## 3 The Proposed Model
### PTA-Based Route Selection in Group Communication  
In our proposed research work, the PTA is applied for the effective election of routes related to the group communication process. The plum is a fruit of the Prunus species, a genus of trees which also includes peach, cherry, nectarine, almond, and apricot trees [24]. Plum fruit has many health benefits. The proposed PTA was based on the CSO technique in the usage of Gaussian distribution to upgrade the flower location and the usage of random integers from the range between \(\mathit{the}(FR_{\text{max}})\) maximum fruitiness rate and the \((FR_{\text{min}})\) minimum fruitiness rate. The PTA was stimulated using the PSO technique in the expansion of the formula that updates the flower location. Another reason for inspiration is the GWO because of the fact that this equation considers the best and second-best place obtained. The PTA defines this position as the ripe and unripe locations, correspondingly. The input of PTA can be given as follows: D--the number of dimensions, I--the amount of iterations, FT--the fruitiness threshold, N--the amount of plums, \(FR_{\text{in}}\)--the minimal fruitiness rate, \(X_{\text{min}}\) and \(X_{\text{max}}\)--the maximal and minimum potential value of the location, RT--the ripeness threshold,\(e\)--\(a\) constant used to prevent division by zero, \(FR_{\text{max}}\)--the maximal fruitiness rate, and OF--the objective function. The output of PTA is \(p_{gbest}\), the global better  
Figure 2: Flowchart of SCA. plum location. \(N\) flower is initialized in \(D\)-dimensional search space with value ranges within \([\,X_{\text{min}},X_{\text{max}}]\):  
\[flowers= \begin{bmatrix}F_{1,1}^{0}&\cdots&F_{1,D}^{0}\\ \cdots&\cdots&\cdots\\ F_{N,1}^{0}&\cdots&F_{N,D}^{0}\end{bmatrix} , \tag{6}\]  
and \(N\) plums are initialized with the value of flower:  
\[plums= \begin{bmatrix}P_{1,1}^{0}&\cdots&P_{1,D}^{0}\\ \cdots&\cdots&\cdots\\ P_{N,1}^{0}&\cdots&P_{N,D}^{0}\end{bmatrix} =flowers. \tag{7}\]  
The fitness value of flowers and plums is calculated using OF, and the value of global better plum \(p_{gbest}\) is upgraded to the plum location that has a better fitness value. The instruction is implemented \(I\) times so that \(iter\) defines the values of the existing iteration. The ripe location Pipe is upgraded to the plum location with better fitness value, while the unripe location \(P_{unripe}\) is upgraded to the plum location with second better fitness value. The flower location can be represented as \(F_{i}^{iter}\), where \(i=1,N\) is upgraded. Consider the value of random integer \(r\) in \([0,1]\). When the \(r\) value is larger than or equivalent to \(FT\), the flower location can be upgraded as follows:  
\[F_{i}^{iter}=F_{i}^{iter-1}+random(PR_{\text{min}},PR_{\text{max}})\times \left(P_{i}^{iter-1}-F_{i}^{iter-1}\right), \tag{8}\]  
so that random \((FR_{in},FR_{ax})\) uniformly return a number ranging from \(FR_{\text{min}}\) to \(FR_{\text{max}}\). When the \(r\) value is lesser than \(FT\) and larger than or equivalent to \(RT\), the flower location can be upgraded as follows:  
\[F_{i}^{iter}=F_{i}^{iter-1}+2\times r_{1}\times\left(P_{ripe}-F_{i}^{iter-1} \right)+2\times r_{2}\times\left(P_{unripe}-F_{i}^{iter-1}\right), \tag{9}\]  
where \(r_{1}\) and \(r_{2}\) denote a random number within \([0,1]\), and \(P_{ripe}\) and \(P_{unripe}\) show the ripe and the unripe location, correspondingly. When the \(r\) value is lesser than \(RT\), the flower location can be upgraded using the following equation:  
\[F_{i}^{iter}=P_{i}^{iter-1}\times\left(1+\mathcal{N}\Big{(}0,\sigma^{2}\Big{)}\right), \tag{10}\]  
so that \(\mathcal{N}\big{(}0,\sigma^{2}\big{)}\) is a Gaussian distribution that has the standard deviation \(\sigma^{2}\) and mean 0 as follows:  
\[\sigma^{2}= \begin{cases}\frac{1,if\;OF\Big{(}P_{i}^{iter-1}<OF\big{(}P_{ripe} \big{)}}{\frac{OP\big{(}P_{ripe}\big{)}-OP\big{(}P_{i}^{iter-1}\big{)}if\;OP \big{(}P_{i}^{iter-e}\big{)}}{|OF\big{(}P_{i}^{iter-1}\big{)}|+e}},\text{ otherwise},\end{cases}