Enhancing TEEN Protocol Using Sectored KNN-Genetic-Fuzzy Clustering, Load Balancing, and Lifetime Optimization in WSNs

Enhancing TEEN Protocol Using Sectored KNN-Genetic-Fuzzy Clustering, Load Balancing, and Lifetime Optimization in WSNs | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Enhancing TEEN Protocol Using Sectored KNN-Genetic-Fuzzy Clustering, Load Balancing, and Lifetime Optimization in WSNs Shahd Mhsun, Noor Raad Saadallah, Bilal A. Jebur This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7609797/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Wireless Sensor Networks (WSNs) are increasingly utilized for environmental monitoring, industrial control, and smart infrastructure because of their distributed nature and low-power capabilities. However, energy efficiency remains a fundamental challenge due to limited battery capacity and uneven energy consumption. This paper proposes SKNN-GFL-TEEN, a novel hybrid framework that integrates Sector-based K-Nearest Neighbors (SKNN) with Genetic-Fuzzy Logic (GFL) under the Threshold-sensitive Energy Efficient Network (TEEN) protocol to enhance network lifetime and stability. The SKNN model partitions the network into distinct sectors and selects candidate nodes based on spatial proximity. Simultaneously, the GFL mechanism further refines cluster head (CH) selection through genetic optimization and fuzzy rule-based evaluation. Simulation results demonstrate that SKNN-GFL-TEEN outperforms conventional protocols, including LEACH, TEEN, and PEGASIS, in terms of network lifetime, energy consumption, and data delivery rate. Moreover, the proposed method demonstrates improved adaptability, scalability, and robustness, making it suitable for real-time and large-scale WSN deployments. Energy Efficiency K-Nearest Neighbors (KNN) Genetic Algorithm Fuzzy Logic Clustering TEEN Protocol Sector-based Routing Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction Wireless sensor networks (WSNs) consist of geographically independent sensors that observe physical or environmental parameters. Given that WSN is often utilized in remote locations, prolonging its operational lifespan is crucial for ensuring effective data transmission. Conventional protocols, like LEACH and TEEN, have achieved notable progress in hierarchical group construction and energy-efficient routing; yet, they are inadequate in dynamically adapting to node mobility, residual energy distributions, and environmental variables. The rapid expansion of Internet of Things (IoT) applications and smart infrastructure systems has revolutionized WSN, necessitating real-time environmental monitoring, automation of industrial malfunctions, and intelligent decision-making. Contemporary WSN must equilibrate energy optimization, network resilience, scalability, and adaptive performance in fluctuating operating environments. [1].These scattered networks with resource-granting nodes require complex protocols to balance energy use, data transmission efficiency, and network flexibility. Large-scale deployments, where battery replacement or recharging is impractical or informal, have made energy efficiency more important in WSN design. Clustering and routing techniques help WSNs to save energy and extend their lifetime, but maximizing energy is their primary challenge [2]. A recent study suggests that traditional clustering algorithms sometimes show disproportionate energy zones, leading to node failure and network fragmentation. Random patterns can create clusters where a limited number of member nodes use significant energy zones to transmit data to the cluster head; on the contrary, evenly distributed clusters will save large quantities of energy. Computational intelligence-based optimization strategy for Energy is to consider issues and increase network efficiency. The application of AI and machine learning techniques in WSN optimization has revolutionized energy savings and network performance [3]. Moreover, machine learning methods, especially the deep education framework, show encouraging results to increase energy and zero efficiency for network nodes. These processes explain how intelligent algorithms can transform WSN patterns through adaptive learning and optimization. Recent research in WSN clustering has used nature-induced optimization strategies and bio-computing methods. Recently, energy-efficient clustering methods employ a strong optimization approach, such as the African Vulture Optimization Algorithm, to eliminate the reduction of energy in WSN. The selection of communication modes and the formation of adaptive clusters enhance clustering in these methods. The selection of cluster heads in metaheuristic algorithms, routing path identification, and complex optimization framework for distribution of ENERGY zones has increased. Hierarchical network integrates central approaches with advanced cluster construction techniques, duty-cycling schedules, transmission power, and routing paths to optimized energy consumption [4]. Recently, advanced clustering and routing methods have integrated cluster head (CH) selection and vague forecasts with metaheuristic search techniques to optimize inter-cluster routing. For example, by increasing CH qualities such as residual energy density, neighboring density, and proximity to the base station (BS), the stability period with quantum-inspired Particle Swarm Optimization with Fuzzy Logic (QPSOFL) and Fuzzy Quantum Annealing (FQA) and operational perturbation with a significant quantity in the bouquet optimization. The connection of Harris Hawks Optimization with fuzzy logic (CHHFO) improves both life and packet delivery ratio through the use of collaborative search mobility. This study combines the importance of incorporating intelligent CH selection with the best routing [5]. The rapid progression of the smart grid, powered by the increase in global energy demand and the integration of renewable energy, requires an intelligent, adaptive, and energy-efficient resource allocation strategy, as traditional energy management techniques depend on stable or rigid models. [6] prove insufficient to operate. Conversion of genetic algorithms, obscure logic systems, machine learning, and nature-induced optimization presents unprecedented opportunities for the development of adaptive, scalable, and energy-efficient clustering protocols that can be required for the next Pay Gene. Despite these advances, two limitations recur. First, many algorithms assume global optimization or dense training but do not explicitly exploit spatial sectorization with lightweight local structures (e.g., KNN) to reduce control overhead and stabilize CH neighborhoods. Second, while reactive schemes like TEEN can suppress redundant transmissions, relatively few recent AI/metaheuristic solutions integrate reactive thresholding tightly with their clustering logic. The proposed SKNN-GFL-TEEN addresses both points by (i) enforcing sector-aware, KNN-guided cluster formation to limit re-clustering churn and (ii) embedding genetic-fuzzy (GFL) CH optimization within a TEEN-style reactive channel, thereby improving energy balance, stability period, and end-to-end delivery without excessive computation at the node side. (See Section 3 .). To address these challenges, we introduce SKNN-GFL-TEEN, a hybrid model that brings together sector-based node grouping, KNN-based neighbor identification, genetic algorithm optimization, and fuzzy logic for intelligent cluster head selection. This model operates within the TEEN framework, which introduces thresholds to minimize redundant transmissions, thereby reducing energy usage. The key contributions of this work are as follows: Novel hybrid framework—this study presents the first integration of Sector-based K-Nearest Neighbors (SKNN) clustering with Genetic-Fuzzy Logic (GFL) optimization under the TEEN protocol, combining spatial sectoring, adaptive learning, and evolutionary optimization for WSNs. Enhanced cluster head (CH) selection—a new sector-based CH selection mechanism is introduced, which considers residual energy, intra-cluster distance, and proximity to the BS, refined through fuzzy inference and optimized using a genetic algorithm. Improved energy efficiency and network lifetime—The proposed SKNN-GFL-TEEN achieves significant improvements in stability period, half-node death, network lifetime, and packet delivery rate compared to conventional TEEN, LEACH, and PEGASIS protocols. Performance superiority over state-of-the-art—beyond classical benchmarks, the proposed method is explicitly compared to recent AI-based and metaheuristic clustering approaches as illustrated in Table 1 , demonstrating superior adaptability, scalability, and energy savings. Practical deployment relevance—the framework is designed for real-time and large-scale WSN applications, making it directly applicable to IoT-enabled smart cities, industrial monitoring, and environmental sensing, where energy constraints are critical. The remainder of the study encompasses relevant studies in Section 2 , the methodology of the proposed protocol in Section 3 , the simulation setup in Section 4 , the results of the proposed protocol in Section 5 , and concludes in Section 6 . Table 1 Comparative summary of SKNN-GFL-TEEN with classical and recent state-of-the-art WSN clustering protocols. Protocol Core Technique Energy Efficiency Scalability Adaptability to Dynamic Conditions Computational Complexity Key Limitation LEACH [7] Random CH rotation Medium Medium Low Low Uneven energy distribution in extensive networks TEEN [8] Threshold-based reactive routing High (event-driven) Medium Low–Medium Low Limited adaptability; static clustering PEGASIS [9] Chain-based routing High Low Low Low–Medium High delays in large-scale deployments Cross-layered Fuzzy Optimization [1] Fuzzy logic + congestion control High High High Medium–High Higher computation cost Improved Squirrel Search Fuzzy Clustering [10] Meta-heuristic + fuzzy clustering High High Medium–High High Convergence speed depends on parameter tuning Quantum Annealing Fuzzy Routing [2] Fuzzy logic + quantum-inspired optimization High High High High Requires specialized hardware for optimal speed SKNN-GFL-TEEN (Proposed) Sector-based KNN + Genetic-Fuzzy Logic + TEEN Very High Very High High Medium Slightly higher processing cost than TEEN due to GA–FIS, but offset by energy savings 2. Related Work Numerous clustering and routing protocols have been developed to solve the energy efficiency problem in WSNs, with fundamental contributions laying the theoretical groundwork for further developments. With the Low-Energy Adaptive Clustering Hierarchy (LEACH) protocol, Heinzelman et al. led the way by introducing the idea of randomized cluster head rotation to distribute energy usage evenly throughout the network [7]. Manjeshwar and Agrawal advanced the Threshold-sensitive Energy Efficient Network (TEEN) protocol, markedly improving energy efficiency of reactive data transmission predicated on threshold values, thus minimizing the redundant communication overhead[8]. Qing et al.'s Distributed Energy-Efficient Clustering (DEEC) protocol addressed heterogeneity in WSNs by considering node initial energy levels during cluster head selection, prolonging the network lifetime of the nodes than homogeneous approaches [11]. Comparative studies consistently emphasize the trade-offs inherent in various classical protocols. Sengupta et al. performed a thorough preliminary analysis of the LEACH, TEEN, and DEEC protocols. Their findings indicate that LEACH offers uniform energy distribution, TEEN is optimal for event-driven data collection, and DEEC shows enhanced adaptability in heterogeneous network settings[12]. IKG PTU's performance studies comparing LEACH, DEEC, and PEGASIS protocols found that the clustering algorithm significantly affects network longevity, with PEGASIS being better in chain-based communication patterns but slower in large-scale deployments[13]. These basic studies have shown the requirement of hybrid approaches that benefit from the power of various protocols when addressing their related limits. The integration of computational intelligence techniques has emerged as a promising approach to enhancing WSN's influence. Recent chapters have investigated hybrid particle Swarm optimization methods for the Internet of Things application, showing that bio-inspired algorithms effectively optimize cluster composition and Energy distribution [14]. Alancie et al. Fuzzy Clustering and Energy Efficient Routing Protocol (FCERP) was introduced, which uses vague logic to improve the selection of cluster heads and ease the routing, thereby increasing network stability and reducing energy consumption [15]. Zhao and Yuan examine the use of intelligent models to optimize sensor networks, creating adaptive algorithms that dynamically adjust network parameters in accordance with real-time energy-access trends [16]. Fuzzy logic methodologies have gained popularity in WSN clustering due to their ability to manage the imprecision and unpredictability inherent in wireless communication. Verma et al. emphasized computing cost, scalability issues, and the need for adaptive fuzzy rule sets to respond to evolving network conditions in their comprehensive assessment of fuzzy-based clustering techniques[17]. The combination of fuzzy logic and genetic algorithms (CFGA) was initially introduced in seminal research by Saeedian et al., indicating that the integration of fuzzy invented systems with genetic adaptation has greatly improved the efficiency and energy balance of cluster formation [18]. Nithya et al. demonstrated the growth of this hybrid strategy using cross-level optimization techniques, integrating fuzzy logic with congestion management strategies to augment the overall performance and reliability of the network [19]. In terms of WSN clustering, adaptation using evolutionary algorithms and fuzzy logic systems has demonstrated considerable efficacy. Saadaldeen et al. highlight the ability to reduce excesses and establish energy-skilled groups using evolutionary computation techniques in their intensive evaluation of fuzzy logic and genetic algorithm functioning [20]. The authors illustrated the practical application of these principles by using evolutionary algorithms to create a maximum blurred rule set for Dynamic Cluster Head Selection [21], resulting in an innovative clustering approach for IoT networks. The latest progress in optimization methods has been featured by Le-NGOC et al., who introduced an improved squirrel search strategy for optimizing fuzzy clustering. This