Training and Learning Swarm Intelligence Algorithm (TLSIA) for Selecting the Optimal Cluster Head in Wireless Sensor Networks
Research Areas : Wireless Network
Ali Sedighimanesh
^{
1
}
Hessam Zandhessami
^{
2
}
Mahmood Alborzi
^{
3
}
mohammadsadegh Khayyatian
^{
4
}
Keywords: Hierarchical routing, TLBO algorithm, TS algorithm, wireless sensor network,
Abstract :
Background: Wireless sensor networks include a set of nonrechargeable sensor nodes that interact for particular purposes. Since the sensors are nonrechargeable, one of the most important challenges of the wireless sensor network is the optimal use of the energy of sensors. The selection of the appropriate cluster heads for clustering and hierarchical routing is effective in enhancing the performance and reducing the energy consumption of sensors. Aim: Clustering sensors in different groups is one way to reduce the energy consumption of sensor nodes. In the clustering process, selecting the appropriate sensor nodes for clustering plays an important role in clustering. The use of multistep routes to transmit the data collected by the cluster heads also has a key role in the cluster head energy consumption. Multistep routing uses less energy to send information. Methods: In this paper, after distributing the sensor nodes in the environment, we use a TeachingLearningBased Optimization (TLBO) algorithm to select the appropriate cluster heads from the existing sensor nodes. The teachinglearning philosophy has been inspired by a classroom and imitates the effect of a teacher on learner output. After collecting the data of each cluster to send the information to the sink, the cluster heads use the Tabu Search (TS) algorithm and determine the subsequent step for the transmission of information. Findings: The simulation results indicate that the protocol proposed in this research (TLSIA) has a higher last node dead than the LEACH algorithm by 75%, ASLPR algorithm by 25%, and COARP algorithm by 10%. Conclusion: Given the limited energy of the sensors and the nonrechargeability of the batteries, the use of swarm intelligence algorithms in WSNs can decrease the energy consumption of sensor nodes and, eventually, increase the WSN lifetime.
[1] A. Belfkih, C. Duvallet, and B. Sadeg, “A survey on wireless sensor network databases,” Wirel. Networks, vol. 25, no. 8, pp. 4921–4946, 2019.
[2] M. Sedighimanesh* and H. Z. and A. Sedighimanesh, “Presenting the Hybrid Algorithm of Honeybee  Harmony in Clustering and Routing of Wireless Sensor Networks,” International Journal of Sensors, Wireless Communications and Control, vol. 9, no. 3. pp. 357–371, 2019.
[3] A. Kochhar, P. Kaur, P. Singh, and S. Sharma, “Protocols for wireless sensor networks: A survey,” Journal of Telecommunications and Information Technology. 2018.
[4] Z. Ullah, “A Survey on Hybrid, Energy Efficient and Distributed (HEED) Based Energy Efficient Clustering Protocols for Wireless Sensor Networks,” Wirel. Pers. Commun., vol. 112, no. 4, pp. 2685–2713, 2020.
[5] A. Shahraki, A. Taherkordi, Ø. Haugen, and F. Eliassen, “Clustering objectives in wireless sensor networks: A survey and research direction analysis,” Comput. Networks, vol. 180, p. 107376, 2020.
[6] S. A. Susan T and B. Nithya, “Cluster Based Key Management Schemes in Wireless Sensor Networks: A Survey,” Procedia Comput. Sci., vol. 171, pp. 2684–2693, 2020.
[7] P. Sarzaeim, O. BozorgHaddad, and X. Chu, “TeachingLearningBased Optimization (TLBO) Algorithm BT  Advanced Optimization by NatureInspired Algorithms,” O. BozorgHaddad, Ed. Singapore: Springer Singapore, 2018, pp. 51–58.
[8] M. Gendreau, “An Introduction to Tabu Search,” in Handbook of Metaheuristics, 2006.
[9] U. E. Zachariah and L. Kuppusamy, “A hybrid approach to energy efficient clustering and routing in wireless sensor networks,” Evol. Intell., 2021.
[10] F. Fanian and M. K. Rafsanjani, “Clusterbased routing protocols in wireless sensor networks: A survey based on methodology,” J. Netw. Comput. Appl., vol. 142, pp. 111–142, 2019.
