## 3 The Proposed Model
### Design of CEPOC Technique
The initial manner is to upgrade the location of EPO by altering the search size and direction of the variations using belief space that can be executed while fulfilled \(\lambda_{i}\leq\beta\). The location of EPO in the \(jth\) parameter will be upgraded as follows  
\[x_{ij}^{t+1}= \begin{cases}x_{ij}^{t}+\left|\text{size}\left(\text{I}_{j}^{t} \right)\cdot N(0,1)\right|,&if\ x_{ij}^{t}<s_{j}^{t},\\ x_{ij}^{t}-\left|\text{size}\left(\text{I}_{j}^{t}\right)\cdot N(0,1)\right|,&if\ x_{ij}^{t}>s_{j}^{t},\\ x_{ij}^{t}+\eta\text{-size}\left(\text{I}_{j}^{t}\right)\cdot N(0,1),&else, \end{cases}  \tag{9}\]  
where \(N(0,\ 1)\) represents an arbitrary value subject to the standard distribution [34]. The size \(\left(\text{I}_{j}^{t}\right)\) means the length of adaptable range of \(jth\) dimension in belief space in \(tth\) generation. \(\eta\) is fixed between the interval [0.01, 0.6]. Another approach is using a sequence of phases in EPO, i.e., the temperature profile around the huddle computing, the huddle boundary generation, the position update of emperor penguins, and the distance calculation between emperor penguins, which would be brought while fulfilled \(\lambda_{i}>\beta\). The certain phases could be denoted in the following equation:  
\[T^{\prime}=T-\frac{t-\text{Max}_{\text{iteration}}}{\text{Max}_{\text{iteration}}} \tag{10}\]  
\[T= \begin{cases}0,&\text{if }R\geq 0.5\\ 1,&\text{if }R<0.5\end{cases} \]  
where \(T^{\prime}\) denotes the temperature profile around the huddle, \(T\) indicates the time to find an optimum solution, and \(R\) signifies an arbitrary parameter in the interval of zero and one. \[\text{D}_{\text{ep}}^{t}=S_{\text{ep}}\left(A^{t}\right)\cdot\text{x}_{\text {best}}^{t}-B^{t}\cdot\text{x}_{i}^{t} \tag{11}\]  
where \(\text{D}_{\text{ep}}^{t}\) indicates the distance between the EPO and optimum solutions, \(\text{x}_{\text{best}}^{t}\) denotes the present optimum solution attain in EPO population space in the \(tth\) generation, \(S_{\text{ep}}\) represent the social force of the EPO which is accountable for convergence towards the best solution, \(A^{t}\) & \(B^{t}\) are employed for avoiding the collisions between adjacent EPO, and \(B^{t}\) denotes an arbitrary parameter in the interval of zero and one [35]. \(A^{t}\) could be calculated by:  
\[A^{t}= \begin{pmatrix}M\times\left(T^{\prime}+P_{\text{grid}}^{t}\left(Accuracy \right)\right)\times rand\ ()\end{pmatrix} -T^{\prime} \tag{12}\]  
where \(M\) denotes the motion variable that holds a gap among EPOs for avoiding collisions and \(P_{\text{grid}}^{t}\) (Accuracy) determines the accurate variance by relating the differences between the EPOs. \(S_{\text{ep}}\left(A^{t}\right)\) in Equation (11) is calculated by:  
\[S_{\text{ep}}\left(A^{t}\right)=\sqrt{\varepsilon\cdot e^{-t/\rho}-e^{-t}} \tag{13}\]where \(e\) is the base of natural logarithm. \(\varepsilon\)\(\&\)\(\rho\) represent the 2 control variables for improved exploitation and exploration within the interval of [1.5, 2] and [2, 3], respectively. Finally, the location of EPO is upgraded by:  
\[x_{i}^{t+1}=x_{\text{best}}^{t}-A^{t}\cdot\text{D}_{\text{ep}}^{t}. \tag{14}\]  
In the CEPO algorithm, a \(M\times N\) grid of sensor nodes can be generated in a geographical area [36]. Each sensor in a mesh network is assigned a unique ID, and these sensors are referred to as penguins. On the basis of this penguin, a search space is formed. The distance between each node is calculated and stored in a matrix using Euclidean distance [37]. The search space is parameterized by the dimension, as well as the lower and upper limits. Each penguin's fitness value is determined by its location in the search space. The fitness matrix is used to track each penguin's fitness level. Due to the repetitive nature of this process, the estimated fitness value is stored in a matrix on each iteration, and such matrices supply penguins with a low fitness value.