample <italic>x</italic>. For a vector <italic>u</italic>, <italic>m</italic> of likelihood density function parameter, the optimization problems could be converted to estimate the likelihood <inline-formula id="ieqn-15"><mml:math id="mml-ieqn-15"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi>u</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>S</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mspace width="thinmathspace" /><mml:mo>&#x2265;</mml:mo><mml:mspace width="thinmathspace" /><mml:mi>&#x03B3;</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>. Integrating with indicator function, the likelihood could be evaluated as follows:
<disp-formula id="eqn-4"><label>(4)</label><mml:math id="mml-eqn-4" display="block"><mml:mi>l</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03B3;</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi>u</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>S</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2265;</mml:mo><mml:mi>&#x03B3;</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:munder><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mi>x</mml:mi></mml:munder><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mo fence="false" stretchy="false">{</mml:mo><mml:mrow><mml:mi>S</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2265;</mml:mo><mml:mrow><mml:mi>&#x03B3;</mml:mi></mml:mrow></mml:mrow><mml:mo fence="false" stretchy="false">}</mml:mo></mml:mrow></mml:msub></mml:mrow><mml:mspace width="thinmathspace" /><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>u</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>u</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mo fence="false" stretchy="false">{</mml:mo><mml:mrow><mml:mi>S</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2265;</mml:mo><mml:mi>&#x03B3;</mml:mi></mml:mrow><mml:mo fence="false" stretchy="false">}</mml:mo></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula>
Whereas <italic>P</italic> denotes the likelihood related to the likelihood density function <inline-formula id="ieqn-16"><mml:math id="mml-ieqn-16"><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mo>.</mml:mo><mml:mo>,</mml:mo><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>, and <inline-formula id="ieqn-17"><mml:math id="mml-ieqn-17"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>u</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> represents the probability function. If <inline-formula id="ieqn-18"><mml:math id="mml-ieqn-18"><mml:mi>&#x03B3;</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:msup><mml:mi>&#x03B3;</mml:mi><mml:mo>&#x2217;</mml:mo></mml:msup></mml:mrow><mml:mo>,</mml:mo><mml:mi>l</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03B3;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> could be evaluated by:
<disp-formula id="eqn-5"><label>(5)</label><mml:math id="mml-eqn-5" display="block"><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mfrac><mml:mn>1</mml:mn><mml:mi>N</mml:mi></mml:mfrac><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mo fence="false" stretchy="false">{</mml:mo><mml:mrow><mml:mi>S</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2265;</mml:mo><mml:mi>&#x03B3;</mml:mi></mml:mrow><mml:mo fence="false" stretchy="false">}</mml:mo></mml:mrow></mml:msub></mml:mrow><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>v</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>.</mml:mo></mml:math></disp-formula>
<inline-formula id="ieqn-19"><mml:math id="mml-ieqn-19"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is generated with the help of <inline-formula id="ieqn-20"><mml:math id="mml-ieqn-20"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mo>.</mml:mo><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>v</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>. It is noteworthy that the CE approach find the improved sampling density <inline-formula id="ieqn-21"><mml:math id="mml-ieqn-21"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mo>.</mml:mo><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mrow><mml:msup><mml:mi>v</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> thus the optimum solutions could be sampled [<xref ref-type="bibr" rid="ref-18">18</xref>].</p>
<p>The process of CE could be summarised into 3 major stages:
<list list-type="order">
<list-item><p>Produce an arbitrary instance from Gaussian distribution using mean <inline-formula id="ieqn-22"><mml:math id="mml-ieqn-22"><mml:mi>m</mml:mi><mml:mi>u</mml:mi></mml:math></inline-formula> and standard deviation <inline-formula id="ieqn-23"><mml:math id="mml-ieqn-23"><mml:mi>s</mml:mi><mml:mo>.</mml:mo></mml:math></inline-formula></p></list-item>
<list-item><p>Choose a certain amount of optimal samples from the entire sample.</p></list-item>
<list-item><p>Upgrade <inline-formula id="ieqn-24"><mml:math id="mml-ieqn-24"><mml:mi>m</mml:mi><mml:mi>u</mml:mi></mml:math></inline-formula> &#x0026; <italic>s</italic> according to the optimal samples using best fitness.</p></list-item>
</list></p>
<p>To increase the network lifespan of a clustered based WSN, the CEROAC technique is derived to choose an optimal set of best positions CH. To satisfy this aim, a multiobjective FF is created that has 4 variables like degree of node, residual node energy, coverage ratio, and intracluster distance. The derivation and definition of this parameter can be expressed in the following:
<list list-type="alpha-lower">
<list-item><label>(a)</label><p>Node Energy <inline-formula id="ieqn-25"><mml:math id="mml-ieqn-25"><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>N</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>: The presented clustering protocol utilizes maximal energy node as an optimal candidate for the election of <inline-formula id="ieqn-26"><mml:math id="mml-ieqn-26"><mml:mi>C</mml:mi><mml:mi>H</mml:mi></mml:math></inline-formula>. As a <inline-formula id="ieqn-27"><mml:math id="mml-ieqn-27"><mml:mi>C</mml:mi><mml:mi>H</mml:mi></mml:math></inline-formula> endure further responsibilities like data aggregation and cluster management when compared to <inline-formula id="ieqn-28"><mml:math id="mml-ieqn-28"><mml:mi>C</mml:mi><mml:mi>M</mml:mi></mml:math></inline-formula>, it must have improved energy budget for facilitating balanced power utilization in the network. It is determined as the residual energy of the sensors.