[11] W. R. Heinzelman, A. Chandrakasan, and H. Balakrishnan, “Energyefficient communication protocol for wireless microsensor networks,” System Sciences, 2000. Proceedings of the 33rd Annual Hawaii International Conference on. p. 10 pp. vol.2, 2000.
[12] M. Shokouhifar and A. Jalali, “A new evolutionary based application specific routing protocol for clustered wireless sensor networks,” AEU  Int. J. Electron. Commun., vol. 69, no. 1, pp. 432–441, Jan. 2015.
[13] M. Khabiri and A. Ghaffari, “EnergyAware ClusteringBased Routing in Wireless Sensor Networks Using Cuckoo Optimization Algorithm,” Wirel. Pers. Commun., vol. 98, no. 3, pp. 2473–2495, 2018.
[14] P. K. Roy, C. Paul, and S. Sultana, “Oppositional teaching learning based optimization approach for combined heat and power dispatch,” Int. J. Electr. Power Energy Syst., 2014.
[15] W. Shao, D. Pi, and Z. Shao, “An extended teachinglearning based optimization algorithm for solving nowait flow shop scheduling problem,” Appl. Soft Comput. J., 2017.
[16] X. Wang, L. Wang, and Y. Wu, “An Optimal Algorithm for Prufer Codes,” JSEA, vol. 2, pp. 111–115, Jan. 2009.
http://jist.acecr.org ISSN 23221437 / EISSN:23452773 
Journal of Information Systems and Telecommunication

Training and Learning Swarm Intelligence Algorithm (TLSIA) for Selecting the Optimal Cluster Head in Wireless Sensor Networks 
Ali Sedighimanesh1, Hessam Zandhessami1*, Mahmood Alborzi1, Mohammadsadegh Khayyatian2

1.Department of Management and Economics, Science and Research branch, Islamic Azad University, Tehran, Iran 2.Institute for science and technology studies, shahid Beheshti university, Tehran, Iran 
Received: 28 Nov 2020 / Revised: 29 Apr 2021/ Accepted: 29 May 2021 
DOI: https://doi.org/10.52547/jist.15638.10.37.37 
Abstract
Background: Wireless sensor networks include a set of nonrechargeable sensor nodes that interact for particular purposes. Since the sensors are nonrechargeable, one of the most important challenges of the wireless sensor network is the optimal use of the energy of sensors. The selection of the appropriate cluster heads for clustering and hierarchical routing is effective in enhancing the performance and reducing the energy consumption of sensors. Aim: Clustering sensors in different groups is one way to reduce the energy consumption of sensor nodes. In the clustering process, selecting the appropriate sensor nodes for clustering plays an important role in clustering. The use of multistep routes to transmit the data collected by the cluster heads also has a key role in the cluster head energy consumption. Multistep routing uses less energy to send information.
Methods: In this paper, after distributing the sensor nodes in the environment, we use a TeachingLearningBased Optimization (TLBO) algorithm to select the appropriate cluster heads from the existing sensor nodes. The teachinglearning philosophy has been inspired by a classroom and imitates the effect of a teacher on learner output. After collecting the data of each cluster to send the information to the sink, the cluster heads use the Tabu Search (TS) algorithm and determine the subsequent step for the transmission of information. Findings: The simulation results indicate that the protocol proposed in this research (TLSIA) has a higher last node dead than the LEACH algorithm by 75%, ASLPR algorithm by 25%, and COARP algorithm by 10%.
Conclusion: Given the limited energy of the sensors and the nonrechargeability of the batteries, the use of swarm intelligence algorithms in WSNs can decrease the energy consumption of sensor nodes and, eventually, increase the WSN lifetime.
Keywords: Hierarchical Routing; TLBO Algorithm; TS Algorithm; Wireless Sensor Network.
