## 4 Comparative Analysis and Results  
In this study, the efficiency and execution of the proposed work are correlated with the methods based on the algorithms of machine learning (ML) and routing protocols. The simulation parameters used for the analysis of wireless sensor networks are depicted in Table 1.  
The results obtained for the proposed methodology and the performance evaluation and comparison with other studies are discussed in this section. The energy consumed for data transfer, the data transfer rate, the computation time, and the criteria of the first dead node end-to-end delay and throughput are compared. Figure 2 shows the comparative analysis between the proposed method and other studies for the average residual energy spent on the number of rounds. Residual energy is the total amount of energy depleted in each stage of the nodes. The outcomes of the simulation graphs signify that the proposed method has better recorded residual energy than Optimal Cluster-Based Routing (CBR). Compared with k-means, Chain-Based Hierarchical Routing Protocol (CHIRON), and Low-Energy Adaptive Clustering Hierarchy Centralized (LEACH-C) protocols, the proposed method has an increased lifespan. This is mainly due to the quicker optimum solution techniques of the combined GWO-DFO technique. An improved k-means algorithm is used to choose a cluster head and transform it into a chain route in a network just after the threshold value is larger than the node energy. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline
3D area & \(100\times 100\times 50\) m \\ \hline Simulation time & 3600 s \\ \hline No. of nodes & 100 \\ \hline No. of layers & varied from 1 to 9 \\ \hline Transmission range & 30 m \\ \hline Routing protocol & Leach \\ \hline Type of antenna & Omnidirectional \\ \hline Message rate & 1 packet/s \\ \hline Size of message & 38 bytes \\ \hline Energy model & Generic \\ \hline Transmit circuitry power consumption & 24.75 mW \\ \hline Receive circuitry power consumption & 13.5 mW \\ \hline Idle circuitry power consumption & 13.5 mW \\ \hline Sleep circuitry power consumption & 0.05 mW \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters used for the analysis of wireless sensor networks. Figure 2: Comparative analysis between the proposed methods and several other methods. Another method is a basic clustering algorithm termed clustering by k-means that belongs to an unreasoned approach of clustering. The estimation of the mean value (1, 10) as a centroid is estimated by partitioning the provided node set into k-clusters. The steps involved in the k-means algorithm are as follows:  
* The selection of k points non-specifically as a centroid in which k is considered to be a number of clusters. * Allocate every node to the nearest median (centroid) by using Euclidean distance to produce clusters. * Calculate the latent centroid for each cluster. * The repetition of the last two steps is performed until no fluctuation occurs in the centroid of each cluster. By eliminating some sensors in a network, this method extends its useful life while also improving performance metrics. Another protocol implemented here is a chain-based routing approach called the Chain-Based Hierarchical Routing Protocol (CHIRON) used to reduce several defects related to the data dissemination delay. In the initial stage, the segregation of the network causes various fan-shaped fragments to occur. The base station supplies the control message to each individual node in a group and helps the node determine the group it belongs to. The second step involves far-away nodes available from a base station activated to produce group chains inside a single group. A greedy algorithm is implemented to find the nearest node associated with a node that converts to a new node, which starts the consecutive association levels. The leader/head node is elected in the third level or step and the distant node away from the base station is the head in a community chain.