<disp-formula id="eqn-6"><label>(6)</label><mml:math id="mml-eqn-6" display="block"><mml:mi>M</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>z</mml:mi><mml:mi>e</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>N</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mfrac></mml:math></disp-formula>
</p></list-item>
</list></p>
<p>Now <inline-formula id="ieqn-29"><mml:math id="mml-ieqn-29"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> denotes residual energy of ith <inline-formula id="ieqn-30"><mml:math id="mml-ieqn-30"><mml:mi>C</mml:mi><mml:mi>H</mml:mi></mml:math></inline-formula> and <italic>m</italic> represent amount of <inline-formula id="ieqn-31"><mml:math id="mml-ieqn-31"><mml:mi>C</mml:mi><mml:mi>H</mml:mi><mml:mi>s</mml:mi></mml:math></inline-formula>.
<list list-type="simple">
<list-item><label>(b)</label><p>Degree of node <inline-formula id="ieqn-32"><mml:math id="mml-ieqn-32"><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>N</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>e</mml:mi><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>: It is determined as an amount of sensors accessible from a <inline-formula id="ieqn-33"><mml:math id="mml-ieqn-33"><mml:mi>C</mml:mi><mml:mi>H</mml:mi></mml:math></inline-formula>. It is employed for balancing the load at CH [<xref ref-type="bibr" rid="ref-19">19</xref>]<inline-formula id="ieqn-34"><mml:math id="mml-ieqn-34"><mml:mo>.</mml:mo></mml:math></inline-formula>
<disp-formula id="eqn-7"><label>(7)</label><mml:math id="mml-eqn-7" display="block"><mml:mi>M</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>z</mml:mi><mml:mi>e</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>N</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>e</mml:mi><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mrow><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow></mml:math></disp-formula>
</p></list-item>
</list>
Here, <inline-formula id="ieqn-35"><mml:math id="mml-ieqn-35"><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mrow><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow></mml:math></inline-formula> is the number of cluster members of the ith CH.
<list list-type="simple">
<list-item><label>(c)</label><p>Intracluster distance <inline-formula id="ieqn-36"><mml:math id="mml-ieqn-36"><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>u</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>: It is determined as the normal intracluster distance of <inline-formula id="ieqn-37"><mml:math id="mml-ieqn-37"><mml:mi>C</mml:mi><mml:mi>H</mml:mi></mml:math></inline-formula> from its <italic>CM</italic>. This variable ensures the quality of cluster and increases the connection quality among <inline-formula id="ieqn-38"><mml:math id="mml-ieqn-38"><mml:mi>C</mml:mi><mml:mi>H</mml:mi></mml:math></inline-formula> and <italic>CMs</italic>.
<disp-formula id="eqn-8"><label>(8)</label><mml:math id="mml-eqn-8" display="block"><mml:mi>M</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>z</mml:mi><mml:mi>e</mml:mi><mml:mspace width="thickmathspace" /><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>u</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:msubsup><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mrow><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow></mml:mrow></mml:msubsup><mml:mo>&#x2061;</mml:mo><mml:mi>d</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mrow><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mspace width="thickmathspace" /></mml:math></disp-formula>
</p></list-item>
</list>
Now, <inline-formula id="ieqn-39"><mml:math id="mml-ieqn-39"><mml:mi>d</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> is the Euclidean distance among jth <inline-formula id="ieqn-40"><mml:math id="mml-ieqn-40"><mml:mi>C</mml:mi><mml:mi>H</mml:mi></mml:math></inline-formula> &#x0026; <inline-formula id="ieqn-41"><mml:math id="mml-ieqn-41"><mml:mi>i</mml:mi><mml:mrow><mml:mtext>th</mml:mtext></mml:mrow></mml:math></inline-formula> <italic>CM</italic>.
<list list-type="simple">
<list-item><label>(d)</label><p>Coverage of CH <inline-formula id="ieqn-42"><mml:math id="mml-ieqn-42"><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>C</mml:mi><mml:mi>C</mml:mi><mml:mi>H</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>: The major goal of this variable is to remove the unclustered sensors and to guarantee participation of the few left-out sensors in the clustering. This variable reduces the amount of left-out nodes which cannot be a portion of the cluster. Therefore, enhance the coverage of the elected <italic>CH</italic>. The parameter could be calculated in the following equation:
<disp-formula id="eqn-9"><label>(9)</label><mml:math id="mml-eqn-9" display="block"><mml:mi>M</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>z</mml:mi><mml:mi>e</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>v</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>g</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>N</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>m</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:msubsup><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mrow><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msubsup><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:msubsup><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mrow><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:math></disp-formula>
</p></list-item>
</list>
where <italic>N</italic> indicates an overall amount of sensors, <italic>m</italic> denotes amount of <italic>CHs</italic> and <inline-formula id="ieqn-43"><mml:math id="mml-ieqn-43"><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mrow><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow></mml:math></inline-formula> represent quantity of cluster members in the jth cluster.</p>
<p>The last multi-objective FF <inline-formula id="ieqn-44"><mml:math id="mml-ieqn-44"><mml:mo stretchy="false">(</mml:mo><mml:mi>F</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> could be equated as weighted amount of the aforementioned 4 variables which are given in the following equation:
<disp-formula id="eqn-10"><label>(10)</label><mml:math id="mml-eqn-10" display="block"><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>N</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>N</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>e</mml:mi><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>u</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>v</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>g</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula>
</p>
<p>Linear programming equations for an optimum location CH election problems are given below:
<disp-formula id="ueqn-1">
<mml:math id="mml-ueqn-1" display="block"><mml:mi>M</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>z</mml:mi><mml:mi>e</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>N</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>N</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>e</mml:mi><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>u</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>v</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>g</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula>subject to
<disp-formula id="eqn-11"><label>(11)</label><mml:math id="mml-eqn-11" display="block"><mml:mi>N</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x003E;</mml:mo><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-12"><label>(12)</label><mml:math id="mml-eqn-12" display="block"><mml:mi>N</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>e</mml:mi><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mo>&#x2264;</mml:mo><mml:mi>N</mml:mi><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-13"><label>(13)</label><mml:math id="mml-eqn-13" display="block"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>f</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>u</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x003C;</mml:mo><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">x</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-14"><label>(14)</label><mml:math id="mml-eqn-14" display="block"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mspace width="thickmathspace" /><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow><mml:mo>&#x2208;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></disp-formula>