1 Introduction
The wireless sensor network consists of several nonrechargeable sensor nodes applied for particular purposes [1]. One of the most important issues and challenges related to wireless sensor networks is the use of methods to reduce the energy consumption of sensor nodes. One of the methods is the clustering of the sensor nodes; instead of the sensor nodes consuming a great deal of energy and transmitting the data directly to the sink, they fall into a group called the cluster and send the data to the cluster head, and the cluster heads are required to transmit the data, thus consuming less energy of the sensor nodes and extending the network’s lifetime [2]. Cluster heads can either send the received data directly to the sink or work together to send the data to the sink in a hierarchical routing process. In general, transmitting data hierarchically reduces the energy consumption of cluster heads farther from the sink [3],[4].
The process of selecting cluster heads from available sensors and the routing between clusters to transmit data to the sink are of the optimization issues; therefore, the use of optimization algorithms has an effective role in the proper performance of these two processes, and ultimately, the efficiency of the wireless sensor network [5],[6]. TeachingLearningBased Optimization (TLBO) algorithm is one of the modern intelligent optimization algorithms implemented in two stages (phases) and can lead to optimization through being inspired by the learning and teaching process. In the teaching phase, the best member of the community is selected as the teacher and directs the average population towards himself/herself; this is similar to what a teacher does in the real world. In the learning phase, the people in the population work together to increase their knowledge, and it is similar to what happens in the company of friends and classmates [7].
The Tabu Search (TS) [8] algorithm is also one of the most powerful algorithms for solving optimization problems, especially graphbased and combinatorial optimization problems. The TS algorithm applies a list named the taboo list, which has been designed to prevent the algorithm from falling at the local optimal point. In summary, TS starts from a point or solution and searches for neighbors around that point, chooses the best neighbor and moves to that point, and continues this search until a stopping criterion to be satisfied. The optimal point is reported at the end of the search.
In the present article, the TLBO swarm intelligence algorithm is applied to select the appropriate cluster heads from the available sensor nodes. Once the cluster heads are identified, the members of each cluster become the member of the nearest cluster head and send the data to their cluster heads. The cluster heads receive data from their members and process and aggregate them subsequently. Then, the TS algorithm is used to transmit data to the sink by cluster heads until the best routes are formed for sending data, which reduces the energy consumption of cluster heads to transfer data. The rest of the article is structured as follows. Section 2 presents the previous work. Section 3 addresses the Proposed algorithm. Section 4 discusses the findings of the article. In Section 5, the authors present open problems for wireless sensor networks, and also the results are presented.
In this research, we will address several routing protocols that have attracted interest in recent years, namely the following: LEACH, ASLPR, and COARP[9][10].
21 Low Energy Adaptive Clustering Hierarchy (LEACH)
In the LEACH protocol [11], there is a probability P for each sensor to be a cluster head (CH) in every round. In other words, LEACH creates groups using a distributed algorithm, in which the sensors automatically decide to become a cluster head and there is no centralized control. Each sensor can be a cluster head only once in 1/P consecutive rounds. First, each sensor makes a decision with a probability of P to become a cluster head. The cluster head roles changes in rounds between the group nodes, and this is to create an equilibrium in the energy consumption distribution. One can divide the performance of LEACH in each round into two phases. These phases are the setup and steadystate phases. A random number between 0 and 1 is chosen by every sensor in the setup phase. If that number is smaller than T(n), the sensor n becomes a CH for that round. The value of T(n) is computed based on (1), where P is the tendency of the sensor to be a node, and r represents the round number. Moreover, G denotes the set of all sensors that have not been chosen as a cluster head during the last 1/P rounds.
 (1) 
After the cluster heads are selected, they are announced to all the sensors in the network as cluster heads. When noncluster head sensor receives an announcement from the cluster heads, it selects the cluster head closest in terms of communication.
22 Application Specific Low Power Routing (ASLPR) protocol
The ASLPR protocol [12] collects specific pieces of information, such as remaining energy, distance from the base station, and distance between the CHs and sensor node, to select the cluster head nodes. Then, each node selects a random number between zero and 1. If the random number selected by a node is less than in (2), this node is converted to a cluster head.
In the above relationships, N represents the total number of live nodes in the current round, and equals the n remaining nodes.
