## 3 Proposed Methodology
### Trust Value Computation
#### 3.4.2 Extended Osprey Optimization Algorithm  
This study proposes an OOA that is a metaheuristic algorithm that is effective in performing the search process in both the global and local problem-solving space to produce a satisfactory solution [34]. There are two stages: exploration and exploitation stages. The capacity of the system to locate the primary suitable region and avoid local optima is improved by combining the global search phase and integrating the idea of exploration. Then, the capability of the approach to arrive at probable superior options in promising regions increases as a result of the search process from the local scale using the possibility of exploitation. Here, the OOA determines the optimal path based on parameters such as link-stability degree and node-stability degree in Equations (14) and (15). \[C_{ij}=\lambda_{1}LQ_{ij}+\lambda_{2}X_{ij}+\lambda_{3}S_{ij} \tag{14}\]  
where, \(C_{ij}\) represents link stability from \(i\) and \(j\), \(X_{ij}\) indicates safety degree, \(\lambda_{1},\lambda_{2},\lambda_{3}\) represent weighting vector, \(LQ_{ij}\) represents link quality, and \(S_{ij}\) denotes factor for predicting mobility. \[V(Y)=\left(\sum_{h}\frac{Y_{h}^{2}}{n}\right)-\left(\sum_{h}\frac{Y_{h}}{n} \right)^{2} \tag{15}\]  
Hence, \(V(Y)\) represents variance, \(h\) denotes the total quantity of nodes, \(Y_{h}\) represents the message level acquired from every adjacent node. The fitness is obtained using Equation (16),  
\[fitness\ value=\max(\text{Node stability degree }+\text{ Link stability degree}) \tag{16}\]  
Initialization  
The OOA describes a population-based strategy that utilizes the benefit of the searching ability of population members in the area of problem-solving to identify a feasible solution over a replication-based approach. As an individual of the OOA population, every search agent determines the ranges of variables related to their specific location within the search region. Consequently, every search agent is a possible fix for the problem, represented statistically by a vector. All search agents comprise an OOA populace, which is given in Equation (17). When the OOA is initially applied, Equation (18) is used to initialize at random search agents' locations in the search area. \[p=\left[ \begin{array}{c}p_{1}\\ \vdots\\ p_{2}\\ \vdots\\ p_{n}\end{array} \right]_{N\times M}=\left[ \begin{array}{c}p_{1,1}\ \cdots\ \ p_{1,j}\cdots\ \ p_{1,m}\\ \vdots\ \ddots\ \vdots\ \cdots\ \vdots\\ p_{i,1}\ \cdots\ \ p_{i,j}\ \cdots\ \ p_{i,m}\\ \vdots\ \cdots\ \vdots\ \ddots\ \vdots\\ p_{N,1}\ \cdots\ \ p_{N,j}\ \cdots\ p_{N,M}\end{array} \right]_{N\times m} \tag{17}\]  
\[p_{i,j}=lb_{j}+r_{ij}.\big{(}ub_{j}-lb_{j}\big{)},\ \ i=1,2,\ldots,N.\ \ j=1,2, \ldots,m. \tag{18}\]  
Hence, \(p\) indicates search agents' positions, \(p_{i}\) represents the \(i^{th}\) search agents, \(p_{i,j}\) indicates the \(j^{th}\) dimension, \(N\) represents the number of search agents, \(M\) denotes the problem variable, \(r_{ij}\) indicates a random variable in the range between \([0,1]\), \(lb_{j}\) represents the lower bound, and \(ub_{j}\) indicates the upper bound. Equation (19) can be utilized to represent the objective function as a set of vectors. \[G=\left[ \begin{array}{c}G_{1}\\ \vdots\\ G_{i}\\ \vdots\\ G_{N}\end{array} \right]_{N\times 1}=\left[ \begin{array}{c}G(P_{1})\\ \vdots\\ G(P_{i})\\ \vdots\\ G(P_{N})\end{array} \right]_{N\times 1} \tag{19}\]  
where \(G_{i}\) represents the objective function of the \(i^{th}\) search agents, and \(G\) denotes the range of objective function. Exploration Stage  
The base for the initial level of the OOA population-updating system is produced by simulating search agents' natural behavior. The OOA explores capacity in the search region, enabling the identification of the ideal position while avoiding the local optimum. The positions of different search agents within the search area that provide a higher objective function score are measured to be less than ideal for each search agent regarding the overall area.