method demonstrates a higher conversion rate and improved energy zoning economy when compared to traditional genetic mathematical rules [10]. Recent tasks have focused on quantum computing concepts with vague logic systems and the connection between advanced metaheuristic algorithms. Wang et al. Cluster composition develops an energy-efficient clustering protocol, which combines vague logic and quantum animating methods, depicting significant improvements in optimization, stability, and energy consumption [2]. Shekrollahi and Mazloumnejad-Maibodi conducted an in-depth study of genetic fuzzy systems and proposed an energy-efficient clustering algorithm using C-means fuzzy clustering enhanced by genetic optimization, demonstrating remarkable effectiveness in extending network lifetime and load balancing [22]. Rana et al. conducted a comprehensive review of existing techniques, highlighting notable research shortcomings and future avenues for investigation. They noted the value of adaptive protocols that can dynamically respond to changing environmental conditions and application needs [23]. Bical et al. examined query-based wireless sensor networks in a comprehensive evaluation of energy-efficient routing algorithms, noting the importance of intelligent data aggregation and selective routing techniques [24]. Next-generation wireless sensor networks are evolving via protocols such as TEZEM, developed by Jafari et al., which provides novel energy-efficient routing techniques designed for emerging wireless sensor network applications [25]. Sharma and Chawla studied the integration of IoT-compatible methodologies via their RME-SEP protocol. This study demonstrates the potential for developing hybrid systems that integrate traditional wireless sensor network protocols with modern IoT requirements, leading to significant improvements in energy savings and data routing reliability in heterogeneous network environments [26]. These collaborative efforts have laid a solid foundation for the development of advanced hybrid aggregation protocols that combine multiple optimization strategies to address the complex challenges of energy efficiency, scalability, and flexibility in contemporary wireless sensor networks. 3. Methodology The SKNN-GFL-TEEN framework seeks to address the fundamental challenges of energy efficiency and network lifetime faced by the TEEN clustering protocol. It does this by incorporating a sector-based k-nearest neighbors (SKNN) technique to form uniformly distributed clusters, using genetic fuzzy logic (GFL) to select cluster heads, and recognizing that the TEEN protocol operates based on data transmission thresholds, thus improving energy consumption and extending the lifetime of WSNs. The proposed framework proceeds in several stages, as illustrated in Fig. 1 . The process includes initializing the network and sectors, forming clusters, selecting cluster heads, and transmitting data based on specific thresholds. 3 .1 Network Initialization The network size and BS position are initially set. N nodes are randomly deployed in the network with an initial energy Eo. The energy parameters to be used in the first-order radio energy model Fig. 2 , are initialized to compute the remaining energy of each node after each round. The model uses both the free space and multi-path fading depending on the distance d between the transmitter and receiver. Free space model used when the distance d is less than the threshold distance do $$\:{\:\:\text{d}}_{\text{o}}=\sqrt{\frac{{\text{E}}_{\text{f}\text{s}}}{{\text{Ɛ}}_{\text{a}\text{m}\text{p}}}},$$ 1 where \(\:{\text{E}}_{\text{f}\text{s}}\) denote the free space amplifier coefficient and \(\:{\text{Ɛ}}_{\text{a}\text{m}\text{p}}\) denote multi-path fading, multi-path fading is used when the distance d is bigger than the threshold distance do. The energy required by the radio to transmit K-bit data over a distance d is given as where \(\:{E}_{elec}\) the energy consumed by the electronic circuit in a transmitter or receiver to process a single bit, regardless of the distance of the communication. The energy required by the radio to receive K-bit data over a distance d is given as 3.2 Sector Initialization The two-dimensional network area is divided into four equal sectors as explained in Algorithm 1. The sector boundaries are defined according to the network dimensions (Xm, Ym), and the center of each sector is computed. TEEN protocol with Sector-based KNN Clustering Algorithm 1: Sector Initialization 1 Input : Xm, Ym, num_sectors 2 Output : sector structure 3 Begin 4 Initialize sector structure : sectors.num_sectors = num_sectors sectors.boundaries = Array(num_sectors) sectors.centroids = Array(num_sectors)(2) sectors.node_assignments = Array(num_sectors) sectors.cluster_heads = Array(num_sectors) 5 sectors.boundaries (1) ⃪ (0, Xm/2, 0, Ym/2) sectors.boundaries (2) ⃪ (Xm/2, Xm, 0, Ym/2) sectors.boundaries (3) ⃪ (0, Xm/2, Ym/2, Ym) sectors.boundaries (4) ⃪ (Xm/2, Xm, Ym/2, Ym) 6 For i = 1: num_sectors do 7 bound = sectors.boundaries(i) 8 sectors.centroids(i) = ((bound (1) + bound (2))/2, (bound (3) + bound (4))/2) 9 End 10 Return sectors 11 End 3.2 Sector-Based KNN Clustering The KNN algorithm clusters nodes within each sector to create smaller, well-distributed clusters. Algorithm 2 illustrates the clustering process phases. TEEN protocol with Sector-based KNN Clustering Algorithm 2: Sector-based KNN Clustering 1 Input : S[N], sectors 2 Output : update S, sector with Cluster assignments 3 Begin 4 Initialize : sectors.node_assignments = [] sectors.cluster_heads = [] 5 For i = 1: n do 6 If S[i] > 0 then 7 sector_id ⃪ assignNodeToSector 8 sectors.node_assignments(sector_id).add(i) 9 End 10 End 11 For Sector_id = 1:4 do 12 Sector-nodes = sectors.node_assignments(sector_id) 13 If length ( sector_nodes ) > 2 then 14 ApplysectorKNN 15 End 16 End 17 Return S[N] 18 End 19 End 3.2.1 Node Assignment to Sectors Once the network has been divided into sectors, each node is assigned to the sector to which it belongs based on its coordinates. This process is illustrated in Algorithm 3. TEEN protocol with sector-based KNN clustering Algorithm 3: Apply Assign node to sector 1 Input : S[N], sectors 2 Output : sector_id 3 Begin 4 For sector_id = 1:4 do 5 Bound = sectors.boundaries(i) 6 If (node.xd > = bound(1) & node.xd = bound(3) & node.yd < bound(4)) Then 7 Return sector_id 8 End 9 End 10 End 3.2.2 Clustering The clustering process only occurs if the number of nodes in the sector exceeds two. The algorithm extracts features, including position and energy, from each node in the sector to determine cluster centers. This step adjusts clusters to maintain energy balance and to prevent any single CH from overloading. The algorithm identifies the cluster's center to be well-distributed, and nodes assign their membership to the clusters using the KNN algorithm. Algorithm 4 illustrated this step. TEEN protocol with Sector-based KNN Clustering Algorithm 4: Apply sector KNN 1 Input : S[N], sector_nodes, sectors, sector_id 2 Output : update S[N], sector with Cluster assignments Initialize : node_coords, node_features 3 Begin 4 For i = 1:length ( sector_nodes ) do 5 node_features( i ) = (S(node_idx).xd/100, S(node_idx).yd/100, S(node_idx).E/Eo) 6 node_coords( i ) = (S(node_idx).xd, S(node_idx).yd) 9 End num_clusters = max(1, floor(length(sector_nodes) * 0.1)) cluster_centers = selectClusterCentersKNN(node_features, num_clusters) For i = 1:length(sector_nodes) do For j = 1:length(sector_nodes) do If i ≠ j then Distance( j ) = euclidean Distance End End Nearest_k = sort(distance) Cluster_id = ClusterAssignmentusingKNN End 10 End 3.2.3 Cluster Center Selection Algorithm 5 identifies the center of the clusters to guarantee their adequate distribution. The algorithm picks the node with the highest residual energy to be the first cluster's center. To choose the center of the second cluster, the algorithm seeks the node furthest from the center of the first cluster and with sufficient energy. TEEN protocol with Sector-based KNN Clustering Algorithm 5 : Select Cluster Centers KNN 1 Input : node_features, num_clusters 2 Output : cluster_centers Initialize : cluster_centers = [] 3 Begin 4 [~, first_center_idx] = max(node_features[:, 3]) 5 cluster_centers[1] = node_features[first_center_idx] 6 node_coords( i ) = (S(node_idx).xd, S(node_idx).yd) 7 For i = 2:num_clusters do ⃪ max_weighted_distance =-1 8 For j = 1:num_nodes do 9 For k = 1: i -1 do 10 Calculate minimum distance to the exit centers 11 If distance max_weighted_distance then 17 max_weighted_distance = weighted_distance 18 weighted_distance best_center_idx = j 19 End 20 End 21 End 3.2.4 Neighbor-based Voting Each node considers its K nearest neighbors and uses a weighted voting mechanism combining neighbor preferences and proximity to cluster centers to determine its final cluster membership, as in Algorithm 6. TEEN protocol with Sector-based KNN Clustering Algorithm 6: Cluster Assignment using KNN 1 Input : node_features, cluster_centers, neareest_k_indices 2 Output : cluster_id Initialize: num_clusters = length(cluster_centers) 3 Begin 4 For i = 1: num:clusters do 5 Calculate distance to cluster center 6 End 7 If i = max(center_distance) > 0 then 8 center_similarities = 1 - (center_distances / max(center_distances)) 9 End 10 For i = 1 to length(nearest_k_indices) do 11 For j = 1 to num_clusters do 12 Calculate the distance to the center 13 End 14 neighbor_votes[preferred_cluster] = neighbor_votes[preferred_cluster] + 1 15 final_scores = 0.7 * center_similarities + 0.3 * neighbor_votes 16 End 3.3 Genetic-Fuzzy Logic for CH Selection A hybrid genetic-fuzzy approach is used to optimize CH selection further. The process involves: Chromosome encoding A set of chromosomes is generated randomly. Each represents a potential candidate for CHs. Fitness function The algorithm evaluates candidates based on residual energy, intra-cluster distance, and distance to BS. The algorithm evaluated each candidate using a fuzzy interference system (FIS) as follows $$\:\text{F}\text{F}\:=\:FIS(RE,\:ICD,\:DBS),$$ 4 Where RE denotes residual energy, ICD denotes to intra-cluster distance, and \(\:DBS\) Denotes to distance to BS. Low to high is defined as a range for the residual energy input variable, a Gaussian $$\:{\text{y}\left(\text{x}\right)\:=\text{e}}^{-\frac{{(\text{x}-\text{c})}^{2}}{{2{\sigma\:}}^{2}}},$$ 5 Where c distribution center in the Gaussian curve, \(\:{\sigma\:}\) variance, and the x input value. The type of membership is adapted from low to high. Close to Far is defined as a range for the intra-cluster distance input variable, a Gaussian type of membership is adapted by medium, and a trapezoidal $$\:y\left(\text{x}\right)=\left\{\begin{array}{c}\:\:\:\:\:\:\:\:\:\:\:0,\:\:x\le\:a\:or\:x\:\ge\:d\\\:1\:,\:\:b\le\:x\le\:c\\\:\frac{\text{x}-\text{a}}{\text{b}-\text{a}},\:\:a<x<b\\\:\frac{\text{d}-\text{x}}{\text{d}-\text{c}},\:\:c<x<d\\\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\end{array},\right.$$ 6 Where a starting point, b left peak point, c right peak point, and d end point. The type of membership is adapted to close and far. Close to far is defined as a range for the distance to the BS input variable, and a trapezoidal type of membership is adapted for close to far. Table 2 defines the fuzzy set of mapping rules for three fuzzy input variables and one fuzzy output. Table 2 Fuzzy rules. Inputs Output Residual Energy Intra-Cluster Distance Distance to BS suitability of the CHs Low Far Far Very Low Low Medium Close Low Low Close Medium Medium Low Medium Close Far Medium Medium Close Close Medium High High Close Medium High High Close Close Very High The procedure of defuzzification to obtain a crisp output value y is applied with the (Takagi-Sugeno) weighted average method computed as follows: $$\:y=\:\frac{\sum\:_{i=1}^{n}{w}_{i}{y}_{i}}{\sum\:_{i=1}^{n}{w}_{i}},$$ 7 Where yi (the degree of input affiliation) is represented by numeric values, w firing strength, n number of rules with an affiliation score, and i index of the fuzzy rule. Selection: The rank selection method selects the fitness of the fittest individuals. Crossover: To generate a new generation, two parents are selected from the selected individuals by the selection process, and single-point crossover is applied to create new generations. Crossover rate is 0.8. Mutation:Random change to the new generations is introduced to maintain diversity and prevent the occurrence of local solutions. The mutation rate is 0.15. The process is terminated when the specified number of generations is achieved. This approach combines the exploration capability of genetic algorithms with the adaptive decision-making of fuzzy logic, ensuring optimal and dynamic CH selection. 3.4 TEEN-Based Threshold Data Transmission The TEEN protocol’s reactive nature is incorporated to minimize redundant transmissions. Nodes sense environmental parameters continuously but transmit data only when they exceed a predefined threshold: Hard Threshold (HT)–The senses value exceeds a predefined limit. Soft Threshold (ST)–The change in the sense value after crossing HT exceeds a predefined margin. By transmitting only significant data changes, communication energy consumption is substantially reduced. 