In (3), denotes the subthreshold of the node energy, and refers to the weight of this subthreshold. Moreover, represents the subthreshold for the distance between the nodes and the base station, and denotes the weight of this subthreshold. In addition, is the subthreshold for the distance between the node and the cluster head, and refers to the weight of this subthreshold. The subthreshold denotes the number of rounds where a node has been the cluster head, and represents the weight of this subthreshold. Then, the cluster head nodes announce their existence to all the nodes in the network by issuing a message. After receiving this message from different cluster heads, the regular (noncluster head) nodes select the closest cluster head to join. In this protocol, genetic algorithm (GA) combined with the simulated annealing (SA) algorithm has been used to optimize the special parameters utilized for determining the threshold for applicationspecific cluster heads. The objective functions of the GA and SA algorithms in this protocol are defined as follows:
 (2) 
 (3) 
In the above relationships, , , and denote the weights of the First Node Dead (FND), Half Node Dead (HND), and Last Node Dead (LND), respectively. The ranges of the mentioned weights are between 0 and 1, depending on the application, such that their sum equals 1 according to (7). Moreover, refers to the subthreshold values in (3), and in (4) represents the weight of the subthreshold in (3).
23 Cuckoo Optimization Algorithm  Based Routing Protocol (COARP)
In COARP [13], measurements to determine the CHs are performed within a centralized control system. The model of the network is a singlestep model where the CHs communicate directly with the base station. During every round, the base station is aware of the position and energy level of the nodes in the network. During each round, every node sense and gathers the surrounding data. Then, it processes the data and sends it to the cluster head in a data packet form. The COARP clustering method involves the following steps: (1) the startup phase, which involves determining the cluster head and creating the cluster, (2) the register phase, which involves creating a data scheduling and transmission plan. In CAORP, the CHs are accurately chosen by the cuckoo algorithm in the base station. Then, the cluster creation process and the register phase are performed. Every CH receives the information relating to all the nodes belonging to its own cluster. Then, it sends the received information to the base station in the form of a packet.
3 Proposed Algorithm
The appropriate selection of cluster heads from the available sensor nodes is one of the methods that lead to the reduction of the energy consumption of sensor nodes and cluster heads. Besides, the data transmission in a hierarchical manner instead of the onestep method highly affects the reduction of the energy consumption of sensors since the farther apart the two nodes are, the more energy they have to expend for data transmission. Therefore, selecting the appropriate cluster head from the available nodes and the hierarchical routing can lead to the reduction of the energy consumption of the sensor nodes, which will increase the lifetime of the wireless sensor network. For this purpose, there are various methods; the application of optimization methods for solving such problems will enhance decisionmaking and increase the efficiency of algorithms.
The proposed algorithm described in three sections: sensor node distribution, clustering process, routing. In the sensor node distribution section, the authors explain how to distribute the nodes in the simulation environment. In the clustering section, there is an attempt to classify sensor nodes into different clusters for the purpose of reducing energy consumption. For this purpose, a swarm intelligence algorithm called TLBO is employed to select the optimal cluster heads from the sensor nodes. In the routing section, the objective is to apply the best routes to transmit data hierarchically with less energy consumption; hence, the TS algorithm is used to choose the best route for data transmission. In the following, the authors will explain these steps step by step. The general algorithm of the proposed algorithm is as follows.
 (4) 
 (5) 
 (6) 
 (7) 
TLSIA Algorithm 
Select nodes in sensing area for clustering 1 CHs= TLBO 2 For i=1: number of nodes 3 If node(i) is in sensing area && node(i) is normal node 4 node(i) joins to nearest CH 5 end if 6 end for Routing to send cluster head information 7 Route= TS 8 For i= Cluster heads 9 CH(i) joins to route; 10 end for 
31 Node Distribution and Sink Location
During the simulation, the sensor nodes are randomly distributed in an environment. Then, the location of the sink is determined, which is usually outside the environment.
Fig. 1. Random distribution of the nodes in the environment
The process of choosing the optimal cluster heads from between the sensors in the network is performed using the TeachingLearningBased Optimization (TLBO) algorithm. The teachinglearning philosophy has been inspired by a classroom and imitates a teacher’s effect on the learner output. Similar to other swarm intelligence algorithms, the TLBO algorithm is a populationbased evolutionary optimization algorithm and consists of a teaching phase and a learner phase.
