## 3 Materials and Methods
### Design of TLBO-MHR Technique
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Packet Delivery Ratio (\%)**} \\ \hline \hline \begin{tabular}{c} **Density of** \\ **Sensor Nodes** \\ \end{tabular} & \begin{tabular}{c} **IMD-** \\ **EACBR** \\ \end{tabular} & \begin{tabular}{c} **SFO Alg.** \\ **Algorithm** \\ \end{tabular} & \begin{tabular}{c} **GWO** \\ **Alg.** \\ \end{tabular} & \begin{tabular}{c} **Genetic** \\ **Alg.** \\ \end{tabular} & \
\begin{tabular}{c} **ALO Alg.** \\ \end{tabular} &
\begin{tabular}{c} **PSO Alg.** \\ \end{tabular} \\ \hline
100 & 98.83 & 98.40 & 96.47 & 95.65 & 94.37 & 93.79 \\
150 & 98.46 & 97.90 & 96.47 & 95.54 & 94.07 & 93.16 \\
200 & 98.46 & 97.64 & 96.43 & 95.35 & 93.73 & 92.82 \\
250 & 98.25 & 97.68 & 96.34 & 95.13 & 93.53 & 92.52 \\
300 & 98.03 & 97.40 & 96.10 & 94.81 & 93.29 & 92.34 \\
350 & 97.62 & 96.58 & 95.85 & 94.50 & 92.88 & 91.97 \\
400 & 97.19 & 96.60 & 95.39 & 94.35 & 92.71 & 91.72 \\
450 & 96.97 & 96.15 & 95.00 & 93.94 & 92.52 & 91.48 \\
500 & 96.56 & 95.20 & 94.66 & 93.47 & 92.30 & 91.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: PDR analysis of the IMD-EACBR technique compared to other approaches under different densities of SNs. Figure 7: Throughput analysis of the IMD-EACBR technique under different densities of SNs. Finally, a cost function examination of the IMD-EACBR model compared to other optimization techniques is summarised in Figure 9. The results indicate that the GA performed poorly with increased cost function values. The other algorithms, except for the GWO and the IMD-EACBR model, exhibited similar cost function values. Although the GWO algorithm achieved a reasonable outcome, the IMD-EACBR model displayed superior performance. The aforementioned tables and figures report the superiority of the IMD-EACBR approach over all other methods in IoT-assisted WSNs. ## 5 Conclusions

In this study, a new IMD-EACBR procedure has been designed to maximise the energy efficiency and lifetime of WSNs. At the primary level, the IoT nodes in the network are randomly placed and communicate with one another via information collection processes. Then, the presented IMD-EACBR technique primarily selects CHs and organises clusters using the IAOAC technique. Following this, the optimal selection of routes takes place using the TLBO-MHR technique. Once the optimal routes are identified, the CHs use optimal routes to transmit data to the BS. The recommended protocol makes use of an energy-saving method, in which optimum CHs are chosen on the basis of an improved search equation and an effective fitness function, as opposed to relying on a conventional search procedure. These processes make the protocol more effective. In order to demonstrate that the suggested protocol is valid across a range of presentation criteria, we compared its performance to that of other well-known cluster-based conventions. The design of IAOAC and TLBO-MHR techniques with multiple input parameters helps to achieve maximum network efficiency. The performance of the IMD-EACBR model has been examined in several aspects. The outcomes of the simulation experiments demonstrated the effectiveness of the enhancements of the IMD-EACBR technique over existing approaches. Among the technical limitations of the IMD-EACBR approach is the requirement for parameter tweaking. In the future, the energy efficiency of the IMD-EACBR technique may be further enhanced by data aggregation and sleep scheduling schemes. Figure 9: Cost function analysis of the IMD-EACBR technique compared to other methodologies. **Author Contributions:** Conceptualization, K.L. and N.S. ; organization, N.S. and Y.A. ; validation, N.S. and Y.A. ; formal analysis, K.L. and N.S. ; investigation, K.L. and N.S. ; resources, N.S. and A.K.N. ; data curation, K.L., S.A., and O.I.K. ; writing--original draft preparation, K.L. ; writing--review and editing, N.S. and Y.A. ; visualization, O.I.K. and S.A.; supervision, N.S. and Y.A. ; project administration, N.S. and Y.A.