4. Simulation Setup The performance evaluation of the proposed SKNN-GFL-TEEN protocol was conducted using MATLAB. The simulation environment models a 100 m × 100 m2 two-dimensional sensing area populated with 100 homogeneous sensor nodes, each initialized with 0.5 J of energy. Nodes were randomly deployed, and a fixed BS was positioned at coordinates (50, 50). Energy consumption was calculated using the first-order radio energy model, which accounts for electronics energy (Eelec​), free-space amplification energy (Efs​), and multipath fading amplification energy ( \(\:{\text{Ɛ}}_{\text{a}\text{m}\text{p}}\) ), and data aggregation energy (Eda​). The TEEN protocol's hard threshold (HT) and soft threshold (ST) mechanisms were integrated to reduce redundant transmissions, with HT set to 100 and ST to 2. A packet size of 4,000 bits was used in all transmissions. Table 3 summarizes the parameters employed in the simulation. Table 3 simulation parameters Parameter Value Network Area Size 100 × 100 m² Number of Nodes 100 Initial energy of nodes (E o ) 0.5 J Energy required for running transmitter and receiver (E elec ) 50 nJ/bit Threshold distance (do) 87 m Amplification energy required for free space model d ≤ do (E fs ) 10 pJ/bit/m² Amplification energy required for multipath fading model d > do ( \(\:{\varvec{Ɛ}}_{\varvec{a}\varvec{m}\varvec{p}}\) ) 0.0013 pJ/bit/m² Energy consumption incurred while data aggregation (E da ) 5 nJ/bit/signal Data packet size (k) 4000bit Probability (p) 0.05 Hard Threshold (HT) 100 Soft Threshold (ST) 2 Population Size (P) 50 Number of Generations (G) 100 Crossover rate (P c ) 0.8 Mutation rate (P m ) 0.15 Type of crossover Single Point Selection method Rank selection method 5. Results and Discussion To evaluate the performance of the SKNN-GFL-TEEN framework, it has been compared against LEACH, PEGASIS, and TEEN protocols across key performance metrics, including stability period, half-node death (HND), network lifetime (LND), energy consumption, and packets delivered to the BS. Stability: It is the first round in which the node completely loses its energy. Table 4 illustrates a comparison between traditional protocols and the proposed framework. The FND round was (984 rounds), (975 rounds), (1,206 rounds), and (1,632 rounds) for the LEACH, PEGASIS, TEEN, and SKNN-GFL-TEEN framework, respectively. Figure 3 illustrates that this improvement reflects the protocol’s ability to balance energy usage across the network, preventing early node deaths. Half Node Dead is the round in which the network loses half of its nodes. Table 4 illustrates the superiority of the proposed framework over traditional WSNs protocols. The rounds to HND were (2,214 rounds) for SKNN-GFL-TEEN compared to TEEN (1,478 rounds), PEGASIS (1,326 rounds), and LEACH (1,191 rounds). Table 4 Comparative analysis of TEEN with others for different metrics PROTOCOLS FND HND LND Packet-to-BS LEACH 984 1326 1386 21427 PEGSIS 975 1191 1458 1438 TEEN 1206 1478 1737 26346 SKNN-GFL-TEEN 1632 2214 3107 30302 Network Lifetime: it is the round in which the network completely loses all of its nodes, as illustrated in Fig. 4 . The LND was recorded at (3,107 rounds) for the SKNN-FGL-TEEN framework, and (1,386 rounds), (1,458 rounds), (1,737 rounds) for LEACH, PEGASIS, TEEN, respectively. Table 6 demonstrates that the proposed framework is 78.87% superior to the TEEN protocol. These improvements are attributed to the sector-based clustering and genetic-fuzzy CH optimization, which reduce communication distances and distribute load evenly. Energy Consumption: Fig. 5 illustrates that the proposed framework consumes less energy per round compared to the conventional TEEN, PEGASIS, and LEACH protocols. This reduction is driven by KNN-based local aggregation, which reduces intra-cluster communication distances, and a threshold-based transmission mechanism that eliminates redundant transmissions. Packets to the BS: this refers to the total number of packets that have been delivered successfully from CH to BS. Figure 6 indicates that the proposed framework realized an enhanced packet delivery compared to the traditional protocols. As shown in Table 4 , the number of packets is (21,427), (1,458), (26,346), and (30,302) for LEACH, PEGASIS, TEEN, and SKNN-GFL-TEEN, respectively. The findings are illustrated in Table 5 . Indicate that sectoral segmentation is most effective in small and mid-size network areas with an identical number of nodes, whereas it is less effective in wide network areas due to the long transmission distance within a single sector. Table 5 Network lifetime comparison between TEEN and SKNN-GFL-TEEN protocols over various network areas Network Area Size TEEN SKNN-GFL-TEEN LND Packet-to-BS LND Packet-to-BS 100×100 m 2 1737 26346 3107 30302 200×200 m 2 1465 17195 2805 20238 300×300 m 2 1415 9989 2716 11676 500×500 m 2 1346 3605 1926 5761 This improvement is attributed to the combination of genetic-fuzzy CH selection and sector-based clustering that ensures reliable and energy-efficient data aggregation and transmission to the BS. Table 6 summarizes the percentage improvement of SKNN-GFL-TEEN over TEEN for key performance metrics. The proposed protocol demonstrated substantial gains in network lifetime, stability, and packet delivery while achieving lower energy consumption. These results confirm that SKNN-GFL-TEEN successfully integrates the strengths of sector-based clustering, KNN-based neighbor selection, and genetic-fuzzy CH optimization to deliver robust and scalable performance in WSN environments. Table 6 Comparative percentage improvement of SKNN-GFL-TEEN over other protocols. Percentage improvement by SKKN-GFL-TEEN to TEEN Protocol Network Lifetime Stability Packet-to-BS TEEN 78.87% 35.32% 15.01% 5.1 Computational Complexity Analysis To evaluate the algorithm’s scalability and efficiency, we analyze the time complexity of each core phase of the SKNN-GFL-TEEN framework. Let: N = total number of sensor nodes S = number of sectors (fixed at 4 in our simulation) K = number of the nearest neighbors considered in KNN clustering C = number of candidate CHs in the genetic algorithm population G = number of generations in the genetic algorithm 1. Sector-based KNN Clustering Node assignment to sectors: Each node is compared against the S sector boundaries ⇒ O (N⋅S), which simplifies to O (N) for fixed S. KNN clustering within each sector: For each node in a sector, distances to other nodes are computed ⇒ O ((N/S) 2 ) per sector, giving an overall cost of O (N 2 /S). With S fixed, the complexity remains O (N 2 ). Cluster center selection: Requires finding the node with the highest residual energy and farthest from the first center ⇒ O (N). Overall KNN phase complexity: O (N 2 ), dominant term from distance computation. 2. Genetic-Fuzzy Logic (GFL) CH Selection Chromosome evaluation: Each chromosome encodes a CH set and is evaluated using the fuzzy inference system (FIS) based on three parameters (residual energy, intra-cluster distance, distance to BS). This evaluation is O(N) per chromosome. Per generation complexity: O (C⋅N). Over G generations: O (G⋅C⋅N). In our setup, C and G are fixed constants (50 and 100, respectively), so the complexity scales linearly as O(N). 3. TEEN Threshold-based Data Transmission Sensing and threshold check : Each node performs constant-time threshold checks per sensing cycle ⇒ O (N). Transmission : Only nodes exceeding hard/soft thresholds transmit data; cost is proportional to active transmitters (N active ≤ N), so worst case remains O(N). Performance Gain vs. Overhead : The KNN phase introduces O(N 2 ) computation per round, which is acceptable for WSN simulation and small–medium scale deployments (< 500 nodes), but may become heavy in very large networks unless optimized with spatial indexing (e.g., KD-trees) to reduce to O(NlogN). The GFL phase scales linearly with N for fixed C and G, making it computationally efficient even in large-scale networks. The TEEN phase adds negligible computational overhead since it involves only simple comparisons and conditional transmissions. Energy-Performance Trade-off: The extra processing in KNN and GFL is offset by reduced communication energy due to shorter intra-cluster distances and fewer redundant transmissions. Simulation results show that even with the additional computation, overall network lifetime improves by 78.87% compared to TEEN, making the overhead–gain trade-off favorable. A summary of how hard it is to compute and what effect it has on the SKNN-GFL-TEEN steps is shown in Table 7 . Table 7 Summary of computational complexity and impact for SKNN-GFL-TEEN phases Phase Main Operations Time Complexity Impact on Energy Efficiency / Lifetime Notes Sector-based KNN Clustering Node-to-sector assignment, pair-wise distance computation, cluster center selection O (N 2 ) (distance computation dominates) High–reduces intra-cluster communication distance, balances load Can be optimized with KD-tree or spatial hashing to O(NlogN) for large-scale deployments Genetic-fuzzy logic (GFL) CH selection Chromosome evaluation via fuzzy inference, rank selection, crossover, and mutation O (G⋅C⋅N) (linear for fixed G, C) High–adaptive CH selection improves stability period and network lifetime. G and C fixed in simulations; low per-round overhead TEEN Threshold-based Data Transmission Continuous sensing, hard/soft threshold checks, conditional transmission O(N) Very high – eliminates redundant transmissions, reduces energy waste Overhead is negligible compared to the energy saved Overall Framework A combination of above phases Dominated by O(N 2 )KNN step Significant lifetime improvement (+ 78.87% over TEEN) Processing overhead is outweighed by communication energy savings 6. Conclusion The suggested method adeptly tackles significant issues in energy efficiency, network longevity, and load distribution by including geographical sectoring, intelligent clustering, and adaptive optimization of cluster heads. Simulation findings demonstrate that SKNN-GFL-TEEN outperforms known protocols, including LEACH, PEGASIS, and TEEN, in several performance parameters such as stability period, network longevity, and packet delivery to the BS. The proposed approach achieves sustained operational stability by uniformly spreading energy consumption among nodes, decreasing communication costs, and diminishing redundant transmissions using TEEN-based thresholding. The integration of genetic optimization and fuzzy inference enables dynamic, context-sensitive selection of cluster heads; while sector-based clustering reduces intra-cluster communication distances and enhances scalability for large-scale deployments. These synergistic enhancements render SKNN-GFL-TEEN especially appropriate for real-time monitoring applications, heterogeneous environments, and energy-constrained WSN deployments. The proposed framework is directly applicable to next-generation IoT-driven scenarios, including smart cities (e.g., air quality monitoring, traffic analysis, and structural health monitoring), environmental monitoring (e.g., forest fire detection, precision agriculture, and wildlife tracking), and industrial IoT (e.g., predictive maintenance in energy grids, oil pipelines, and manufacturing plants). SKNN-GFL-TEEN can be effectively implemented on low-power sensor motes, including the MicaZ wireless sensor mote, the TelosB wireless sensor node, and the Waspmote wireless sensor platform mote. This approach allows for sector-based clustering and genetic-fuzzy cluster head optimization using lightweight firmware, while TEEN’s thresholding mechanism minimizes radio usage, thereby prolonging battery life. The advent of 5G and 6G IoT networks enables integration into edge gateways for cloud-assisted decision-making, ensuring low-latency and energy-efficient operations at the edge. This supports interoperability and ultra-reliable low-latency communications (URLLC) for essential applications. However, certain limitations persist: the SKNN clustering phase incurs a (𝑁²) computational cost, potential latency may arise in dense networks due to CH optimization, and current evaluations are based on static node positions. Future research will concentrate on enhancing SKNN-GFL-TEEN to accommodate mobile and heterogeneous nodes, adjusting cluster head selection based on fluctuating energy levels, investigating multi-base station and multi-sink configurations, and utilizing reinforcement learning to dynamically optimize parameters such as K in KNN, mutation rates in genetic algorithms, and TEEN thresholds in real-time scenarios. SKNN-GFL-TEEN exhibits notable adaptability and scalability, making it a compelling candidate for next-generation, energy-efficient WSN protocols in the Internet of Things and industrial settings. Declarations Author Contribution Sh. M. Abdeljabbar and N.R. Saadallah conceived the main idea of the study, developed the methodology, and carried out the simulations.Bilal A. Jebur and N.R. Saadallah contributed to algorithm design, optimization techniques, and data analysis.Sh. M. Abdeljabbar prepared the figures, graphs, and tables and assisted in interpreting the results.Sh. M. Abdeljabbar and N.R. Saadallah wrote the first draft of the manuscript and integrated feedback from all co-authors.N.R. Saadallah and Bilal A. Jebur reviewed the related literature and contributed to the writing of the Introduction and Related Work sections.All authors discussed the results, revised the manuscript critically for intellectual content, and approved the final version of the manuscript. Data Availability The simulator source code generated and analyzed during the current study is not publicly available because it is part of ongoing research and making the code public could compromise the direction of future studies. 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06:31:00","extension":"xml","order_by":39,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":153407,"visible":true,"origin":"","legend":"","description":"","filename":"90b508d39831462f9111c6ce20e30cb61structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7609797/v1/72558f1c8fb3920278684c56.xml"},{"id":93200033,"identity":"169b8748-da2b-4dc0-a59b-f00196febce1","added_by":"auto","created_at":"2025-10-10 06:47:00","extension":"html","order_by":40,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":164654,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7609797/v1/4420f111a9c2a7eb043c42d7.html"},{"id":93200023,"identity":"ee406ba7-564f-465a-ba52-7b81de9c5a1e","added_by":"auto","created_at":"2025-10-10 06:46:58","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":129853,"visible":true,"origin":"","legend":"\u003cp\u003eFlowchart of the proposed framework\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7609797/v1/7ca92405ade2e6f92e7899c3.png"},{"id":93199600,"identity":"20d4e257-3a28-4dd6-843b-c5ebc7044289","added_by":"auto","created_at":"2025-10-10 06:38:58","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":35951,"visible":true,"origin":"","legend":"\u003cp\u003eFirst-order radio model for energy consumption analysis\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7609797/v1/02a0643a5bf0a2a47d640ca6.png"},{"id":93198727,"identity":"342264ac-8f5c-41b6-8520-7a7a543469ba","added_by":"auto","created_at":"2025-10-10 06:30:58","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":84290,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of dead nodes vs. rounds of the proposed algorithm with other protocols\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7609797/v1/b659455cf447a85f9965d575.png"},{"id":93198730,"identity":"b6f18861-e570-4032-95d1-7de4f4d00685","added_by":"auto","created_at":"2025-10-10 06:30:58","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":71795,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of alive nodes vs. rounds of the proposed algorithm with other protocols\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7609797/v1/671240f84096defa1abdb0f9.png"},{"id":93199603,"identity":"5668f291-60a3-4002-9995-a2518b2dbcb8","added_by":"auto","created_at":"2025-10-10 06:38:59","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":80692,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of Average Energy Consumption vs. rounds of the proposed algorithm with other protocols\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-7609797/v1/e578c865ef618111ecc7a079.png"},{"id":93200907,"identity":"be420f63-b4fc-4e32-b3a5-b949d15ae24e","added_by":"auto","created_at":"2025-10-10 06:54:59","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":69630,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of packet to BS vs. rounds of the proposed algorithm with other protocols\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-7609797/v1/6c2bc288ae107845e7ebb0ef.png"},{"id":93201274,"identity":"4e64769d-28c3-43fa-b761-20ea0a6696ba","added_by":"auto","created_at":"2025-10-10 07:03:01","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1860119,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7609797/v1/d29adf1b-203f-40fb-90dc-45149651faaf.