In the teaching phase, the teacher has the main role and attempts to transfer their knowledge to all the learners in the classroom to increase the average score. The average result of the learners and the improvement in results completely depends on the teacher. In each step, the best learner in the population is selected as the teacher, and, accordingly, the cost function and the average position for improving the position of the learners are computed.
In the learning phase, the learners increase their knowledge either via the teacher or via interacting with each other. The main difference between the teaching and learning phases is that in the teaching phase, the teacher transfers the knowledge to the learners, but in the learning phase, the learners gain knowledge from the teacher and by communicating with each other. In populationbased optimization methods, a population has a set of members, each of which has a number of variables. Every member of the population is a solution to the optimization problem. In this paper, we first form an initial population consisting of a number of members, named learners, to determine the cluster head. Each learner includes 2 variables: Position, which consists of a string of variables, and cost. The figure below shows an overview of a population.
Learner 01  Position  Node 01  Node 02  Node 03  ….  Node (n1)  Node (n) 
Cost  
Learner 02  Position  Node 01  Node 02  Node 03  ….  Node (n1)  Node (n) 
Cost  
.  
.  
.  
Learner 0N  Position  Node 01  Node 02  Node 03  ….  Node (n1)  Node (n) 
 Cost 
Fig. 2. Overview of a population
First, the variables inside the position are given a random value between 0 and 1 (0 ≤ Position (i) ≤ 1). The most important issue in optimization algorithms is how to determine the cost for the learners in the population. In this paper, the cost is equal to (8):
(8)
In the above formula, x is the variable inside the population member, RE is the remaining energy of each variable, density is the ratio of the number of neighbors to the total number of nodes, centrality is the sum of distances of the nodes from the neighbors, Beta= 0.3, Alpha= 0.5, and Gamma=0.2.
In the TLBO method, every member of the population is considered a learner. In every iteration of the TLBO algorithm, we select the member with the lowest cost between the population members as the best member of the population. Then, we sort the variables inside the selected member in descending order and select 10% of these variables as the optimal cluster head. For example, if after the end of the maximum iteration of the algorithm, the output is as follows:

 01  02  03 
 n1  n 
Learner 01  Position  0.36  0.47  0.25  ….  0.12  0.22 
Cost= 1.25  
Learner 02  Position  0.26  0.17  0.45  ….  0.32  0.52 
Cost=1.35  
. . .  
Learner N  Position  0.14  0.32  0.54  ….  0.33  0.63 
Cost=1.05 
Learner 02 is selected as the best member of the population; hence, the variables inside this member are sorted in descending order, and 10% of them are considered as the cluster head.
In implementing the TLBO algorithm, 3 values have a vital role in the optimal performance of the algorithm: (1) initialization of the learners, (2) updating of the teaching phase, and (3) updating of the learning phase.
Learner initialization: In this method, we first create a random population and calculate the second population from the first using (9). Subsequently, we combine the 2 populations and compute and sort the costs of the learners. Then, we select from the learners with less cost a number equal to the learner members of the population[14], [15].
Fig. 3. Oppositionbased learning and quasioppositional learning[15].
Teaching phase: In the teaching phase, the learners increase their knowledge via learning from the difference between the class average and the teacher. The update mechanism for the ith learner has been expressed as follows:
 (9) 
 (10) 
newXi is the learner’s new state, Xi is the ith learner, Teacher is the learner with the best fitness, NP denotes the number of learners present in the population, and TF is a teaching factor that determines the value of the average that must be changed. Also, rand is a random vector the element of which is a random number in the range [0, 1].
Learning phase: During the learning phase, the learners also increase their knowledge interactively. The update mechanism for the ith learner has been expressed as follows:
 (11) 
 (12) 
 (13) 
where newXi is the ith learner’s position, represents the learners chosen randomly from the class, and and respectively denote the fitness values of the learners and . In addition, rand denotes a random vector in the [0, 1] range.