Here, <inline-formula id="ieqn-45"><mml:math id="mml-ieqn-45"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is threshold node energy, <inline-formula id="ieqn-46"><mml:math id="mml-ieqn-46"><mml:mi>N</mml:mi><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> denotes the threshold value of node amount value is initiated by <inline-formula id="ieqn-47"><mml:math id="mml-ieqn-47"><mml:mi>N</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>m</mml:mi><mml:mo>.</mml:mo><mml:mspace width="thickmathspace" /><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> represents the maximal broadcast range of a sensor.</p>
</sec>
<sec id="s2_2"><label>2.2</label><title>Process Involved in OCGOR Based Routing</title>
<p>At this stage, the OCGOR based routing technique is designed to elect an optimal set of routes to sink nodes. The CGO technique has been presented dependent upon the projected rules of chaos theory. The fundamental models of fractals and chaos games were employed for formulating a mathematical method to the CGO technique. Due to the fact that several natural evolution techniques continue a population of solutions that are progressed with arbitrary alteration as well as selection. The CGO technique assumes the amount of solution candidates (S) during this determination that signifies few suitable seeds inside a Sierpinski triangle. The Sierpinski triangle has been assumed as search space to solution candidates from the optimized technique. The mathematical model of these features is as follows:
<disp-formula id="eqn-15"><label>(15)</label><mml:math id="mml-eqn-15" display="block"><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>:</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mtable columnalign="left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mtable columnalign="left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mn>1</mml:mn><mml:mn>1</mml:mn></mml:msubsup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mn>2</mml:mn><mml:mn>1</mml:mn></mml:msubsup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mspace width="thickmathspace" /></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mi>i</mml:mi><mml:mn>1</mml:mn></mml:msubsup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mi>n</mml:mi><mml:mn>1</mml:mn></mml:msubsup></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mtable columnalign="left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mtable columnalign="left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mn>2</mml:mn><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mi>i</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mi>n</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mtable columnalign="left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mtable columnalign="left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mn>1</mml:mn><mml:mi>j</mml:mi></mml:msubsup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mn>2</mml:mn><mml:mi>j</mml:mi></mml:msubsup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mspace width="thickmathspace" /></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:msubsup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mi>n</mml:mi><mml:mi>j</mml:mi></mml:msubsup></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mtable columnalign="left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mspace width="thickmathspace" /></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22F1;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mspace width="thickmathspace" /></mml:mtd></mml:mtr></mml:mtable><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mtable columnalign="left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mn>1</mml:mn><mml:mi>d</mml:mi></mml:msubsup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mspace width="thickmathspace" /></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:msubsup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mspace width="thickmathspace" /></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:math></disp-formula>
<inline-formula id="ieqn-48"><mml:math id="mml-ieqn-48"><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mn>2</mml:mn><mml:mo>&#x2026;</mml:mo><mml:mi>n</mml:mi><mml:mo>.</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>J</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>&#x2026;</mml:mo><mml:mo>.</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>d</mml:mi><mml:mo>.</mml:mo></mml:math></inline-formula> Where n implies the amount of eligible seeds (solution candidate) inside the Sierpinski triangle (search space), and <italic>d</italic> represents the dimensional of these seeds. The first places of these eligible seeds were defined arbitrarily in the search space as:
<disp-formula id="eqn-16"><label>(16)</label><mml:math id="mml-eqn-16" display="block"><mml:msubsup><mml:mi>S</mml:mi><mml:mn>1</mml:mn><mml:mi>j</mml:mi></mml:msubsup><mml:mspace width="thickmathspace" /><mml:mo stretchy="false">(</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msubsup><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow><mml:mi>j</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow><mml:mi>j</mml:mi></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow><mml:mi>j</mml:mi></mml:msubsup></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></disp-formula>where R represents the arbitrary number from the interval of 0 and 1. The procedure to the initial seed has been demonstrated under:
<disp-formula id="eqn-17"><label>(17)</label><mml:math id="mml-eqn-17" display="block"><mml:mi>S</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi><mml:msubsup><mml:mi>d</mml:mi><mml:mi>i</mml:mi><mml:mn>1</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mi>G</mml:mi><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:mi>b</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mi>M</mml:mi><mml:mi>e</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>V</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mi>u</mml:mi><mml:mi>e</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></disp-formula>where <inline-formula id="ieqn-49"><mml:math id="mml-ieqn-49"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> signifies the arbitrary integer of 0 or 1 for demonstrating the possibilities of rolling a dice. Afterward, the schematic presentation of explained procedure to the second seed has been formalized as under [<xref ref-type="bibr" rid="ref-20">20</xref>]:
<disp-formula id="eqn-18"><label>(18)</label><mml:math id="mml-eqn-18" display="block"><mml:mi>S</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi><mml:msubsup><mml:mi>d</mml:mi><mml:mi>i</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:mi>G</mml:mi><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:mi>b</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mi>M</mml:mi><mml:mi>e</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>V</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mi>u</mml:mi><mml:mi>e</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></disp-formula>
</p>
<p>A schematic demonstration of seeds 3<sup>rd</sup> and 4<sup>th</sup> has been explained as under:
<disp-formula id="eqn-19"><label>(19)</label><mml:math id="mml-eqn-19" display="block"><mml:mi>S</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi><mml:msubsup><mml:mi>d</mml:mi><mml:mi>i</mml:mi><mml:mn>3</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:mi>M</mml:mi><mml:mi>e</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>V</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mi>u</mml:mi><mml:mi>e</mml:mi><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mi>G</mml:mi><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:mi>b</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></disp-formula>
<disp-formula id="eqn-20"><label>(20)</label><mml:math id="mml-eqn-20" display="block"><mml:mi>S</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi><mml:msubsup><mml:mi>d</mml:mi><mml:mi>i</mml:mi><mml:mn>4</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mi>i</mml:mi><mml:mi>k</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mi>S</mml:mi><mml:mi>i</mml:mi><mml:mi>k</mml:mi></mml:msubsup><mml:mo>+</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 stretchy="false">)</mml:mo></mml:math></disp-formula>where k implies the arbitrary integer from the interval of 0 and 1. The CGO technique, distinct formulations were projected to <inline-formula id="ieqn-50"><mml:math id="mml-ieqn-50"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> that manages the movement restricts of seeds.
