## 2 Methodology
### Optimal Bio-Inspired Algorithm  
The CH selection is obtained through the multi-criteria decision-making grid-based method. The optimal path is estimated using the optimal bio-inspired optimization algorithm. This methodology combines the MF algorithm [24; 25], and the SS algorithm [26] is utilized to obtain optimal routing path. The main phases of the optimal bio-inspired algorithms are initialization, fitness evaluation, updation of solution, and selection of optimal [27; 28]. _(i) Initialization_  
The path is routed between the CH and sink nodes as an initial approach to optimization. At first, only one CH is selected and the other CH is treated as a sink or intermediate path. Thus, all the possible paths are represented in Equation (9),  
\[K=K_{i},\ i=1,2,\ldots,p \tag{9}\]  
where, '\(K\)' provides the initial population set as provided in Equation (10), '\(K_{i}\)' describes the \(i\)th path among CH and destination, and '\(p\)' gives number of paths. \[K=\{R_{e}E,ND\} \tag{10}\]  
where '\(R_{e}E\)' represents the residual energy, and '\(ND\)' is distance among line. The \(\sigma R_{e}E\) is used to estimate characteristics of load distribution among the available sensor nodes and it equated as  
\[\sigma R_{e}E=\sqrt{\frac{1}{m}\sum_{i=1}^{m}\left[\frac{1}{m}\sum_{i=1}^{m}E_{ (node_{i})}-e(a,b)\right]^{2}} \tag{11}\]  
where '\(m\)' gives number of nodes present in path and '\(E_{(node_{i})}\)' represents residual energy of \(i\)th node. Euclidean distance measures distance between sender CH to destination and it is represented by Equation (12)  
\[dis=\sum_{i=1}^{m-1}\sqrt{\left[CH_{i}(x)+CH_{i}(y)-CH_{i+1}(x)-CH_{i+1}(y) \right]} \tag{12}\]  
where '\(CH_{i}(x)\)' and '\(CH_{i}(y)\)' give the x and y coordinate of \(i\)th path, respectively. Therefore, the energy efficiency is provided by formulating residual energy and minimization of distance amongst the path is provided by Euclidean distance. _(ii) Evaluation of fitness_  
The main reason for estimating the fitness is to obtain the optimal path with minimal energy and distance requirements. Hence, the objective function is based on the energy and distance on each path. \[F_{i}=min\{R_{e}E\times ND\} \tag{13}\]  
where '\(\text{F}_{i}\)' gives the fitness at the \(i\)th population, '\(R_{e}E\)' is the residual energy, and '\(ND\)' is the total distance. _(iii) Updation of Solution and selection of optimal_  
In this level, a path is either chosen or taken to revise the solution based on the fitness value. Here, the optimization is carried out by combining the moth search and SSO. A contemporary optimization technique, the MFO algorithm, was introduced in 2015. Since then, it has found extensive usage in both research and a variety of industrial fields. The moths are similar to butterflies, which maintain fixed angle concern to the moon. Getting the solution for the optimization problem depends on the position of the moth. The next optimization approach is based on the salps method. The salp algorithm navigates as two groups' heads and followers by using a jellyfish movement concept. These groups are worked together in swarms and search for food. The head of the salp will lead the group and the follower will follow the salp leader. Thus, this salp search algorithm utilizes the low-level nodes to get a high-level network. Once fitness is estimated, the population is ordered in ascending order, and an equal half of the total d population is updated through arranged levy flight as per moth search optimization and salp swarm rule optimization. The accelerating factor (AF) is defined as the ratio between high temperatures and lower temperatures. In this work, the AF value is chosen as 1.7 experimentally with an assumption, and assumed that the maximum step size should be greater than zero. The updation of the CH based on salp swarm optimization is equated as,  
\[Z_{T}^{i+1}= \begin{cases}\begin{array}{l}Z_{T}^{i}+\beta levy(s)i<\frac{m}{2} \\ \frac{1}{2}\Big{(}Z_{T}^{i+1}+Z_{T}^{i}\Big{)}otherwise\end{array}\end{cases}