## 3 Proposed FP-SFOA-DQN-FL for Real-World Object Recognition in FL
### Object Recognition Using Proposed FP-SFOA  
The extracted feature \(F_{a}\) is subjected to the object-recognition stage, where objects are identified employing the DQN classifier. The training of DQN is efficiently conducted using the proposed FP-SFOA, which includes the incorporation of the FC concept with PO [26; 30] and SFOA [29]. i. Architecture of DQN  
A combination of deep learning (DL) and reinforcement learning (RL) was successfully used to introduce a fascinating network that surpasses all other neural networks, named DQN [37]. This DQN is very popular in solving most of the highly dimensional optimization problems. Moreover, this network consists of a deep convolution neural network for \(Q\)-function approximation, whereas mini-batches are employed for uneven training data. The remaining network parameters are utilized to estimate the \(Q\)-values of the next state. The architectural diagram of DQN is portrayed in Figure 5. The feature vector \(F_{a}\) is applied over DQN for a given state \(Nn\), \(jj\) vector of action value \(Q(Nn\), \(jj\); \(\theta)\), in which \(\theta\) shows the learning factor of DQN. In addition, the loss parameter of DQN is computed using the below expression:  
\[Loss_{ii}\left(\theta_{ii}\right)=E_{Nn,\,jj,\,\omega,\,Nn^{\prime}}\left[\left( L_{ii}-Q\left(Nn,\,jj,\,\theta_{ii}\right)\right)^{2}\right] \tag{35}\]  
where  
\[L_{ii}=\left(\omega_{ii}+\lambda\text{max}_{jj^{\prime}}\,Q\left(Nn^{\prime},\,jj^{\prime},\,\theta^{-}\right)\right) \tag{36}\]  
The obtained error is denoted as \(\text{Loss}_{ii}\) if the factor is \(\theta_{ii}\) Here, \(\theta^{-}\) refers to the factors of a partitioned target structure, and the online structure factors are specified as \(\theta_{ii}\). The gradient descent function is expressed in the following manner:  
\[\
abla_{\theta_{ii}}\,Loss_{ii}\left(\theta_{ii}\right)=E_{Nn,\,jj,\,\omega, \,Nn^{\prime}}\left[\left(L_{ii}-Q\left(Nn,\,jj;\,\theta_{ii}\right)\right) \
abla_{\theta_{ii}}\,Q\left(Nn,\,jj\right)\right] \tag{37}\]  
In order to discard the associated updates, both the experience replay and constant maximal volume are fed to DQN. Thus, the divergence problem is solved in an effective way, and the recognized object result obtained from DQN is illustrated as \(H_{a}\). 2. Training of DQN using FP-SFOA  
The parameters of DQN are optimally tuned using FP-SFOA; thus, the optimal solution for the recognized object result is attained. However, the introduction of hybrid algorithms results in superior performance with a high convergence speed that can easily solve the highly dimensional optimization problem. Fractional political position encoding  
This is used to determine the finest solution for a given optimization problem in a G-dimensional search area, such that \(G=\left[1\times\theta\right]\). Here, \(\theta\) refers to the learning parameter of DQN. Fitness function  
The fitness factor is employed to find the finest solution, which is described as the change in variation amongst the targeted result and outcome of DQN. \[\Im=\frac{1}{b}\sum_{a=1}^{b}\left[\tau_{a}-H_{a}\right]^{2} \tag{38}\]  
where \(b\) symbolizes the overall quantity of image samples, \(\tau_{a}\) is the targeted outcome, and the output of DQN is signified as \(H_{a}\). The algorithmic steps of FP-SFOA are the same as that of PSFOA, which is already elaborated under Section 3.1.2.