<disp-formula id="eqn-21"><label>(21)</label><mml:math id="mml-eqn-21" display="block"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mtable columnalign="left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mn>2</mml:mn><mml:mo>&#x2217;</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:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="normal">&#x03A8;</mml:mi><mml:mo>&#x2217;</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 stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="normal">&#x03A9;</mml:mi><mml:mo>&#x2217;</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 stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mo>&#x223C;</mml:mo><mml:mi mathvariant="normal">&#x03A9;</mml:mi></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula>where <inline-formula id="ieqn-51"><mml:math id="mml-ieqn-51"><mml:mi>R</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:math></inline-formula> represents the uniformly distributed arbitrary number from the interval of 0 and 1. But <inline-formula id="ieqn-52"><mml:math id="mml-ieqn-52"><mml:mi mathvariant="normal">&#x03A8;</mml:mi></mml:math></inline-formula> and <inline-formula id="ieqn-53"><mml:math id="mml-ieqn-53"><mml:mi mathvariant="normal">&#x03A9;</mml:mi></mml:math></inline-formula> are arbitrary integers from the interval of 0 and 1.</p>
<p>To boost the convergence rate of the CGO algorithm, OBL concept is employed. OBL concepts are utilized for enhancing the quality of initial population solutions with the divergence of the solution. The OBL scheme searches in each direction in the search space, namely opposite and original solution directions. At last, the OBL concepts consider the appropriate solution from every solution.</p>
<p>The opposite amount <italic>x</italic> could be defined as a real value over the interval <inline-formula id="ieqn-54"><mml:math id="mml-ieqn-54"><mml:mi>x</mml:mi><mml:mo>&#x2208;</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:mrow><mml:mi>l</mml:mi><mml:mi>b</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>u</mml:mi><mml:mi>b</mml:mi></mml:mrow><mml:mo stretchy="false">]</mml:mo></mml:math></inline-formula>. The opposite amount of <italic>x</italic> could be represented as <inline-formula id="ieqn-55"><mml:math id="mml-ieqn-55"><mml:mrow><mml:mover><mml:mi>x</mml:mi><mml:mo stretchy="false">&#x007E;</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> and employed for computing the value:
<disp-formula id="eqn-22"><label>(22)</label><mml:math id="mml-eqn-22" display="block"><mml:mrow><mml:mover><mml:mi>x</mml:mi><mml:mo stretchy="false">&#x007E;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mi>l</mml:mi><mml:mi>b</mml:mi><mml:mo>+</mml:mo><mml:mi>u</mml:mi><mml:mi>b</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>x</mml:mi></mml:math></disp-formula>
</p>
<p>The aforementioned formula could be normalized to apply in a search space with multiple dimensions. So, for normalization, each search agent and the corresponding opposite positions can be defined using <xref ref-type="disp-formula" rid="eqn-23">Eqs. (23)</xref>&#x2013;<xref ref-type="disp-formula" rid="eqn-24">(24)</xref>:
<disp-formula id="eqn-23"><label>(23)</label><mml:math id="mml-eqn-23" display="block"><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>D</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo stretchy="false">]</mml:mo></mml:math></disp-formula>
<disp-formula id="eqn-24"><label>(24)</label><mml:math id="mml-eqn-24" display="block"><mml:mrow><mml:mover><mml:mi>x</mml:mi><mml:mo stretchy="false">&#x007E;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mover><mml:mi>x</mml:mi><mml:mo stretchy="false">&#x007E;</mml:mo></mml:mover></mml:mrow></mml:mrow><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mover><mml:mi>x</mml:mi><mml:mo stretchy="false">&#x007E;</mml:mo></mml:mover></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mover><mml:mi>x</mml:mi><mml:mo stretchy="false">&#x007E;</mml:mo></mml:mover></mml:mrow></mml:mrow><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mover><mml:mi>x</mml:mi><mml:mo stretchy="false">&#x007E;</mml:mo></mml:mover></mml:mrow></mml:mrow><mml:mi>D</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo stretchy="false">]</mml:mo></mml:math></disp-formula>
</p>
<p>The value of each individual component in <inline-formula id="ieqn-56"><mml:math id="mml-ieqn-56"><mml:mrow><mml:mover><mml:mi>x</mml:mi><mml:mo stretchy="false">&#x007E;</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> could be calculated as <xref ref-type="disp-formula" rid="eqn-25">Eq. (25)</xref>:
<disp-formula id="eqn-25"><label>(25)</label><mml:math id="mml-eqn-25" display="block"><mml:mrow><mml:msub><mml:mrow><mml:mover><mml:mi>x</mml:mi><mml:mo stretchy="false">&#x007E;</mml:mo></mml:mover></mml:mrow><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mi>l</mml:mi><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mi>u</mml:mi><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mspace width="thickmathspace" /><mml:mi>w</mml:mi><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>D</mml:mi></mml:math></disp-formula>
</p>
<p>Now, the fitness function is <inline-formula id="ieqn-57"><mml:math id="mml-ieqn-57"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mo>.</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>. Once the fitness value <inline-formula id="ieqn-58"><mml:math id="mml-ieqn-58"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mrow><mml:mover><mml:mi>x</mml:mi><mml:mo stretchy="false">&#x007E;</mml:mo></mml:mover></mml:mrow></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> of the opposite solutions exceed <inline-formula id="ieqn-59"><mml:math id="mml-ieqn-59"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> of the actual solutions <italic>x</italic>, then <inline-formula id="ieqn-60"><mml:math id="mml-ieqn-60"><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mover><mml:mi>x</mml:mi><mml:mo stretchy="false">&#x007E;</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula>; otherwise <inline-formula id="ieqn-61"><mml:math id="mml-ieqn-61"><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mi>x</mml:mi></mml:math></inline-formula>.</p>
<p>The process included in the CGO algorithm is listed as follows.
