## 4 Proposed Methodology
### Pull Requests' Duplicate Detection  
Duplication pull requests go through the standard evaluation procedure up until the reviewers recognize their duplicate relation. Duplicate pull requests are common, according to earlier studies, and these issues have an impact on how efficiently work proceeds. We order the historical pull requests based on the combined similarity after computing the combined similarities between the historical and new pull requests. To determine whether any new pull requests duplicate any previously proposed pull requests, we suggest the top \(k\) items within the rated pull requests as candidate duplicates. Here, we introduce a hybrid deep learning technique, i.e., GAN-GS for pull-request duplicate detection. The layers of the GAN consist of two main parts. In order to create a sample of fake data that might confuse another neural network, the generator approximates the distribution of genuine data, whereas the discriminator determines if the sample creation was done from fake or real data. It is difficult to explain whether the sample is fake or real if precisely the generator shows the real data distribution. GANs are neural networks designed to become more effective by repeated resolving of a two-player minimax game issue. Loss function instructs the generator and discriminator,  
\[\min_{H}\max_{d}\,v(H,d)=E_{y\sim qdata(y)}[\log d(y)]+E_{z\sim qz(y)}[\log d(1 -d(H(z)))], \tag{31}\]  
where, \(q_{z}(z)\) is a latent vector \(y\) taken from a data distribution, which is normal or uniform, which is given to generator \(H\) to produce a data point H(z). The main objective function is used to optimize the hyperparameters that show the relative weighting of the margin loss in the enhanced adversarial loss compared to the baseline adversarial loss. Then, the margin loss is applied to avoid mode collapse and training instability as follows:  
\[v_{k}=Capsule\,d(y_{k}) \tag{32}\]  
\[ \begin{array}{l}l_{m}=\sum\limits_{K=1}^{k}S_{K}\max(0,\,M^{+}-||v_{K}||)^{ 2}\\ +\lambda(1-S_{K})\max(0,\,||v_{K}||-m^{-})^{2},\end{array}  \tag{33}\]  
where \(v_{k}\) represents the input to the model in our framework and \(y_{k}\) represents the final layer's output vector. Here, \(H\) tries to provide some examples that most closely fuse domain X features, and \(d_{1}\) and \(d_{2}\) make an effort to distinguish between translated and original images X. The generator has two fully linked layers and deconvolution layers, and batch normalization was utilized to improve learning efficiency for all other levels except the output layer. Except for the last output layer, we used the group search (GS) method as an activation function for the other layers. We used the hyperbolic tangent function to line up the range of pixels in the final output layer with the output value of the final image. The distance function given by the below equation, which tells how far apart two places are and has the most general type of distance \(l_{q}\),  
\[||y-x||_{q}=\left(\sum\limits_{j=1}^{N}|y_{j}-x_{j}|^{q}\right)^{1/q}. \tag{34}\]  
This is frequently employed when \(p\) is 0, 2, and \(\infty\). \(l_{0}\) counts the number of non-zero components, or the number of updated data points, \(l_{1}\) denotes the distance in Euclidean space between the two points y and x, which is the root mean squared error, and Q denotes the biggest change in all data points when it is infinite. Routing is the process of determining the best route for sending traffic flows between source and destination nodes. Prior to the routing problem formulation, we first present the network utility function of the flow set \(f^{(k)}\). Then,  
\[U_{K}(T)=\sum\limits_{F\in F^{(K)}}\sum\limits_{p\in P^{(K)}}y_{pf}(T)[\alpha \cdot G_{p}(T)-\beta\cdot T_{p}(T)] \tag{35}\]  
is denoted as path \(p\)'s end-to-end latency over the time slot. Here, the throughput is \(G_{p}(T)\) for path \(p\) at\(\tau\), \(\alpha\) and \(\beta\), which are constant coefficients formed by traffic flow needs.