## 3 Proposed Methodology
### Trust Value Computation
#### 3.4.2 Extended Osprey Optimization Algorithm
Equation (20) is used to uniquely identify each search agent's collection of features. \[GL_{i}=\{P_{h}|h\in\{1,2,\ldots,N\}\wedge G_{h}<G_{i}\}\cup\{P_{best}\} \tag{20}\]  
Hence \(GL_{i}\) represents the feature locations of the \(i^{th}\) search agents, \(P_{best}\) indicates the best search agents' positions. The new position of the associated search agents is found by a simulation that involves the search agents' approaching feature. The objective function numerical value, which is provided in Equation (21), is increased by the search agent's new location. \[p_{i,j}^{L_{i}}=p_{i,j}+r_{i,j}.\big{(}SG_{i,j}-R_{i,j}.p_{i,j}\big{)} \tag{21}\]  
\[p_{i,j}^{L_{1}}=\left\{ \begin{array}{c}p_{i,j}^{L_{1}},\ \ Ib_{j}\leq p_{i,j}^{L_{1}}\leq ub_{j}\\ lb_{j},\ \ p_{i,j}^{L_{1}}<ub_{j}\\ ub_{j},\ p_{i,j}^{L_{1}}>ub_{j}.\end{array} \right. \tag{22}\]  
\[P_{i}=\left\{ \begin{array}{c}P_{i}^{L_{1}}\,\ G_{i}^{L_{1}}<G_{i};\\ P_{i},\ else\end{array} \right. \tag{23}\]  
where \(P_{i}^{L_{1}}\) indicates the new location of the \(i^{th}\) search agents in the initial stage, \(p_{i,j}^{L_{1}}\) represents the \(j^{th}\) vector, \(G_{i}^{L_{1}}\) represents the objective function rate, \(SG_{i}\) indicates an optimal feature of the \(i^{th}\) search agents, \(SG_{i,j}\) represents the \(j^{th}\) vector, and \(R_{i,j}\) represents the random variable range of \([0,1]\). Exploitation Stage  
The second phase of increasing the number of individuals in the OOA is based on a numerical simulation of the natural activities of search agents. Then, the search agent's position is altered by the simulation of moving the feature to the correct location. The local search area's OOA exploitation potential is enhanced by the search area, leading to improved possibilities that exceed the recognized ways through integration. According to the OOA technique, an appropriate location for the absorbing feature is first randomly selected for every individual in the group using Equation (24). \[p_{i,j}^{L_{2}}=p_{i,j}+\frac{lb_{j}+r_{.}(ub_{j}-lb_{j})}{t},\;\;i=1,2,\ldots,m,\;\;k=1,2,\ldots,K \tag{24}\]  
\[P_{i,j}^{L_{2}}=\left\{ \begin{array}{l}p_{i,j}^{L_{2}},\;lb_{j}\leq p_{i,j}^ {L_{2}}\leq ub_{j}\\ ib_{j},\;p_{i,j}^{L_{2}}<lb_{j}\\ ub_{j},\;p_{i,j}^{L_{2}}<ub_{j}\end{array} \right. \tag{25}\]  
This is used to increase the objective function's score in the current position, which modifies the related locations of the search agents, permitting Equation (26),  
\[P_{i}=\left\{ \begin{array}{l}P_{i}^{L_{2}},\;G_{i}^{L_{2}}<G_{i};\\ P_{i},\;else\end{array} \right. \tag{26}\]  
where \(P_{i}^{L_{2}}\) represents the location of the \(i^{th}\) search agents in the second sage, \(P_{i,j}^{L_{2}}\) represents the \(j^{th}\) vector, \(G_{i}^{L_{2}}\) indicates the objective function value, \(r_{i,j}\) represents a random variable in the range [0, 1], \(K\) represents the number of iterations, and \(k\) denotes iteration area. The proposed model frequently produces training errors, because the hyper parameters are difficult to learn. Thus, to resolve these issues, the opposition-based learning (OBL) approach uses the extended osprey optimization (Ex-OOA) algorithm to optimize the hyperparameters of the proposed model. The OBL method uses the fitness function \(f\) value to determine whether the current choice is better or not. A different value \(\overline{p}\) for the true value \(p\in[v,l]\) is adopted in the fundamental definition of OBL, and this value can be found using the following formula:  
\[\overline{p}=v+l-p \tag{27}\]  
The description can be extended to n dimensions using the following formula:  
\[\overline{p}_{i}=v_{i}+l_{i}-p_{i},\;i=1,2,\ldots,N \tag{28}\]  
where \(p\in R^{n}\) denotes the real vector and \(\overline{p}\in R^{n}\) represents the opposite vector. During the optimization phase, a comparison is also made between the two responses \(p\) and \(\overline{p}\). The better of two options is stored and the other is eliminated through the evaluation of the fitness function.