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Enhancing TEEN Protocol Using Sectored KNN-Genetic-Fuzzy Clustering, Load Balancing, and Lifetime Optimization in WSNs","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eWireless sensor networks (WSNs) consist of geographically independent sensors that observe physical or environmental parameters. Given that WSN is often utilized in remote locations, prolonging its operational lifespan is crucial for ensuring effective data transmission. Conventional protocols, like LEACH and TEEN, have achieved notable progress in hierarchical group construction and energy-efficient routing; yet, they are inadequate in dynamically adapting to node mobility, residual energy distributions, and environmental variables. The rapid expansion of Internet of Things (IoT) applications and smart infrastructure systems has revolutionized WSN, necessitating real-time environmental monitoring, automation of industrial malfunctions, and intelligent decision-making. Contemporary WSN must equilibrate energy optimization, network resilience, scalability, and adaptive performance in fluctuating operating environments. [1].These scattered networks with resource-granting nodes require complex protocols to balance energy use, data transmission efficiency, and network flexibility. Large-scale deployments, where battery replacement or recharging is impractical or informal, have made energy efficiency more important in WSN design. Clustering and routing techniques help WSNs to save energy and extend their lifetime, but maximizing energy is their primary challenge [2]. A recent study suggests that traditional clustering algorithms sometimes show disproportionate energy zones, leading to node failure and network fragmentation. Random patterns can create clusters where a limited number of member nodes use significant energy zones to transmit data to the cluster head; on the contrary, evenly distributed clusters will save large quantities of energy. Computational intelligence-based optimization strategy for Energy is to consider issues and increase network efficiency.\u003c/p\u003e\u003cp\u003eThe application of AI and machine learning techniques in WSN optimization has revolutionized energy savings and network performance [3]. Moreover, machine learning methods, especially the deep education framework, show encouraging results to increase energy and zero efficiency for network nodes. These processes explain how intelligent algorithms can transform WSN patterns through adaptive learning and optimization. Recent research in WSN clustering has used nature-induced optimization strategies and bio-computing methods. Recently, energy-efficient clustering methods employ a strong optimization approach, such as the African Vulture Optimization Algorithm, to eliminate the reduction of energy in WSN. The selection of communication modes and the formation of adaptive clusters enhance clustering in these methods. The selection of cluster heads in metaheuristic algorithms, routing path identification, and complex optimization framework for distribution of ENERGY zones has increased. Hierarchical network integrates central approaches with advanced cluster construction techniques, duty-cycling schedules, transmission power, and routing paths to optimized energy consumption [4].\u003c/p\u003e\u003cp\u003eRecently, advanced clustering and routing methods have integrated cluster head (CH) selection and vague forecasts with metaheuristic search techniques to optimize inter-cluster routing. For example, by increasing CH qualities such as residual energy density, neighboring density, and proximity to the base station (BS), the stability period with quantum-inspired Particle Swarm Optimization with Fuzzy Logic (QPSOFL) and Fuzzy Quantum Annealing (FQA) and operational perturbation with a significant quantity in the bouquet optimization. The connection of Harris Hawks Optimization with fuzzy logic (CHHFO) improves both life and packet delivery ratio through the use of collaborative search mobility. This study combines the importance of incorporating intelligent CH selection with the best routing [5]. The rapid progression of the smart grid, powered by the increase in global energy demand and the integration of renewable energy, requires an intelligent, adaptive, and energy-efficient resource allocation strategy, as traditional energy management techniques depend on stable or rigid models. [6] prove insufficient to operate. Conversion of genetic algorithms, obscure logic systems, machine learning, and nature-induced optimization presents unprecedented opportunities for the development of adaptive, scalable, and energy-efficient clustering protocols that can be required for the next Pay Gene.\u003c/p\u003e\u003cp\u003eDespite these advances, two limitations recur. First, many algorithms assume global optimization or dense training but do not explicitly exploit spatial sectorization with lightweight local structures (e.g., KNN) to reduce control overhead and stabilize CH neighborhoods. Second, while reactive schemes like TEEN can suppress redundant transmissions, relatively few recent AI/metaheuristic solutions integrate reactive thresholding tightly with their clustering logic. The proposed SKNN-GFL-TEEN addresses both points by (i) enforcing sector-aware, KNN-guided cluster formation to limit re-clustering churn and (ii) embedding genetic-fuzzy (GFL) CH optimization within a TEEN-style reactive channel, thereby improving energy balance, stability period, and end-to-end delivery without excessive computation at the node side. (See Section \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.). To address these challenges, we introduce SKNN-GFL-TEEN, a hybrid model that brings together sector-based node grouping, KNN-based neighbor identification, genetic algorithm optimization, and fuzzy logic for intelligent cluster head selection. This model operates within the TEEN framework, which introduces thresholds to minimize redundant transmissions, thereby reducing energy usage. The key contributions of this work are as follows: Novel hybrid framework\u0026mdash;this study presents the first integration of Sector-based K-Nearest Neighbors (SKNN) clustering with Genetic-Fuzzy Logic (GFL) optimization under the TEEN protocol, combining spatial sectoring, adaptive learning, and evolutionary optimization for WSNs. Enhanced cluster head (CH) selection\u0026mdash;a new sector-based CH selection mechanism is introduced, which considers residual energy, intra-cluster distance, and proximity to the BS, refined through fuzzy inference and optimized using a genetic algorithm. Improved energy efficiency and network lifetime\u0026mdash;The proposed SKNN-GFL-TEEN achieves significant improvements in stability period, half-node death, network lifetime, and packet delivery rate compared to conventional TEEN, LEACH, and PEGASIS protocols. Performance superiority over state-of-the-art\u0026mdash;beyond classical benchmarks, the proposed method is explicitly compared to recent AI-based and metaheuristic clustering approaches as illustrated in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, demonstrating superior adaptability, scalability, and energy savings. Practical deployment relevance\u0026mdash;the framework is designed for real-time and large-scale WSN applications, making it directly applicable to IoT-enabled smart cities, industrial monitoring, and environmental sensing, where energy constraints are critical. The remainder of the study encompasses relevant studies in Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the methodology of the proposed protocol in Section \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the simulation setup in Section \u003cspan refid=\"Sec13\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the results of the proposed protocol in Section \u003cspan refid=\"Sec14\" class=\"InternalRef\"\u003e5\u003c/span\u003e, and concludes in Section \u003cspan refid=\"Sec16\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eComparative summary of SKNN-GFL-TEEN with classical and recent state-of-the-art WSN clustering protocols.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"7\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eProtocol\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCore Technique\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eEnergy Efficiency\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eScalability\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eAdaptability to Dynamic Conditions\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eComputational Complexity\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eKey Limitation\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLEACH [7]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRandom CH rotation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMedium\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMedium\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eLow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eLow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eUneven energy distribution in extensive networks\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTEEN [8]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eThreshold-based reactive routing\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eHigh (event-driven)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMedium\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eLow\u0026ndash;Medium\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eLow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eLimited adaptability; static clustering\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePEGASIS [9]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eChain-based routing\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eLow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eLow\u0026ndash;Medium\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eHigh delays in large-scale deployments\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCross-layered Fuzzy Optimization [1]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFuzzy logic\u0026thinsp;+\u0026thinsp;congestion control\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eMedium\u0026ndash;High\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eHigher computation cost\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eImproved Squirrel Search Fuzzy Clustering [10]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMeta-heuristic\u0026thinsp;+\u0026thinsp;fuzzy clustering\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMedium\u0026ndash;High\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eConvergence speed depends on parameter tuning\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eQuantum Annealing Fuzzy Routing [2]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFuzzy logic\u0026thinsp;+\u0026thinsp;quantum-inspired optimization\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eRequires specialized hardware for optimal speed\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSKNN-GFL-TEEN (Proposed)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSector-based KNN\u0026thinsp;+\u0026thinsp;Genetic-Fuzzy Logic\u0026thinsp;+\u0026thinsp;TEEN\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eVery High\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eVery High\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eMedium\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eSlightly higher processing cost than TEEN due to GA\u0026ndash;FIS, but offset by energy savings\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"2. Related Work","content":"\u003cp\u003eNumerous clustering and routing protocols have been developed to solve the energy efficiency problem in WSNs, with fundamental contributions laying the theoretical groundwork for further developments. With the Low-Energy Adaptive Clustering Hierarchy (LEACH) protocol, Heinzelman et al. led the way by introducing the idea of randomized cluster head rotation to distribute energy usage evenly throughout the network [7]. Manjeshwar and Agrawal advanced the Threshold-sensitive Energy Efficient Network (TEEN) protocol, markedly improving energy efficiency of reactive data transmission predicated on threshold values, thus minimizing the redundant communication overhead[8]. Qing et al.'s Distributed Energy-Efficient Clustering (DEEC) protocol addressed heterogeneity in WSNs by considering node initial energy levels during cluster head selection, prolonging the network lifetime of the nodes than homogeneous approaches [11]. Comparative studies consistently emphasize the trade-offs inherent in various classical protocols. Sengupta et al. performed a thorough preliminary analysis of the LEACH, TEEN, and DEEC protocols. Their findings indicate that LEACH offers uniform energy distribution, TEEN is optimal for event-driven data collection, and DEEC shows enhanced adaptability in heterogeneous network settings[12]. IKG PTU's performance studies comparing LEACH, DEEC, and PEGASIS protocols found that the clustering algorithm significantly affects network longevity, with PEGASIS being better in chain-based communication patterns but slower in large-scale deployments[13]. These basic studies have shown the requirement of hybrid approaches that benefit from the power of various protocols when addressing their related limits. The integration of computational intelligence techniques has emerged as a promising approach to enhancing WSN's influence. Recent chapters have investigated hybrid particle Swarm optimization methods for the Internet of Things application, showing that bio-inspired algorithms effectively optimize cluster composition and Energy distribution [14].