33 Routing
TLSIA Clustering Algorithm 
1 Initialize learners; 2 Evaluate learners; 3 For all learners 4 For i=each dimension 5 6 7 End_For 8 End_For 9 Combine first population and Quasiopposite population; 10 Select best learners as new population; 11 Xteacher=best learner; 12 Xmean=average of learners; 13 While (stopping condition is not met) 14 For i=all learners 15 TF = round (1 + rand (0,1)); 16 Xnewi=Xi+rand*(XteacherTF*Xmean); 17 End_For 18 Evaluate new learners; 19 If new learner is better than old one 20 Xi=Xnewi; 21 End_If 22 For i=all learners 23 Randomly select another learner which is different from i (Xk); 24 If Xi is better than Xk 25 Xnewi=Xi+rand*(XiXk); 26 Else 27 Xnewi=Xi+rand*(XkXi); 28 End_If 29 End_For 30 If new learner is better than existing 31 Xi=Xnewi; 32 End_If 33 Xteacher=best learner; 34 Xmean=average of learners; 35 End_While 
To optimize routing using the TS algorithm, we use the Prüfer algorithm [16] to create a tree between the cluster head nodes. This algorithm maps a sequence of numbers to the corresponding tree.
First, we create a solution that assigns a random number between 0 and 1 to each position variable. Then, the solution cost is computed. To calculate the cost of each solution, we first convert it to the corresponding tree using the Prüfer algorithm. Then, the routing is performed according to the obtained tree, and the cost is calculated from (14). E1 is the network energy before applying the routing, and E2 is the computed energy after applying the routing.
Given the actions considered in the TS algorithm, all the states relating to these actions are created in a list named Action List. We perform these actions on the obtained solution and update the cost and position for each action. If a lower cost results, it replaces the best solution, and the corresponding action is placed in the Tabu List and is not performed for a specific number of rounds. The desired number of actions is computed using (15).
 (14) 
This is continued until the best solution is obtained. Finally, the obtained solution is given to the Prüfer algorithm, the output of which is an optimal tree according to which the routing is performed. For example, assume the number of cluster heads is 10 in a known round. First, the number of variables inside the solution of the TS algorithm is equal to 9. We consider a random number between 0 and 1 for each variable and compute the initial solution cost.
(n is the number of position variables.)
 (15) 

 01  02  03  04  05  06  07  08  09 
Solution  Position  0.37  0.26  0.88  0.76  0.44  0.55  0.45  0.35  0.25 
Cost= 2 
TLSIA Routing Algorithm 
1 Create initiate solution; 2 Sbest=best solution; 3 While (stopping condition is not met) 4 Generate candidate solutions in the neighborhood of Sbest 5 For i=candidate solutions 6 If candidate_i is not in TabuList 7 If candidate_i is better than bestnewsol 8 Bestnewsol=candidate_i 9 End_If 10 End_If 11 End_For 12 If bestnewsol is better than Sbest 13 Sbest= bestnewsol 14 End_If 15 Push the bestnewsol to TabuList 16 If TabuListSize>maxTabuListSize 17 Remove the first element from TabuList; 18 End_If 19 End_While 
34 Network Operations and Energy Consumption Computation
The network operations in the proposed algorithm are divided into startup and register phases. The energy consumption of every node in each round is computed by examining what has occurred in both phases.
341 Startup Phase
The sink uses the control packet to communicate with the sensor nodes. These control packets contain short messages that request the ID, position, and the level of energy from each of the sensor nodes. The energy is consumed in the process of receiving the control packets from the sink according to (16). Moreover, all the nodes utilize the energy to transfer to the sink the control packets that contain data relating to the IDs, positions, and levels of energy.
Where is the threshold distance. The amplifier energy or is based on the distance of the receiver and the acceptable bit error. The sink processes the control packets and, according to the proposed algorithm, determines which nodes will be cluster heads and which cluster head each node will become a member of. Moreover, all the nodes (CH or other nodes) use the energy to receive their status information from the sink. The energy consumed by the CHs to send TDMA (Timedivision multiple access) schedules to their respective members is obtained by the following relationship:
 (16) 
 (17) 
The member consumes energy to receive the TDMA schedules from the cluster head, which is computed from (16).
342 Register Phase
In the register phase, the active nodes send kbit data to their respective cluster heads in terms of the TDMA schedule they have received from the sink. The cluster head is always ready to receive these sensed data from its members and processes and aggregates all the data received from its members before sending them to the sink. The energy consumed by the cluster head sensor transmitter to perform work, i.e., , is computed from (19).