<list list-type="order">
<list-item><label>1.</label><p>Population initiation X as <inline-formula id="ieqn-62"><mml:math id="mml-ieqn-62"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <italic>where</italic> <inline-formula id="ieqn-63"><mml:math id="mml-ieqn-63"><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> .</p></list-item>
<list-item><label>2.</label><p>Compute the opposite position of individuals OX as <inline-formula id="ieqn-64"><mml:math id="mml-ieqn-64"><mml:mrow><mml:msub><mml:mrow><mml:mover><mml:mi>x</mml:mi><mml:mo stretchy="false">&#x007E;</mml:mo></mml:mover></mml:mrow><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <italic>where</italic> <inline-formula id="ieqn-65"><mml:math id="mml-ieqn-65"><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>.</p></list-item>
<list-item><label>3.</label><p>Elect the <italic>n</italic> fittest individuals from <inline-formula id="ieqn-66"><mml:math id="mml-ieqn-66"><mml:mo fence="false" stretchy="false">{</mml:mo><mml:mrow><mml:mi>X</mml:mi><mml:mrow><mml:mo>&#x222A;</mml:mo></mml:mrow><mml:mo>&#x2061;</mml:mo><mml:mi>O</mml:mi><mml:mi>X</mml:mi></mml:mrow><mml:mo fence="false" stretchy="false">}</mml:mo></mml:math></inline-formula> and denote the novel primary population of CGO algorithm.</p></list-item>
</list></p>
<p>In routing, the FF of the OCGOR technique implies the data forwarding route in CH to sink node. The importance of FF is related to CH being reachable from the network, and further locations are added in the sink. The superiority of FF is interrelated to <inline-formula id="ieqn-67"><mml:math id="mml-ieqn-67"><mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula>, where <italic>m</italic> represents the number of CH included in the system. Now, <inline-formula id="ieqn-68"><mml:math id="mml-ieqn-68"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> be <inline-formula id="ieqn-69"><mml:math id="mml-ieqn-69"><mml:mrow><mml:msup><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> FF, and the location <inline-formula id="ieqn-70"><mml:math id="mml-ieqn-70"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mtext>i</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2264;</mml:mo><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow><mml:mi>i</mml:mi><mml:mo>&#x2264;</mml:mo><mml:mrow><mml:mtext>m</mml:mtext></mml:mrow><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mtext>d</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2264;</mml:mo><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow><mml:mi>d</mml:mi><mml:mo>&#x2264;</mml:mo><mml:mrow><mml:mtext>m</mml:mtext></mml:mrow><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow></mml:math></inline-formula>determine next hop send the data to BS<inline-formula id="ieqn-71"><mml:math id="mml-ieqn-71"><mml:mo>.</mml:mo><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow></mml:math></inline-formula>It is highly focused on determining optimum route from CH to sink. It can be achieved with the help of FF in various sub objectives such as node degree, intervehicle distance, and energy. For delivering data, successive hop achieves the data and transferring to BS. Therefore, maximum RE of next hop is prominently prioritized. Moreover, key sub objective using energy <inline-formula id="ieqn-72"><mml:math id="mml-ieqn-72"><mml:mi>f</mml:mi><mml:mn>1</mml:mn></mml:math></inline-formula> is enhanced by:
<disp-formula id="eqn-26"><label>(26)</label><mml:math id="mml-eqn-26" display="block"><mml:mi>f</mml:mi><mml:mn>1</mml:mn><mml:mo>=</mml:mo><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>C</mml:mi><mml:mi>H</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula>
</p>
<p>Distance is represented as distance between CH to next hop &#x0026; sink. While the distance is minimum afterward the energy utilization rate is also diminished. The next objectives to minimize the distance amongst CHs to sink is estimated by:
<disp-formula id="eqn-27"><label>(27)</label><mml:math id="mml-eqn-27" display="block"><mml:mi>f</mml:mi><mml:mn>2</mml:mn><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msubsup><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:msubsup><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:mrow></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mi mathvariant="normal">B</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:mrow></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac></mml:math></disp-formula>
</p>
<p>Node degree represents the number of vehicles in next hop. When the next hop is comprised of limited CH members, then it employs minimum energy in attained data in neighbouring members and remains active for a long period. Later, the next hop using limited node degree is prominently selected. Lastly, node degree is determined based on node degree of <inline-formula id="ieqn-73"><mml:math id="mml-ieqn-73"><mml:mi>f</mml:mi><mml:mn>3</mml:mn></mml:math></inline-formula> as follows:
<disp-formula id="eqn-28"><label>(28)</label><mml:math id="mml-eqn-28" display="block"><mml:mi>f</mml:mi><mml:mn>3</mml:mn><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msubsup><mml:mi>&#x03A3;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:msubsup><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">I</mml:mi></mml:mrow><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mfrac></mml:math></disp-formula>
</p>