\u003c/p\u003e\u003cp\u003eAlancie et al. Fuzzy Clustering and Energy Efficient Routing Protocol (FCERP) was introduced, which uses vague logic to improve the selection of cluster heads and ease the routing, thereby increasing network stability and reducing energy consumption [15]. Zhao and Yuan examine the use of intelligent models to optimize sensor networks, creating adaptive algorithms that dynamically adjust network parameters in accordance with real-time energy-access trends [16]. Fuzzy logic methodologies have gained popularity in WSN clustering due to their ability to manage the imprecision and unpredictability inherent in wireless communication. Verma et al. emphasized computing cost, scalability issues, and the need for adaptive fuzzy rule sets to respond to evolving network conditions in their comprehensive assessment of fuzzy-based clustering techniques[17].\u003c/p\u003e\u003cp\u003eThe combination of fuzzy logic and genetic algorithms (CFGA) was initially introduced in seminal research by Saeedian et al., indicating that the integration of fuzzy invented systems with genetic adaptation has greatly improved the efficiency and energy balance of cluster formation [18]. Nithya et al. demonstrated the growth of this hybrid strategy using cross-level optimization techniques, integrating fuzzy logic with congestion management strategies to augment the overall performance and reliability of the network [19]. In terms of WSN clustering, adaptation using evolutionary algorithms and fuzzy logic systems has demonstrated considerable efficacy. Saadaldeen et al. highlight the ability to reduce excesses and establish energy-skilled groups using evolutionary computation techniques in their intensive evaluation of fuzzy logic and genetic algorithm functioning [20]. The authors illustrated the practical application of these principles by using evolutionary algorithms to create a maximum blurred rule set for Dynamic Cluster Head Selection [21], resulting in an innovative clustering approach for IoT networks. The latest progress in optimization methods has been featured by Le-NGOC et al., who introduced an improved squirrel search strategy for optimizing fuzzy clustering. This method demonstrates a higher conversion rate and improved energy zoning economy when compared to traditional genetic mathematical rules [10]. Recent tasks have focused on quantum computing concepts with vague logic systems and the connection between advanced metaheuristic algorithms. Wang et al. Cluster composition develops an energy-efficient clustering protocol, which combines vague logic and quantum animating methods, depicting significant improvements in optimization, stability, and energy consumption [2].\u003c/p\u003e\u003cp\u003eShekrollahi and Mazloumnejad-Maibodi conducted an in-depth study of genetic fuzzy systems and proposed an energy-efficient clustering algorithm using C-means fuzzy clustering enhanced by genetic optimization, demonstrating remarkable effectiveness in extending network lifetime and load balancing [22]. Rana et al. conducted a comprehensive review of existing techniques, highlighting notable research shortcomings and future avenues for investigation. They noted the value of adaptive protocols that can dynamically respond to changing environmental conditions and application needs [23]. Bical et al. examined query-based wireless sensor networks in a comprehensive evaluation of energy-efficient routing algorithms, noting the importance of intelligent data aggregation and selective routing techniques [24]. Next-generation wireless sensor networks are evolving via protocols such as TEZEM, developed by Jafari et al., which provides novel energy-efficient routing techniques designed for emerging wireless sensor network applications [25]. Sharma and Chawla studied the integration of IoT-compatible methodologies via their RME-SEP protocol. This study demonstrates the potential for developing hybrid systems that integrate traditional wireless sensor network protocols with modern IoT requirements, leading to significant improvements in energy savings and data routing reliability in heterogeneous network environments [26]. These collaborative efforts have laid a solid foundation for the development of advanced hybrid aggregation protocols that combine multiple optimization strategies to address the complex challenges of energy efficiency, scalability, and flexibility in contemporary wireless sensor networks.\u003c/p\u003e"},{"header":"3. Methodology","content":"\u003cp\u003eThe SKNN-GFL-TEEN framework seeks to address the fundamental challenges of energy efficiency and network lifetime faced by the TEEN clustering protocol. It does this by incorporating a sector-based k-nearest neighbors (SKNN) technique to form uniformly distributed clusters, using genetic fuzzy logic (GFL) to select cluster heads, and recognizing that the TEEN protocol operates based on data transmission thresholds, thus improving energy consumption and extending the lifetime of WSNs. The proposed framework proceeds in several stages, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The process includes initializing the network and sectors, forming clusters, selecting cluster heads, and transmitting data based on specific thresholds.\u003c/p\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e\u003cb\u003e3\u003c/b\u003e.1 \u003cb\u003eNetwork Initialization\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eThe network size and BS position are initially set. N nodes are randomly deployed in the network with an initial energy Eo. The energy parameters to be used in the first-order radio energy model Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e2\u003c/span\u003e, are initialized to compute the remaining energy of each node after each round. The model uses both the free space and multi-path fading depending on the distance d between the transmitter and receiver. Free space model used when the distance d is less than the threshold distance do\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{\\:\\:\\text{d}}_{\\text{o}}=\\sqrt{\\frac{{\\text{E}}_{\\text{f}\\text{s}}}{{\\text{Ɛ}}_{\\text{a}\\text{m}\\text{p}}}},$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{E}}_{\\text{f}\\text{s}}\\)\u003c/span\u003e\u003c/span\u003e denote the free space amplifier coefficient and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Ɛ}}_{\\text{a}\\text{m}\\text{p}}\\)\u003c/span\u003e\u003c/span\u003e denote multi-path fading, multi-path fading is used when the distance d is bigger than the threshold distance do. The energy required by the radio to transmit K-bit data over a distance d is given as\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" width=\"643\" height=\"82\"\u003e\u003c/p\u003e\n\u003cp\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{E}_{elec}\\)\u003c/span\u003e\u003c/span\u003e the energy consumed by the electronic circuit in a transmitter or receiver to process a single bit, regardless of the distance of the communication. The energy required by the radio to receive K-bit data over a distance d is given as\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"577\" height=\"60\"\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Sector Initialization\u003c/h2\u003e\u003cp\u003eThe two-dimensional network area is divided into four equal sectors as explained in Algorithm 1. The sector boundaries are defined according to the network dimensions (Xm, Ym), and the center of each sector is computed.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e\u003cp\u003eTEEN protocol with Sector-based KNN Clustering\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003eAlgorithm 1: Sector Initialization\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eInput\u003c/b\u003e: Xm, Ym, num_sectors\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eOutput\u003c/b\u003e: sector structure\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eBegin\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eInitialize sector structure\u003c/b\u003e:\u003c/p\u003e\u003cp\u003esectors.num_sectors\u0026thinsp;=\u0026thinsp;num_sectors\u003c/p\u003e\u003cp\u003esectors.boundaries\u0026thinsp;=\u0026thinsp;Array(num_sectors)\u003c/p\u003e\u003cp\u003esectors.centroids\u0026thinsp;=\u0026thinsp;Array(num_sectors)(2)\u003c/p\u003e\u003cp\u003esectors.node_assignments\u0026thinsp;=\u0026thinsp;Array(num_sectors)\u003c/p\u003e\u003cp\u003esectors.cluster_heads\u0026thinsp;=\u0026thinsp;Array(num_sectors)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003esectors.boundaries (1) ⃪ (0, Xm/2, 0, Ym/2)\u003c/p\u003e\u003cp\u003esectors.boundaries (2) ⃪ (Xm/2, Xm, 0, Ym/2)\u003c/p\u003e\u003cp\u003esectors.boundaries (3) ⃪ (0, Xm/2, Ym/2, Ym)\u003c/p\u003e\u003cp\u003esectors.boundaries (4) ⃪ (Xm/2, Xm, Ym/2, Ym)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eFor i\u003c/b\u003e\u0026thinsp;=\u0026thinsp;1: num_sectors \u003cb\u003edo\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003ebound\u0026thinsp;=\u0026thinsp;sectors.boundaries(i)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003esectors.centroids(i) = ((bound (1)\u0026thinsp;+\u0026thinsp;bound (2))/2, (bound (3)\u0026thinsp;+\u0026thinsp;bound (4))/2)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eReturn\u003c/b\u003e sectors\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Sector-Based KNN Clustering\u003c/h2\u003e\u003cp\u003eThe KNN algorithm clusters nodes within each sector to create smaller, well-distributed clusters. Algorithm 2 illustrates the clustering process phases.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabc\" border=\"1\"\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e\u003cp\u003eTEEN protocol with Sector-based KNN Clustering\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003eAlgorithm 2: Sector-based KNN Clustering\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eInput\u003c/b\u003e: S[N], sectors\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eOutput\u003c/b\u003e: update S, sector with Cluster assignments\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eBegin\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eInitialize\u003c/b\u003e:\u003c/p\u003e\u003cp\u003esectors.node_assignments = []\u003c/p\u003e\u003cp\u003esectors.cluster_heads = []\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eFor i\u003c/b\u003e\u0026thinsp;=\u0026thinsp;1: n \u003cb\u003edo\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e\u003cp\u003eIf S[i]\u0026thinsp;\u0026gt;\u0026thinsp;0 then\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003esector_id ⃪ assignNodeToSector\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003esectors.node_assignments(sector_id).add(i)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eFor\u003c/b\u003e Sector_id\u0026thinsp;=\u0026thinsp;1:4 \u003cb\u003edo\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e\u003cp\u003eSector-nodes\u0026thinsp;\u003cb\u003e=\u003c/b\u003e\u0026thinsp;sectors.node_assignments(sector_id)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e\u003cp\u003e\u003cb\u003eIf\u003c/b\u003e length\u003cb\u003e(\u003c/b\u003esector_nodes\u003cb\u003e)\u003c/b\u003e\u0026thinsp;\u0026gt;\u0026thinsp;2 \u003cb\u003ethen\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003eApplysectorKNN\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eReturn\u003c/b\u003e S[N]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e19\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\u003ch2\u003e3.2.1 Node Assignment to Sectors\u003c/h2\u003e\u003cp\u003eOnce the network has been divided into sectors, each node is assigned to the sector to which it belongs based on its coordinates. This process is illustrated in Algorithm 3.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabd\" border=\"1\"\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c5\" namest=\"c1\"\u003e\u003cp\u003eTEEN protocol with sector-based KNN clustering\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e\u003cp\u003eAlgorithm 3: Apply Assign node to sector\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eInput\u003c/b\u003e: S[N], sectors\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eOutput\u003c/b\u003e: sector_id\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eBegin\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eFor sector_id\u003c/b\u003e\u0026thinsp;=\u0026thinsp;1:4 \u003cb\u003edo\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003eBound\u0026thinsp;=\u0026thinsp;sectors.boundaries(i)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003e\u003cb\u003eIf\u003c/b\u003e (node.xd\u0026thinsp;\u0026gt;\u0026thinsp;=\u0026thinsp;bound(1) \u0026amp; node.xd\u0026thinsp;\u0026lt;\u0026thinsp;bound(2) \u0026amp; node.yd\u0026thinsp;\u0026gt;\u0026thinsp;=\u0026thinsp;bound(3) \u0026amp; node.yd\u0026thinsp;\u0026lt;\u0026thinsp;bound(4)) \u003cb\u003eThen\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003eReturn\u003c/b\u003e sector_id\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section3\"\u003e\u003ch2\u003e3.2.2 Clustering\u003c/h2\u003e\u003cp\u003eThe clustering process only occurs if the number of nodes in the sector exceeds two. The algorithm extracts features, including position and energy, from each node in the sector to determine cluster centers. This step adjusts clusters to maintain energy balance and to prevent any single CH from overloading. The algorithm identifies the cluster's center to be well-distributed, and nodes assign their membership to the clusters using the KNN algorithm. Algorithm 4 illustrated this step.