 (18) 
The energy lost in the transmission of the sensed data to the cluster head is calculated using the following relationship:
 (19) 
where denotes the member nodes of the series
, and n and L represent the total numbers of sensor nodes and cluster heads, respectively. The energy consumed by the cluster head to collect the sensed data from the members and itself is determined via (19), as follows.
4 Findings:
All the experiments were conducted within MATLAB R2019b. To prove the efficiency, we compare the proposed algorithm to known protocols such as LEACH, ASLPR, and COARP based on FND, HND, LND, and the total number of data packets received at the sink from the start of the simulation to the end of the network lifetime.
41 Network Model Assumptions
The important assumptions for the network model and the radio model in the proposed algorithm are as follows:
❖ The sink is a fixed device and a rich source located outside the simulation environment.
❖ All the sensors are stable after deployment, and the average energy in the homogeneous or heterogeneous environment is constant.
❖ All the sensors are equipped with the Global Positioning System (GPS) or connected to other geographical positioning systems.
❖ The communication channel is considered to be symmetric.
Table 1: Adjusting the parameters of the TLBO algorithm
 (20) 
Parameter  Value 
Population or Learner  50 
Number of iterations  100 
Number of Variables  length (Alive Nodes) 
Variables Lower Bound  VarMin= 0 
Variables Upper Bound  VarMax=1 
Table 2: Adjusting the parameters of the TS algorithm
Parameter  Value 
Population or Solution  1 
Number of iterations  100 
Number of Variables  Nch1 (Nch= Number of Cluster Head) 
Variables Lower Bound  VarMin= 0 
Variables Upper Bound  VarMax=1 
NAction  NSwap+NReversion+NInsertion 
NSwap = NReversion  N × (N1)/2 
NInsertion  N × N (N=Number of position variables) 
Table 3: Simulation parameters
Parameter  Value 
Initial energy of the nodes  1j 
 10 (pj/bit/m2) 
 0.0013 (pj/bit/m4) 
Eelec  50 (nJ/bit) 
Eda  5 (nJ/bit) 
Data packet size  4100 (bit) 
In this section, the authors take into account eight scenarios according to Table (4) to evaluate the proposed algorithm. The number of sensors, the size of the environment, and the sink location are the parameters investigated in these scenarios to evaluate the algorithms in which the parameters change in each scenario.
Table 4: Used scenarios
Number  Number of sensors  Network size  Sink location 
1  100  200m × 200m  (100m, 250m) 
2  100  (250m, 550m)  
3  200  200m × 200m  (100m, 250m) 
4  200  500m × 500m  (250m, 550m) 
5  500  200m × 200m  (100m, 250m) 
6  500  500m × 500m  (250m, 550m) 
7  2000  200m × 200m  (100m, 250m) 
8  2000  500m × 500m  (250m, 550m) 
According to Table (4), the scenarios are simulated in two environments of sizes 200m×200m, and 500m×500m and the number of sensor nodes 100, 200, 500, and 2000, and their results are analyzed. Three factors are investigated in these scenarios: 1) the number of live nodes, 2) energy consumption of the network, 3) packets sent to the sink in each round.
Fig. 4. Number of live nodes in each round in the first scenario.
According to the results obtained in Figure (4) in the first scenario, FND^{1}, HND^{2} and LND^{3} in the proposed algorithm are better compared to other approaches and indicates that in the Proposed algorithm, the energy consumption of sensors in each round is less than other methods. In Figure (5), the network’s lifetime has been compared; in the Proposed algorithm, the networks’ lifetime has increased compared to other methods, which shows the proper performance of the proposed algorithm in clustering and data transmission.
Fig. 5. Network’s energy consumption in each round in the first scenario.
Fig. 6. Packets sent to the sink in each round in the first scenario.
In the simulations, the higher the number of intact packets sent to the sink, the better the performance of the sensor nodes and cluster heads, which leads to an increase in the performance of the wireless sensor network. As shown in Figure (6), in the Proposed algorithm, the number of packets sent to the sink in each round is more than other methods, which indicates the proper performance of the sensor nodes and cluster heads within the wireless sensor network in the TLSIA method.