## 3 Materials and Methods
### Design of TLBO-MHR Technique  
When the CHs are chosen and clusters are optimally generated, the TLBO-MHR algorithm is applied to generate optimal routes in the IoT-assisted WSN. TLBO is a population-based technique simulated by the procedure of teacher as well as learner [29; 30; 31; 32; 33; 34; 35; 36]. Differing from other heuristic techniques, TLBO requires fewer approaches to certain parameters, which is an essential reason for choosing TLBO technique to optimize problems. Other heuristic approaches are heavily dependent on the parameter chosen; that is a significant limitation, as its efficiency is heavily dependent upon parameter tuning. A minor change from some parameters can affect the efficacy of the entire technique. TLBO begins by creating an arbitrary primary population, and then upgrades that population from all its iterations [37; 38; 39; 40; 41; 42; 43]. The rows match to learner, whereas columns relate to subjects. All the subjects of the learner signify the grade of application, while the entire quantity of topics of a beginner assemble to periods on which preparation is executed. The purpose of all the learners is to exploit their skills in all the subjects. The procedure of TLBO was separated into two stages: teacher and learner phases. During the teacher stage, the mean of learners from all the subjects is computed. The fitness of all learners is measured, and the optimum learner is then chosen as a teacher \(\left(X_{old}^{g}\right)\). A novel vector is furthered to represent a population that is created in the existing mean and optimum mean vector, as follows:  
\[X_{new(i)}^{g}=X_{(i)}^{g}+r\times\left(X_{main}^{g}-T_{f}M^{g}\right) \tag{22}\]  
where \(r\) represents the arbitrarily created number between zero and one. \(T_{f}\) signifies the instructor factor and its rate is either 1 or 2. The rate of \(T_{f}\) is arbitrarily chosen as follows:  
\[T_{f}=round[1+r_{1}] \tag{23}\]  
where \(r_{1}\) refers to the arbitrary quantity with a rate between zero and one. \(T_{f}\) is not an input parameter and is arbitrarily obvious by the technique utilised in Equation (12). The value of \(T_{f}\) is chosen as either 1 or 2, depending on rounding up conditions. If \(X_{new(i)}^{g}\) is superior in fitness to \(X_{(i)}^{g}\), then \(X_{(i)}^{g}\) is exchanged by the higher learner \(X_{new(i)}^{g}\). Random variables rand1 and rand2 are accidental numbers with a uniform delivery in the interval \([0,1]\) and are a scale factor in the interval \([0,1]\). During the learner stage, the learner interrelates with everyone and enhances his or her data through mutual communication [44; 45; 46; 47; 48]. All the learners relate with other learners for the sake of data sharing. From among all learners \(X_{(i)}^{g}\), another learner \(X_{(r)}^{g}\) is arbitrarily chosen \((i\
eq r)\) and the population is upgraded as follows:  
\[X_{new(i)}^{g}= \begin{cases}X_{(i)}^{g}+rand\times\left(X_{(i)}^{g}-X_{(r)}^{g }\right)&if\ X_{(i)}^{g}\leq X_{(r)}^{g}\\ X_{(i)}^{g}+rand\times\left(X_{(r)}^{g}-X_{(i)}^{g}\right)&otherwise\end{cases}  \tag{24}\]  
The algorithm endures until the condition is met. Algorithm 1 provides the entire mechanism of TLBO. Figure 2 shows the flow chart of the TLBO method.