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabe\" border=\"1\"\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e\u003cp\u003eTEEN protocol with Sector-based KNN Clustering\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003eAlgorithm 4: Apply sector KNN\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eInput\u003c/b\u003e: S[N], sector_nodes, sectors, sector_id\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eOutput\u003c/b\u003e: update S[N], sector with Cluster assignments\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eInitialize\u003c/b\u003e: node_coords, node_features\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eBegin\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eFor i\u003c/b\u003e\u0026thinsp;=\u0026thinsp;1:length\u003cb\u003e(\u003c/b\u003esector_nodes\u003cb\u003e) do\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e\u003cp\u003enode_features(\u003cb\u003ei\u003c/b\u003e) = (S(node_idx).xd/100, S(node_idx).yd/100, S(node_idx).E/Eo)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e\u003cp\u003enode_coords(\u003cb\u003ei\u003c/b\u003e) = (S(node_idx).xd, S(node_idx).yd)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003enum_clusters\u0026thinsp;=\u0026thinsp;max(1, floor(length(sector_nodes) * 0.1))\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003ecluster_centers\u0026thinsp;=\u0026thinsp;selectClusterCentersKNN(node_features, num_clusters)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eFor i\u003c/b\u003e\u0026thinsp;=\u0026thinsp;1:length(sector_nodes) \u003cb\u003edo\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e\u003cp\u003e\u003cb\u003eFor j\u003c/b\u003e\u0026thinsp;=\u0026thinsp;1:length(sector_nodes) \u003cb\u003edo\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003eIf i\u0026thinsp;\u0026ne;\u0026thinsp;j then\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eDistance(\u003cb\u003ej\u003c/b\u003e)\u0026thinsp;=\u0026thinsp;euclidean Distance\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003eEnd\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e\u003cp\u003eNearest_k\u0026thinsp;=\u0026thinsp;sort(distance)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e\u003cp\u003eCluster_id\u0026thinsp;=\u0026thinsp;ClusterAssignmentusingKNN\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section3\"\u003e\u003ch2\u003e3.2.3 Cluster Center Selection\u003c/h2\u003e\u003cp\u003e\u003cstrong\u003eAlgorithm 5\u003c/strong\u003e\u003cp\u003eidentifies the center of the clusters to guarantee their adequate distribution. The algorithm picks the node with the highest residual energy to be the first cluster's center. To choose the center of the second cluster, the algorithm seeks the node furthest from the center of the first cluster and with sufficient energy.\u003c/p\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabf\" border=\"1\"\u003e\u003ccolgroup cols=\"7\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e\u003cp\u003eTEEN protocol with Sector-based KNN Clustering\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"6\" nameend=\"c7\" namest=\"c2\"\u003e\u003cp\u003eAlgorithm \u003cspan refid=\"FPar1\" class=\"InternalRef\"\u003e5\u003c/span\u003e: Select Cluster Centers KNN\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"6\" nameend=\"c7\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eInput\u003c/b\u003e: node_features, num_clusters\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"6\" nameend=\"c7\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eOutput\u003c/b\u003e: cluster_centers\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"6\" nameend=\"c7\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eInitialize\u003c/b\u003e: cluster_centers = []\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"6\" nameend=\"c7\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eBegin\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e\u003cp\u003e[~, first_center_idx]\u0026thinsp;=\u0026thinsp;max(node_features[:, 3])\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e\u003cp\u003ecluster_centers[1]\u0026thinsp;=\u0026thinsp;node_features[first_center_idx]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c7\" namest=\"c4\"\u003e\u003cp\u003enode_coords(\u003cb\u003ei\u003c/b\u003e) = (S(node_idx).xd, S(node_idx).yd)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eFor i\u003c/b\u003e\u0026thinsp;=\u0026thinsp;2:num_clusters \u003cb\u003edo ⃪\u003c/b\u003e max_weighted_distance =-1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c7\" namest=\"c4\"\u003e\u003cp\u003e\u003cb\u003eFor j\u003c/b\u003e\u0026thinsp;=\u0026thinsp;1:num_nodes \u003cb\u003edo\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e\u003cp\u003e\u003cb\u003eFor k\u003c/b\u003e\u0026thinsp;=\u0026thinsp;1: \u003cb\u003ei\u003c/b\u003e-1 \u003cb\u003edo\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e\u003cp\u003eCalculate minimum distance to the exit centers\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e\u003cp\u003e\u003cb\u003eIf\u003c/b\u003e distance\u0026thinsp;\u0026lt;\u0026thinsp;min_distance \u003cb\u003ethen\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eMin_distance\u0026thinsp;=\u0026thinsp;distance\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c7\" namest=\"c4\"\u003e\u003cp\u003eweighted_distance\u0026thinsp;=\u0026thinsp;min_distance * (0.5\u0026thinsp;+\u0026thinsp;0.5 * node_features[j, 3])\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c7\" namest=\"c4\"\u003e\u003cp\u003eIf weighted_distance \u0026gt;max_weighted_distance \u003cb\u003ethen\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e\u003cp\u003emax_weighted_distance \u003cb\u003e=\u003c/b\u003e weighted_distance\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e\u003cp\u003eweighted_distance\u003c/p\u003e\u003cp\u003ebest_center_idx\u0026thinsp;=\u0026thinsp;j\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e19\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c7\" namest=\"c4\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e20\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e21\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"6\" nameend=\"c7\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section3\"\u003e\u003ch2\u003e3.2.4 Neighbor-based Voting\u003c/h2\u003e\u003cp\u003eEach node considers its K nearest neighbors and uses a weighted voting mechanism combining neighbor preferences and proximity to cluster centers to determine its final cluster membership, as in Algorithm 6.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabg\" border=\"1\"\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c5\" namest=\"c1\"\u003e\u003cp\u003eTEEN protocol with Sector-based KNN Clustering\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e\u003cp\u003eAlgorithm 6: Cluster Assignment using KNN\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eInput\u003c/b\u003e: node_features, cluster_centers, neareest_k_indices\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eOutput\u003c/b\u003e: cluster_id\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eInitialize: num_clusters\u003c/b\u003e\u0026thinsp;=\u0026thinsp;length(cluster_centers)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eBegin\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eFor i\u003c/b\u003e\u0026thinsp;=\u0026thinsp;1: num:clusters \u003cb\u003edo\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003eCalculate distance to cluster center\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eIf i\u003c/b\u003e\u0026thinsp;=\u0026thinsp;max(center_distance)\u0026thinsp;\u0026gt;\u0026thinsp;0 \u003cb\u003ethen\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003ecenter_similarities\u0026thinsp;=\u0026thinsp;1 - (center_distances / max(center_distances))\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eFor i\u003c/b\u003e\u0026thinsp;=\u0026thinsp;1 to length(nearest_k_indices) \u003cb\u003edo\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003e\u003cb\u003eFor j\u003c/b\u003e\u0026thinsp;=\u0026thinsp;1 to num_clusters \u003cb\u003edo\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eCalculate the distance to the center\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e\u003cp\u003eneighbor_votes[preferred_cluster]\u0026thinsp;=\u0026thinsp;neighbor_votes[preferred_cluster]\u0026thinsp;+\u0026thinsp;1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e\u003cp\u003efinal_scores\u0026thinsp;=\u0026thinsp;0.7 * center_similarities\u0026thinsp;+\u0026thinsp;0.3 * neighbor_votes\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eEnd\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Genetic-Fuzzy Logic for CH Selection\u003c/h2\u003e\u003cp\u003eA hybrid genetic-fuzzy approach is used to optimize CH selection further. The process involves:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eChromosome encoding\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eA set of chromosomes is generated randomly. Each represents a potential candidate for CHs.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eFitness function\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eThe algorithm evaluates candidates based on residual energy, intra-cluster distance, and distance to BS. The algorithm evaluated each candidate using a fuzzy interference system (FIS) as follows\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\text{F}\\text{F}\\:=\\:FIS(RE,\\:ICD,\\:DBS),$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere \u003cem\u003eRE\u003c/em\u003e denotes residual energy, \u003cem\u003eICD\u003c/em\u003e denotes to intra-cluster distance, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:DBS\\)\u003c/span\u003e\u003c/span\u003e Denotes to distance to BS. Low to high is defined as a range for the residual energy input variable, a Gaussian\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{\\text{y}\\left(\\text{x}\\right)\\:=\\text{e}}^{-\\frac{{(\\text{x}-\\text{c})}^{2}}{{2{\\sigma\\:}}^{2}}},$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere \u003cem\u003ec\u003c/em\u003e distribution center in the Gaussian curve, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}\\)\u003c/span\u003e\u003c/span\u003e variance, and the \u003cem\u003ex\u003c/em\u003e input value. The type of membership is adapted from low to high. Close to Far is defined as a range for the intra-cluster distance input variable, a Gaussian type of membership is adapted by medium, and a trapezoidal\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:y\\left(\\text{x}\\right)=\\left\\{\\begin{array}{c}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:0,\\:\\:x\\le\\:a\\:or\\:x\\:\\ge\\:d\\\\\\:1\\:,\\:\\:b\\le\\:x\\le\\:c\\\\\\:\\frac{\\text{x}-\\text{a}}{\\text{b}-\\text{a}},\\:\\:a\u0026lt;x\u0026lt;b\\\\\\:\\frac{\\text{d}-\\text{x}}{\\text{d}-\\text{c}},\\:\\:c\u0026lt;x\u0026lt;d\\\\\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\end{array},\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere a starting point, b left peak point, c right peak point, and d end point. The type of membership is adapted to close and far. Close to far is defined as a range for the distance to the BS input variable, and a trapezoidal type of membership is adapted for close to far. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e defines the fuzzy set of mapping rules for three fuzzy input variables and one fuzzy output.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eFuzzy rules.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u003cp\u003eInputs\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eOutput\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eResidual Energy\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIntra-Cluster Distance\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDistance to BS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003esuitability of the CHs\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFar\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eFar\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eVery Low\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMedium\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eClose\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLow\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eClose\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMedium\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMedium Low\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMedium\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eClose\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eFar\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMedium\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMedium\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eClose\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eClose\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMedium High\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eClose\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMedium\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eClose\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eClose\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eVery High\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe procedure of defuzzification to obtain a crisp output value y is applied with the (Takagi-Sugeno) weighted average method computed as follows:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:y=\\:\\frac{\\sum\\:_{i=1}^{n}{w}_{i}{y}_{i}}{\\sum\\:_{i=1}^{n}{w}_{i}},$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eWhere yi (the degree of input affiliation) is represented by numeric values, w firing strength, n number of rules with an affiliation score, and i index of the fuzzy rule.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eSelection: The rank selection method selects the fitness of the fittest individuals.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eCrossover: To generate a new generation, two parents are selected from the selected individuals by the selection process, and single-point crossover is applied to create new generations. Crossover rate is 0.8.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eMutation:Random change to the new generations is introduced to maintain diversity and prevent the occurrence of local solutions. The mutation rate is 0.15.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThe process is terminated when the specified number of generations is achieved. This approach combines the exploration capability of genetic algorithms with the adaptive decision-making of fuzzy logic, ensuring optimal and dynamic CH selection.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003e3.4 TEEN-Based Threshold Data Transmission\u003c/h2\u003e\u003cp\u003eThe TEEN protocol\u0026rsquo;s reactive nature is incorporated to minimize redundant transmissions. Nodes sense environmental parameters continuously but transmit data only when they exceed a predefined threshold:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eHard Threshold (HT)\u0026ndash;The senses value exceeds a predefined limit.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eSoft Threshold (ST)\u0026ndash;The change in the sense value after crossing HT exceeds a predefined margin.