<p>Afterward, the weighted sum model is executed for each sub objective and transformed as single objective as shown in <xref ref-type="disp-formula" rid="eqn-29">Eq. (29)</xref>. Now <inline-formula id="ieqn-74"><mml:math id="mml-ieqn-74"><mml:mrow><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> &#x0026; <inline-formula id="ieqn-75"><mml:math id="mml-ieqn-75"><mml:mrow><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> represents the weight assigned to all the sub objectives, and <inline-formula id="ieqn-76"><mml:math id="mml-ieqn-76"><mml:mrow><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mi>&#x03B5;</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> and <inline-formula id="ieqn-77"><mml:math id="mml-ieqn-77"><mml:mrow><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mn>1.</mml:mn></mml:math></inline-formula>
<disp-formula id="eqn-29"><label>(29)</label><mml:math id="mml-eqn-29" display="block"><mml:mi>F</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>f</mml:mi><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>f</mml:mi><mml:mn>2</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>f</mml:mi><mml:mn>3</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></disp-formula>
</p>
</sec>
</sec>
<sec id="s3"><label>3</label><title>Performance Validation</title>
<p>This section investigates the performance analysis of the EMO-QoSCMR with existing techniques under different dimensions. The proposed model is simulated using MATLAB. <?A3B2 "tbl1",5,"anchor"?><xref ref-type="table" rid="table-1">Tab. 1</xref> shows the result analysis of EMO-QoSCMR model under count of rounds interms of TEC.</p>
<table-wrap id="table-1"><label>Table 1</label><caption><title>Result analysis of EMO-QoSCMR model with different rounds</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" colspan="6">&#x00A0;Total energy consumption (J)</th>
</tr>
<tr>
<th align="left">No. of rounds</th>
<th align="left">LEACH</th>
<th align="left">PSO-ECHS</th>
<th align="left">E_OEERP</th>
<th align="left">iCSHS</th>
<th align="left">EMO-QoSCMR</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" colspan="6">Sink location (100, 100)</td>
</tr>
<tr>
<td align="left">100</td>
<td align="left">10.17</td>
<td align="left">8.72</td>
<td align="left">3.69</td>
<td align="left">3.58</td>
<td align="left">2.43</td>
</tr>
<tr>
<td align="left">200</td>
<td align="left">16.09</td>
<td align="left">14.42</td>
<td align="left">9.00</td>
<td align="left">6.60</td>
<td align="left">5.99</td>
</tr>
<tr>
<td align="left">300</td>
<td align="left">23.36</td>
<td align="left">19.56</td>
<td align="left">13.86</td>
<td align="left">10.40</td>
<td align="left">9.79</td>
</tr>
<tr>
<td align="left">400</td>
<td align="left">29.28</td>
<td align="left">26.82</td>
<td align="left">19.00</td>
<td align="left">13.75</td>
<td align="left">13.25</td>
</tr>
<tr>
<td align="left">500</td>
<td align="left">37.10</td>
<td align="left">34.30</td>
<td align="left">25.70</td>
<td align="left">16.88</td>
<td align="left">16.23</td>
</tr>
<tr>
<td align="left" colspan="6">Sink location (200, 200)</td>
</tr>
<tr>
<td align="left">100</td>
<td align="left">58.27</td>
<td align="left">35.53</td>
<td align="left">16.15</td>
<td align="left">11.10</td>
<td align="left">5.20</td>
</tr>
<tr>
<td align="left">200</td>
<td align="left">108.82</td>
<td align="left">69.22</td>
<td align="left">32.16</td>
<td align="left">18.68</td>
<td align="left">9.41</td>
</tr>
<tr>
<td align="left">300</td>
<td align="left">166.00</td>
<td align="left">97.02</td>
<td align="left">45.64</td>
<td align="left">27.94</td>
<td align="left">13.62</td>
</tr>
<tr>
<td align="left">400</td>
<td align="left">220.00</td>
<td align="left">140.83</td>
<td align="left">58.27</td>
<td align="left">35.53</td>
<td align="left">17.84</td>
</tr>
<tr>
<td align="left">500</td>
<td align="left">269.72</td>
<td align="left">187.16</td>
<td align="left">75.12</td>
<td align="left">43.95</td>
<td align="left">24.58</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><?A3B2 "fig2",5,"anchor"?><xref ref-type="fig" rid="fig-2">Fig. 2</xref> investigates the TEC analysis of the EMO-QoSCMR technique with other techniques under different rounds and sink locations of (100, 100). The figure showcased that the EMO-QoSCMR technique has resulted in the least TEC. For instance, with 100 rounds, the EMO-QoSCMR technique has accomplished a minimal TEC of 2.43J whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS techniques have obtained a maximum TEC of 10.17J, 8.72J, 3.69J, and 3.58J respectively. In addition, with 300 rounds, the EMO-QoSCMR technique has accomplished a lesser TEC of 9.79J whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS methods have gained a maximal TEC of 23.36J, 19.56J, 13.86J, and 10.40J correspondingly. Moreover, with 500 rounds, the EMO-QoSCMR technique has accomplished a lower TEC of 16.23J whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS approaches have gained a higher TEC of 37.10J, 34.30J, 25.70J, and 16.88J correspondingly.</p>
<p><?A3B2 "fig3",5,"anchor"?><xref ref-type="fig" rid="fig-3">Fig. 3</xref> examines the TEC analysis of the EMO-QoSCMR technique with other techniques under varying rounds and sink locations of (200, 200). The figure outperformed that the EMO-QoSCMR approach has resulted in a lower TEC. For instance, with 100 rounds, the EMO-QoSCMR manner has accomplished a minimal TEC of 5.20J whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS techniques have obtained a maximum TEC of 58.27J, 35.53J, 16.15J, and 11.10J correspondingly. Likewise, with 300 rounds, the EMO-QoSCMR algorithm has accomplished a reduced TEC of 13.62J whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS techniques have obtained a maximal TEC of 166J, 97.02J, 45.64J, and 27.94J respectively. Besides, with 500 rounds, the EMO-QoSCMR manner has accomplished a lower TEC of 24.58J whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS methods have gained an increased TEC of 269.72J, 187.16J, 75.12J, and 43.95J correspondingly.</p>
