## 3 The Proposed Model
### Design of MHR-GOA Technique  
Grasshoppers are classified as pests based on the damage they inflict on vegetation and crops. Rather than acting independently, the grasshopper organizes the world's largest swarms. Individuals' influence on a wind, swarm, food supply, and gravity all have an effect on swarm motion [41]. The GOA is a novel metaheuristic approach based on SI that is triggered by the greater range and abrupt movement of adult grasshoppers in a group as shown in Algorithm 1. The metaheuristic algorithm breaks the search technique into stages of exploitation and exploration. ```
Initialize  Start the swarms \(X_{i}(i=1,2,\ldots,n)\),  Initiate \(cmax\), \(cmin\) and maximal amounts of iteration;  Evaluate the fitness of every search agent;  T = optimal search agent;  while (\(l\leq Max\) amounts of iteration)  Upgrade c;  for every search agent  Regulate the distance amongst grasshopper in [1,4];  Upgrade the location of the present search agent;  Bring the present search agent back when it drives outside the boundary;  end for  Upgrade \(T\) when it has an optimal solution; \(l=l+1\);  end while  return \(T\);  End
```  
**Algorithm 1**Pseudo code of GOA  
The grasshopper's greater range and abrupt movements indicate the exploration stage, whereas the grasshopper's limited movements indicate the exploitation stage. [PERSON] et al., provides a numerical module for this behavior, which may be denoted as:  
\[x_{i}=S_{i}+G+A \tag{18}\]  
where \(x_{i}\) denotes the location of \(i\) grasshopper, \(S_{i}\) indicates the social interaction in a group, \(G\) represents the force of gravity performing on \(i\) grasshopper, and \(A\) signifies the wind direction. By extending \(S_{i}\), \(G\) & \(A\) in (1), the formula is given by:  
\[x_{i}=\sum_{j=1,j\
eq i}^{N}s\big{(}|x_{j}-x_{i}|\big{)}\frac{x_{j}-x_{i}}{d_{ ij}}-g\acute{e}_{g}+u\acute{e}_{w} \tag{19}\]  
where \(s(r)=fe^{-r/l}-e^{-r}\) denotes the function which stimulates the influence of social interaction and N represents amount of grasshopper. \(g\acute{e}_{g}\) indicates the extended \(G\) element, while \(g\) signifies gravitational force and \(\acute{e}_{g}\) denotes unit vector directing to the center of the earth. \(u\acute{e}_{w}\) represents the extended A element, \(u\) denotes the constant drift, and \(\acute{e}_{w}\) indicates the unit vector directing towards the wind direction. \(d_{ij}\) is the distance between the \(ith\) & \(jth\) grasshopper and is estimated as:  
\[d_{ij}=\big{|}x_{j}-x_{j}\big{|}\]  
Because grasshoppers swiftly locate their comfortable zone and exhibit poor convergence, the effects of wind and gravity are negligible in comparison to the interaction between grasshoppers [42]. This indicates that the numerical module must be modified as follows:  
\[x_{i}=c\left(\sum_{j=1,j\
eq i}^{N}c\frac{\text{ub}-\text{lb}}{2}s\big{(}|x_{ j}-x_{i}|\big{)}\frac{x_{j}-x_{i}}{d_{ij}}\right)+\hat{T}_{d} \tag{20}\]  
where \(ub\) & \(lb\) represents the upper and lower boundaries of the search space, respectively; \(T_{d}\) indicates value comparative to the target (optimal solution establish until now); and \(c\) de notes the reducing coefficient which balances the process of explorations and exploitations, that is denoted by:  
\[c=c_{\text{max}}-iter\ \frac{c_{\text{max}}-c_{\text{min}}}{\text{Max}_{\text{iter}}} \tag{21}\]  
where \(c_{\text{max}}\) denotes the maximal value (equivalent to one), \(c_{\text{min}}\) represents the minimal value (equivalent to 0.00001), iter indicates the present iteration, and \(\text{Max}_{\text{iter}}\) signifies the maximum number of iterations. The primary objective of MHR-GOA is to find a novel route from CHS to BS [43]. The novel paths are recognized with the help of MHR-GOA as FF metric i.e., comprised of NDE, RE, and DTBS. Initially, each FF defines appropriate solution to the executed problem. In routing, each FF indicates the transmission path in the cluster head to the SN. The significance of FF is associated with network locations of CH which are included in the SN [44].