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eBy transmitting only significant data changes, communication energy consumption is substantially reduced.\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Simulation Setup","content":"\u003cp\u003eThe performance evaluation of the proposed SKNN-GFL-TEEN protocol was conducted using MATLAB. The simulation environment models a 100 m \u0026times; 100 m2 two-dimensional sensing area populated with 100 homogeneous sensor nodes, each initialized with 0.5 J of energy. Nodes were randomly deployed, and a fixed BS was positioned at coordinates (50, 50). Energy consumption was calculated using the first-order radio energy model, which accounts for electronics energy (Eelec​), free-space amplification energy (Efs​), and multipath fading amplification energy (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Ɛ}}_{\\text{a}\\text{m}\\text{p}}\\)\u003c/span\u003e\u003c/span\u003e), and data aggregation energy (Eda​). The TEEN protocol's hard threshold (HT) and soft threshold (ST) mechanisms were integrated to reduce redundant transmissions, with HT set to 100 and ST to 2. A packet size of 4,000 bits was used in all transmissions. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e summarizes the parameters employed in the simulation.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003esimulation parameters\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"2\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eParameter\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eValue\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNetwork Area Size\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e100 \u0026times; 100 m\u0026sup2;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNumber of Nodes\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e100\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eInitial energy of nodes (E\u003csub\u003eo\u003c/sub\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.5 J\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEnergy required for running transmitter and receiver (E\u003csub\u003eelec\u003c/sub\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e50 nJ/bit\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eThreshold distance (do)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e87 m\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAmplification energy required for free space model d\u0026thinsp;\u0026le;\u0026thinsp;do (E\u003csub\u003efs\u003c/sub\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e10 pJ/bit/m\u0026sup2;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAmplification energy required for multipath fading model d\u0026thinsp;\u0026gt;\u0026thinsp;do (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{Ɛ}}_{\\varvec{a}\\varvec{m}\\varvec{p}}\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.0013 pJ/bit/m\u0026sup2;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEnergy consumption incurred while data aggregation (E\u003csub\u003eda\u003c/sub\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e5 nJ/bit/signal\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eData packet size (k)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e4000bit\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eProbability (p)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.05\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHard Threshold (HT)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e100\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSoft Threshold (ST)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePopulation Size (P)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e50\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNumber of Generations (G)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e100\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCrossover rate (P\u003csub\u003ec\u003c/sub\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.8\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMutation rate (P\u003csub\u003em\u003c/sub\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.15\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eType of crossover\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSingle Point\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSelection method\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRank selection method\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"5. Results and Discussion","content":"\u003cp\u003eTo evaluate the performance of the SKNN-GFL-TEEN framework, it has been compared against LEACH, PEGASIS, and TEEN protocols across key performance metrics, including stability period, half-node death (HND), network lifetime (LND), energy consumption, and packets delivered to the BS.\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eStability: It is the first round in which the node completely loses its energy. Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates a comparison between traditional protocols and the proposed framework. The FND round was (984 rounds), (975 rounds), (1,206 rounds), and (1,632 rounds) for the LEACH, PEGASIS, TEEN, and SKNN-GFL-TEEN framework, respectively. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates that this improvement reflects the protocol\u0026rsquo;s ability to balance energy usage across the network, preventing early node deaths.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eHalf Node Dead is the round in which the network loses half of its nodes. Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates the superiority of the proposed framework over traditional WSNs protocols. The rounds to HND were (2,214 rounds) for SKNN-GFL-TEEN compared to TEEN (1,478 rounds), PEGASIS (1,326 rounds), and LEACH (1,191 rounds).\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eComparative analysis of TEEN with others for different metrics\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePROTOCOLS\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFND\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eHND\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLND\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003ePacket-to-BS\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLEACH\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e984\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1326\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1386\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e21427\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePEGSIS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e975\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1191\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1458\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1438\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTEEN\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1206\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1478\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1737\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e26346\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSKNN-GFL-TEEN\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1632\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2214\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3107\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e30302\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eNetwork Lifetime: it is the round in which the network completely loses all of its nodes, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e. The LND was recorded at (3,107 rounds) for the SKNN-FGL-TEEN framework, and (1,386 rounds), (1,458 rounds), (1,737 rounds) for LEACH, PEGASIS, TEEN, respectively. Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e demonstrates that the proposed framework is 78.87% superior to the TEEN protocol. These improvements are attributed to the sector-based clustering and genetic-fuzzy CH optimization, which reduce communication distances and distribute load evenly.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eEnergy Consumption: Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates that the proposed framework consumes less energy per round compared to the conventional TEEN, PEGASIS, and LEACH protocols. This reduction is driven by KNN-based local aggregation, which reduces intra-cluster communication distances, and a threshold-based transmission mechanism that eliminates redundant transmissions.\u003c/p\u003e\u003c/li\u003e \u003cli\u003e\u003cp\u003ePackets to the BS: this refers to the total number of packets that have been delivered successfully from CH to BS. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e6\u003c/span\u003e indicates that the proposed framework realized an enhanced packet delivery compared to the traditional protocols. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the number of packets is (21,427), (1,458), (26,346), and (30,302) for LEACH, PEGASIS, TEEN, and SKNN-GFL-TEEN, respectively. The findings are illustrated in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Indicate that sectoral segmentation is most effective in small and mid-size network areas with an identical number of nodes, whereas it is less effective in wide network areas due to the long transmission distance within a single sector.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eNetwork lifetime comparison between TEEN and SKNN-GFL-TEEN protocols over various network areas\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eNetwork Area Size\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e\u003cp\u003eTEEN\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003eSKNN-GFL-TEEN\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLND\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePacket-to-BS\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLND\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003ePacket-to-BS\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e100\u0026times;100 m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1737\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e26346\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3107\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e30302\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e200\u0026times;200 m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1465\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e17195\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2805\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e20238\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e300\u0026times;300 m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1415\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e9989\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2716\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e11676\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e500\u0026times;500 m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1346\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3605\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1926\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e5761\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThis improvement is attributed to the combination of genetic-fuzzy CH selection and sector-based clustering that ensures reliable and energy-efficient data aggregation and transmission to the BS. Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e summarizes the percentage improvement of SKNN-GFL-TEEN over TEEN for key performance metrics. The proposed protocol demonstrated substantial gains in network lifetime, stability, and packet delivery while achieving lower energy consumption. These results confirm that SKNN-GFL-TEEN successfully integrates the strengths of sector-based clustering, KNN-based neighbor selection, and genetic-fuzzy CH optimization to deliver robust and scalable performance in WSN environments.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eComparative percentage improvement of SKNN-GFL-TEEN over other protocols.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e\u003cp\u003ePercentage improvement by SKKN-GFL-TEEN to TEEN\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eProtocol\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNetwork Lifetime\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eStability\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003ePacket-to-BS\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTEEN\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e78.87%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e35.32%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e15.01%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\u003ch2\u003e5.1 Computational Complexity Analysis\u003c/h2\u003e\u003cp\u003eTo evaluate the algorithm\u0026rsquo;s scalability and efficiency, we analyze the \u003cb\u003etime complexity\u003c/b\u003e of each core phase of the SKNN-GFL-TEEN framework. Let:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eN\u0026thinsp;=\u0026thinsp;total number of sensor nodes\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eS\u0026thinsp;=\u0026thinsp;number of sectors (fixed at 4 in our simulation)\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eK\u0026thinsp;=\u0026thinsp;number of the nearest neighbors considered in KNN clustering\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eC\u0026thinsp;=\u0026thinsp;number of candidate CHs in the genetic algorithm population\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eG\u0026thinsp;=\u0026thinsp;number of generations in the genetic algorithm\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003e1. Sector-based KNN Clustering\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eNode assignment to sectors: Each node is compared against the S sector boundaries \u0026rArr; O (N\u0026sdot;S), which simplifies to O (N) for fixed S.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eKNN clustering within each sector: For each node in a sector, distances to other nodes are computed \u0026rArr; O ((N/S) \u003csup\u003e2\u003c/sup\u003e) per sector, giving an overall cost of O (N\u003csup\u003e2\u003c/sup\u003e/S). With S fixed, the complexity remains O (N\u003csup\u003e2\u003c/sup\u003e).\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eCluster center selection: Requires finding the node with the highest residual energy and farthest from the first center \u0026rArr; O (N). Overall KNN phase complexity: O (N\u003csup\u003e2\u003c/sup\u003e), dominant term from distance computation.