<fig id="fig-2"><label>Figure 2</label><caption><title>TEC analysis of EMO-QoSCMR model under sink location (100, 100)</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_23657-fig-2.png"/></fig>
<fig id="fig-3"><label>Figure 3</label><caption><title>TEC analysis of EMO-QoSCMR model under sink location (200, 200)</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_23657-fig-3.png"/></fig>
<p>An overall TEC analysis of the EMO-QoSCMR technique with existing techniques takes place in <?A3B2 "tbl2",5,"anchor"?><xref ref-type="table" rid="table-2">Tab. 2</xref> and <?A3B2 "fig4",5,"anchor"?><xref ref-type="fig" rid="fig-4">Fig. 4</xref> under varying positions of sink node. The figure demonstrated that the EMO-QoSCMR technique has offered the least TEC over the other existing techniques. For instance, with 100 &#x002A; 100 position of sink node, the EMO-QoSCMR technique has obtained a lower TEC of 16.23J whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS techniques have attained a higher TEC of 37.10J, 34.30J, 25.70J, and 16.88J respectively. Also, with 150 &#x002A; 150 position of sink node, the EMO-QoSCMR method has achieved a lesser TEC of 17.35J whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS techniques have attained a higher TEC of 71.17J, 187.16J, 75.12J, and 43.95J correspondingly. Besides, with 200 &#x002A; 200 position of sink node, the EMO-QoSCMR technique has obtained a reduced TEC of 24.58J whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS methodologies have gained a maximal TEC of 269.72J, 187.16J, 75.12J, and 43.95J correspondingly.</p>
<fig id="fig-4"><label>Figure 4</label><caption><title>Result analysis of EMO-QoSCMR model interms of TEC</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_23657-fig-4.png"/></fig>
<table-wrap id="table-2"><label>Table 2</label><caption><title>TEC analysis of EMO-QoSCMR model with existing approaches</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" colspan="6">Total energy consumption (J)</th>
</tr>
<tr>
<th align="left">Position of sink node</th>
<th align="left">LEACH</th>
<th align="left">PSO-ECHS</th>
<th align="left">E_OEERP</th>
<th align="left">iCSHS</th>
<th align="left">EMO-QoSCMR</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">100 &#x002A; 100</td>
<td align="left">37.10</td>
<td align="left">34.30</td>
<td align="left">25.70</td>
<td align="left">16.88</td>
<td align="left">16.23</td>
</tr>
<tr>
<td align="left">150 &#x002A; 150</td>
<td align="left">71.17</td>
<td align="left">62.18</td>
<td align="left">37.65</td>
<td align="left">22.93</td>
<td align="left">17.35</td>
</tr>
<tr>
<td align="left">200 &#x002A; 200</td>
<td align="left">269.72</td>
<td align="left">187.16</td>
<td align="left">75.12</td>
<td align="left">43.95</td>
<td align="left">24.58</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><?A3B2 "tbl3",5,"anchor"?><xref ref-type="table" rid="table-3">Tab. 3</xref> offers the network lifetime analysis of the EMO-QoSCMR technique over the other techniques under diverse sink locations.</p>
<p><?A3B2 "fig5",5,"anchor"?><xref ref-type="fig" rid="fig-5">Fig. 5</xref> investigates the results analysis of the EMO-QoSCMR technique interms of Number of Alive Nodes (NAN) with the sink location of 100, 100. The figure depicted that the EMO-QoSCMR technique has gained an increased NAN over the other techniques. For instance, with 200 rounds, the EMO-QoSCMR technique has offered an improved NAN of 197 nodes whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS techniques have resulted in a reduced NAN of 139, 160, 188, and 196 rounds. Meanwhile, with 800 rounds, the EMO-QoSCMR approach has existed a higher NAN of 145 nodes whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS methods have resulted in a lesser NAN of 61, 79, 132, and 141 rounds. Eventually, with 1200 rounds, the EMO-QoSCMR manner has offered a superior NAN of 116 nodes whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS techniques have resulted in a reduced NAN of 31, 41, 99, and 111 rounds. Likewise, with 1600 rounds, the EMO-QoSCMR technique has offered an improved NAN of 94 nodes whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS manners have resulted in a minimum NAN of 12, 23, 79, and 85 rounds. Similarly, with 2000 rounds, the EMO-QoSCMR technique has offered an improved NAN of 79 nodes whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS approaches have resulted in a minimum NAN of 6, 16, 54, and 65 rounds.</p>
<table-wrap id="table-3"><label>Table 3</label><caption><title>NAN analysis of EMO-QoSCMR model with distinct rounds</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" colspan="6">Number of alive nodes</th>
</tr>
<tr>
<th align="left">No. of rounds</th>
<th align="left">LEACH</th>
<th align="left">PSO-ECHS</th>
<th align="left">E_OEERP</th>
<th align="left">iCSHS</th>
<th align="left">EMO-QoSCMR</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" colspan="6">Sink location (100, 100)</td>
</tr>
<tr>
<td align="left">200</td>
<td align="left">139</td>
<td align="left">160</td>
<td align="left">188</td>
<td align="left">196</td>
<td align="left">197</td>
</tr>
<tr>
<td align="left">400</td>
<td align="left">110</td>
<td align="left">129</td>
<td align="left">163</td>
<td align="left">168</td>
<td align="left">174</td>
</tr>
<tr>
<td align="left">600</td>
<td align="left">88</td>
<td align="left">101</td>
<td align="left">146</td>
<td align="left">150</td>
<td align="left">155</td>
</tr>
<tr>
<td align="left">800</td>
<td align="left">61</td>
<td align="left">79</td>
<td align="left">132</td>
<td align="left">141</td>
<td align="left">145</td>
</tr>
<tr>
<td align="left">1000</td>
<td align="left">46</td>
<td align="left">56</td>
<td align="left">114</td>
