## 3 Materials and Methods
### Design of TLBO-MHR Technique
```
Input: Populace size (pop-size), quantity of topics, end condition Initialisation: Create primary people while terminating condition is not met do  Teacher phase  Choose the optimum separate as a teacher \(x_{Tencoder}^{g}\) in people  Compute the mean charge \((x_{m})\) of all the subjects  for \(i=1\) to opposite do \(T_{f}=round(1+rand(0,1))\) \(x_{i}^{new}=x_{i}^{old}+rand_{i}(x_{Tencoder}^{g}-T_{f}\times x_{m})\)  Compute fitness of novel individual \(f(x_{i}^{new})\) if \(f(x_{i}^{new})<f(x_{i}^{old})\) then \(x_{i}^{old}=x_{i}^{new}\)  end end  Learner phase  for \(i=1\) to popsize do  Choose an arbitrary individual \(x_{r}\) so as \(r\
eq i\)  if\((x_{i}^{old})<f(x_{r})\) then \(x_{i}^{new}=x_{i}^{old}+rand_{i}(x_{r}-x_{i})\) else \(x_{i}^{new}=x_{i}^{old}+rand_{i}(x_{i}-x_{r})\)  end end end  Return Best
```  
**Algorithm 1**TLBO Algorithm  
``` Input: Populace size (pop-size), quantity of topics, end condition Initialisation: Create primary people while terminating condition is not met do  Teacher phase  Choose the optimum separate as a teacher \(x_{Tencoder}^{g}\) in people  Compute the mean charge \((x_{m})\) of all the subjects  for \(i=1\) to opposite do \(T_{f}=round(1+rand(0,1))\) \(x_{i}^{new}=x_{i}^{old}+rand_{i}(x_{Tencoder}^{g}-T_{f}\times x_{m})\)  Compute fitness of novel individual \(f(x_{i}^{new})\) if \(f(x_{i}^{new})<f(x_{i}^{old})\) then \(x_{i}^{old}=x_{i}^{new}\)  end end During instruction, to define the best group of routes, the TLBO-MHR procedure is applied in order to determine the subsequent hop to BS. This can be shown in the following:

\[f(x)=\left\{i,\ For\ Which\bigg{|}\bigg{(}\frac{i}{k}-X_{ifj}\bigg{)}\bigg{|}is\ Minimum,\ \forall\ i\ \ and\ \ 1\leq i\leq k\ \right\} \tag{25}\]

The procedure aims to define the best group of routes in CHs to the BS through an FF that contains two variables, such as distance and energy [49; 50; 51; 52; 53]. Initially, the RE of the next-hop node is described, and the node with maximum energy serves as the RN. Hence, the node with superior RE becomes the next-hop node. This is given in the following:

\[f1=E_{CH} \tag{26}\]

Furthermore, the Euclidean distance is executed for defining the distance in a CH to BS. Using minimum distance, the energy consumption is kept significantly low [38; 54; 55; 56; 57]. When the distance is increased, additional energy is expended. Thus, the node with lowest distance is chosen as an RN, as follows:

\[f2=\frac{1}{\sum_{i=1}^{m}dist(CH_{i},\ NH)+dist(NH,\ BS)} \tag{27}\]

Figure 2: Flowchart of the TLBO technique. The above-mentioned sub-objective is studied relative to FF, where \(\alpha_{1}\) and \(\alpha_{2}\) denote the weights assigned to each sub-objective. \[Fitness=\alpha_{1}(f1)+\alpha_{2}(f2),\;\;where\;\;\alpha_{1}+\alpha_{2}=1\;;\; \;\alpha_{i}\in(0,\;1) \tag{28}\]

## 4 Experimental Validation

In this section, a complete proportional training of the IMD-EACBR model compared to other current models is carried out. A route damage prototype founded on a cluster is created using both the CI and FI representations. Large-scale features such as PLEs and shadow factors in LOS and NLOS instances are designed and associated with those of the NYU prototype in the same setting. Table 2 and Figure 3 report a brief network lifetime (NLT) examination of the IMD-EACBR model compared to other approaches. The results indicate that the IMD-EACBR model accomplished a maximum NLT under all SNs [58; 59; 60; 61; 62; 63; 64; 65; 66; 67]. For instance, with 100 SNs, the IMD-EACBR model attained an maximum NLT of 1719 rounds, whereas the sunflower optimisation (SFO), gray wolf optimisation (GWO), genetic algorithm (GA), ant line optimisation (ALO), and particle swarm optimisation (PSO) models obtained reduced NLTs of 1593, 1448, 1415, 1349, and 1300 rounds, respectively. Furthermore, with 500 SNs, the IMD-EACBR model reached a superior NLT of 3500 rounds, whereas the SFO, GWO, GA, ALO, and PSO models resulted in lower NLTs of 3501, 3395, 3263, 2966, and 2684 rounds, respectively.