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003e2. Genetic-Fuzzy Logic (GFL) CH Selection\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eChromosome evaluation: Each chromosome encodes a CH set and is evaluated using the fuzzy inference system (FIS) based on three parameters (residual energy, intra-cluster distance, distance to BS). This evaluation is O(N) per chromosome.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003ePer generation complexity: O (C\u0026sdot;N).\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eOver G generations: O (G\u0026sdot;C\u0026sdot;N). In our setup, C and G are fixed constants (50 and 100, respectively), so the complexity scales linearly as O(N).\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003e3. TEEN Threshold-based Data Transmission\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eSensing and threshold check\u003c/b\u003e: Each node performs constant-time threshold checks per sensing cycle \u0026rArr; O (N).\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eTransmission\u003c/b\u003e: Only nodes exceeding hard/soft thresholds transmit data; cost is proportional to active transmitters (N\u003csub\u003eactive\u003c/sub\u003e \u0026le; N), so worst case remains O(N).\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003ePerformance Gain vs. Overhead\u003c/b\u003e:\u003c/p\u003e\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eThe \u003cb\u003eKNN phase\u003c/b\u003e introduces O(N\u003csup\u003e2\u003c/sup\u003e) computation per round, which is acceptable for WSN simulation and small\u0026ndash;medium scale deployments (\u0026lt;\u0026thinsp;500 nodes), but may become heavy in very large networks unless optimized with spatial indexing (e.g., KD-trees) to reduce to O(NlogN).\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eThe GFL phase scales linearly with N for fixed C and G, making it computationally efficient even in large-scale networks.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eThe TEEN phase adds negligible computational overhead since it involves only simple comparisons and conditional transmissions.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eEnergy-Performance Trade-off: The extra processing in KNN and GFL is offset by reduced communication energy due to shorter intra-cluster distances and fewer redundant transmissions. Simulation results show that even with the additional computation, overall network lifetime improves by 78.87% compared to TEEN, making the overhead\u0026ndash;gain trade-off favorable. A summary of how hard it is to compute and what effect it has on the SKNN-GFL-TEEN steps is shown in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eSummary of computational complexity and impact for SKNN-GFL-TEEN phases\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePhase\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMain Operations\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eTime Complexity\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eImpact on Energy Efficiency / Lifetime\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eNotes\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSector-based KNN Clustering\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNode-to-sector assignment, pair-wise distance computation, cluster center selection\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eO (N\u003csup\u003e2\u003c/sup\u003e) (distance computation dominates)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHigh\u0026ndash;reduces intra-cluster communication distance, balances load\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eCan be optimized with KD-tree or spatial hashing to O(NlogN) for large-scale deployments\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGenetic-fuzzy logic (GFL) CH selection\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eChromosome evaluation via fuzzy inference, rank selection, crossover, and mutation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eO (G\u0026sdot;C\u0026sdot;N) (linear for fixed G, C)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHigh\u0026ndash;adaptive CH selection improves stability period and network lifetime.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eG and C fixed in simulations; low per-round overhead\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTEEN Threshold-based Data Transmission\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eContinuous sensing, hard/soft threshold checks, conditional transmission\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eO(N)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eVery high \u0026ndash; eliminates redundant transmissions, reduces energy waste\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eOverhead is negligible compared to the energy saved\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eOverall Framework\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eA combination of above phases\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDominated by O(N\u003csup\u003e2\u003c/sup\u003e)KNN step\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSignificant lifetime improvement (+\u0026thinsp;78.87% over TEEN)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eProcessing overhead is outweighed by communication energy savings\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"6. Conclusion","content":"\u003cp\u003eThe suggested method adeptly tackles significant issues in energy efficiency, network longevity, and load distribution by including geographical sectoring, intelligent clustering, and adaptive optimization of cluster heads. Simulation findings demonstrate that SKNN-GFL-TEEN outperforms known protocols, including LEACH, PEGASIS, and TEEN, in several performance parameters such as stability period, network longevity, and packet delivery to the BS. The proposed approach achieves sustained operational stability by uniformly spreading energy consumption among nodes, decreasing communication costs, and diminishing redundant transmissions using TEEN-based thresholding. The integration of genetic optimization and fuzzy inference enables dynamic, context-sensitive selection of cluster heads; while sector-based clustering reduces intra-cluster communication distances and enhances scalability for large-scale deployments. These synergistic enhancements render SKNN-GFL-TEEN especially appropriate for real-time monitoring applications, heterogeneous environments, and energy-constrained WSN deployments. The proposed framework is directly applicable to next-generation IoT-driven scenarios, including smart cities (e.g., air quality monitoring, traffic analysis, and structural health monitoring), environmental monitoring (e.g., forest fire detection, precision agriculture, and wildlife tracking), and industrial IoT (e.g., predictive maintenance in energy grids, oil pipelines, and manufacturing plants). SKNN-GFL-TEEN can be effectively implemented on low-power sensor motes, including the MicaZ wireless sensor mote, the TelosB wireless sensor node, and the Waspmote wireless sensor platform mote. This approach allows for sector-based clustering and genetic-fuzzy cluster head optimization using lightweight firmware, while TEEN\u0026rsquo;s thresholding mechanism minimizes radio usage, thereby prolonging battery life. The advent of 5G and 6G IoT networks enables integration into edge gateways for cloud-assisted decision-making, ensuring low-latency and energy-efficient operations at the edge. This supports interoperability and ultra-reliable low-latency communications (URLLC) for essential applications. However, certain limitations persist: the SKNN clustering phase incurs a (\u0026#119873;\u0026sup2;) computational cost, potential latency may arise in dense networks due to CH optimization, and current evaluations are based on static node positions. Future research will concentrate on enhancing SKNN-GFL-TEEN to accommodate mobile and heterogeneous nodes, adjusting cluster head selection based on fluctuating energy levels, investigating multi-base station and multi-sink configurations, and utilizing reinforcement learning to dynamically optimize parameters such as K in KNN, mutation rates in genetic algorithms, and TEEN thresholds in real-time scenarios. SKNN-GFL-TEEN exhibits notable adaptability and scalability, making it a compelling candidate for next-generation, energy-efficient WSN protocols in the Internet of Things and industrial settings.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eSh. M. Abdeljabbar and N.R. Saadallah conceived the main idea of the study, developed the methodology, and carried out the simulations.Bilal A. Jebur and N.R. Saadallah contributed to algorithm design, optimization techniques, and data analysis.Sh. M. Abdeljabbar prepared the figures, graphs, and tables and assisted in interpreting the results.Sh. M. Abdeljabbar and N.R. Saadallah wrote the first draft of the manuscript and integrated feedback from all co-authors.N.R. Saadallah and Bilal A. Jebur reviewed the related literature and contributed to the writing of the Introduction and Related Work sections.All authors discussed the results, revised the manuscript critically for intellectual content, and approved the final version of the manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe simulator source code generated and analyzed during the current study is not publicly available because it is part of ongoing research and making the code public could compromise the direction of future studies. However, the code is available from the corresponding author upon reasonable request with appropriate citation of the work.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eH. Hu, X. Fan, and C. Wang, \u0026lsquo;Energy efficient clustering and routing protocol based on quantum particle swarm optimization and fuzzy logic for wireless sensor networks\u0026rsquo;, Sci. Rep., vol. 14, no. 1, p. 18595, 2024.\u003c/li\u003e\n\u003cli\u003eH. Wang, K. Liu, C. Wang, and H. Hu, \u0026lsquo;Energy-efficient, cluster-based routing protocol for wireless sensor networks using fuzzy logic and quantum annealing algorithm\u0026rsquo;, Sensors, vol. 24, no. 13, p. 4105, 2024.\u003c/li\u003e\n\u003cli\u003eN. R. Saadallah and S. A. Alabady, \u0026lsquo;Using Hybrid GA/PSO-Mobile Sink to Improve Energy Efficiency and Network Lifetime for LEACH Protocol in WSNs\u0026rsquo;, in 2023 IEEE 13th International Conference on System Engineering and Technology (ICSET), IEEE, 2023, pp. 250\u0026ndash;255.\u003c/li\u003e\n\u003cli\u003eN. R. Saadallah and S. A. 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Networks, vol. 18, no. 6, p. 15501329221107246, 2022.\u003c/li\u003e\n\u003cli\u003eS. K. Sharma and M. Chawla, \u0026lsquo;RME\u0026ndash;SEP: An IoT favorable approach of minimum energy-efficient hybrid SEP for heterogeneous WSN data routing\u0026rsquo;, Arab. J. Sci. Eng., vol. 49, no. 3, pp. 4005\u0026ndash;4012, 2024.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"wireless-personal-communications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"wire","sideBox":"Learn more about [Wireless Personal Communications](https://www.springer.com/journal/11277)","snPcode":"11277","submissionUrl":"https://submission.nature.com/new-submission/11277/3","title":"Wireless Personal Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Energy Efficiency, K-Nearest Neighbors (KNN), Genetic Algorithm, Fuzzy Logic, Clustering, TEEN Protocol, Sector-based Routing","lastPublishedDoi":"10.21203/rs.3.rs-7609797/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7609797/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWireless Sensor Networks (WSNs) are increasingly utilized for environmental monitoring, industrial control, and smart infrastructure because of their distributed nature and low-power capabilities. However, energy efficiency remains a fundamental challenge due to limited battery capacity and uneven energy consumption. This paper proposes SKNN-GFL-TEEN, a novel hybrid framework that integrates Sector-based K-Nearest Neighbors (SKNN) with Genetic-Fuzzy Logic (GFL) under the Threshold-sensitive Energy Efficient Network (TEEN) protocol to enhance network lifetime and stability. The SKNN model partitions the network into distinct sectors and selects candidate nodes based on spatial proximity. Simultaneously, the GFL mechanism further refines cluster head (CH) selection through genetic optimization and fuzzy rule-based evaluation. Simulation results demonstrate that SKNN-GFL-TEEN outperforms conventional protocols, including LEACH, TEEN, and PEGASIS, in terms of network lifetime, energy consumption, and data delivery rate. Moreover, the proposed method demonstrates improved adaptability, scalability, and robustness, making it suitable for real-time and large-scale WSN deployments.\u003c/p\u003e","manuscriptTitle":"Enhancing TEEN Protocol Using Sectored KNN-Genetic-Fuzzy Clustering, Load Balancing, and Lifetime Optimization in WSNs","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-10 06:30:54","doi":"10.21203/rs.3.rs-7609797/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-01-17T08:52:39+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"176238805966366225904972214561386703077","date":"2025-10-03T14:26:06+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"22659374655904262150452164982848076978","date":"2025-09-30T06:24:03+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-09-28T20:19:54+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-09-19T13:16:33+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-09-19T13:15:54+00:00","index":"","fulltext":""},{"type":"submitted","content":"Wireless Personal Communications","date":"2025-09-14T00:59:59+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"wireless-personal-communications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"wire","sideBox":"Learn more about [Wireless Personal Communications](https://www.springer.com/journal/11277)","snPcode":"11277","submissionUrl":"https://submission.nature.com/new-submission/11277/3","title":"Wireless Personal Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"f97a25dc-17da-4955-a178-aaf99f18c81c","owner":[],"postedDate":"October 10th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-10-10T06:30:54+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-10 06:30:54","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7609797","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7609797","identity":"rs-7609797","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}