<td align="left">122</td>
<td align="left">128</td>
</tr>
<tr>
<td align="left">1200</td>
<td align="left">31</td>
<td align="left">41</td>
<td align="left">99</td>
<td align="left">111</td>
<td align="left">116</td>
</tr>
<tr>
<td align="left">1400</td>
<td align="left">21</td>
<td align="left">36</td>
<td align="left">85</td>
<td align="left">94</td>
<td align="left">103</td>
</tr>
<tr>
<td align="left">1600</td>
<td align="left">12</td>
<td align="left">23</td>
<td align="left">79</td>
<td align="left">85</td>
<td align="left">94</td>
</tr>
<tr>
<td align="left">1800</td>
<td align="left">9</td>
<td align="left">19</td>
<td align="left">65</td>
<td align="left">73</td>
<td align="left">84</td>
</tr>
<tr>
<td align="left">2000</td>
<td align="left">6</td>
<td align="left">16</td>
<td align="left">54</td>
<td align="left">65</td>
<td align="left">79</td>
</tr>
<tr>
<td align="left" colspan="6">Sink location (200, 200)</td>
</tr>
<tr>
<td align="left">200</td>
<td align="left">129</td>
<td align="left">154</td>
<td align="left">179</td>
<td align="left">186</td>
<td align="left">192</td>
</tr>
<tr>
<td align="left">400</td>
<td align="left">98</td>
<td align="left">123</td>
<td align="left">156</td>
<td align="left">162</td>
<td align="left">168</td>
</tr>
<tr>
<td align="left">600</td>
<td align="left">78</td>
<td align="left">93</td>
<td align="left">136</td>
<td align="left">143</td>
<td align="left">151</td>
</tr>
<tr>
<td align="left">800</td>
<td align="left">50</td>
<td align="left">72</td>
<td align="left">125</td>
<td align="left">132</td>
<td align="left">142</td>
</tr>
<tr>
<td align="left">1000</td>
<td align="left">38</td>
<td align="left">47</td>
<td align="left">108</td>
<td align="left">116</td>
<td align="left">127</td>
</tr>
<tr>
<td align="left">1200</td>
<td align="left">23</td>
<td align="left">38</td>
<td align="left">90</td>
<td align="left">100</td>
<td align="left">109</td>
</tr>
<tr>
<td align="left">1400</td>
<td align="left">14</td>
<td align="left">25</td>
<td align="left">84</td>
<td align="left">90</td>
<td align="left">98</td>
</tr>
<tr>
<td align="left">1600</td>
<td align="left">8</td>
<td align="left">18</td>
<td align="left">66</td>
<td align="left">78</td>
<td align="left">86</td>
</tr>
<tr>
<td align="left">1800</td>
<td align="left">5</td>
<td align="left">13</td>
<td align="left">53</td>
<td align="left">62</td>
<td align="left">71</td>
</tr>
<tr>
<td align="left">2000</td>
<td align="left">2</td>
<td align="left">10</td>
<td align="left">42</td>
<td align="left">51</td>
<td align="left">64</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><?A3B2 "fig6",5,"anchor"?><xref ref-type="fig" rid="fig-6">Fig. 6</xref> inspects the outcomes analysis of the EMO-QoSCMR approach with respect to NAN with the sink location of 200, 200. The figure depicted that the EMO-QoSCMR technique has gained an increased NAN over the other algorithms. For instance, with 200 rounds, the EMO-QoSCMR technique has offered a maximal NAN of 192 nodes whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS techniques have resulted in a reduced NAN of 129, 154, 179, and 186 rounds. Meanwhile, with 800 rounds, the EMO-QoSCMR manner has presented a higher NAN of 142 nodes whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS techniques have resulted in a reduced NAN of 50, 72, 125, and 132 rounds. Followed by, with 1200 rounds, the EMO-QoSCMR system has offered an enhanced NAN of 109 nodes whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS manners have resulted in a reduced NAN of 23, 38, 90, and 100 rounds. Similarly, with 1600 rounds, the EMO-QoSCMR technique has offered a maximum NAN of 86 nodes whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS techniques have resulted in a minimum NAN of 8, 18, 66, and 78 rounds. Also, with 2000 rounds, the EMO-QoSCMR technique has accessible an enhanced NAN of 64 nodes whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS methods have resulted in a lesser NAN of 2, 10, 42, and 51 rounds.</p>
<fig id="fig-5"><label>Figure 5</label><caption><title>NAN analysis of EMO-QoSCMR model under sink location (100, 100)</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_23657-fig-5.png"/></fig>
<fig id="fig-6"><label>Figure 6</label><caption><title>NAN analysis of EMO-QoSCMR model under sink location (200, 200)</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_23657-fig-6.png"/></fig>
</sec>
<sec id="s4"><label>4</label><title>Conclusion</title>
<p>In this study, the EMO-QoSCMR protocol is designed to accomplish QoS in WSN by accomplishing energy efficiency and maximizing network lifetime. The EMO-QoSCMR protocol involves a two stage process namely CEROAC based clustering and OCGOR based routing. The proposed EMO-QoSCMR protocol aims to achieve QoS parameters such as energy, throughput, delay, and lifetime. In addition, the EMO-QoSCMR protocol involves OCGOR for the optimal set of routes in the IoT assisted WSN. The proposed model derives a fitness function based on the parameters involved in the IoT nodes. The proposed EMO-QoSCMR technique has resulted to an enhanced NAN of 64 nodes whereas the LEACH, PSO-ECHS, E-OEERP, and iCSHS methods have resulted in a lesser NAN of 2, 10, 42, and 51 rounds. The performance of the presented protocol has been evaluated interms of energy efficiency and network lifetime. As a part of future scope, the data aggregation and MAC scheduling techniques can be designed to improve the overall performance of the WSN.</p>
</sec>
</body>
<back>
<fn-group>
<fn fn-type="other"><p><bold>Funding Statement:</bold> The authors received no specific funding for this study.</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>
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