## 3 The Proposed Model
### Design of CEPOC Technique  
The CEPO's central notion is to derive information about issue resolution from EPO's budding behavior and to use that knowledge to guide EPO's evolution concurrently. Assume CEPO is designed to solve situations with minimum optimization:  
\[\min f(x_{i}) \tag{4}\]  
where \(x_{i}=(x_{i1},x_{i2},\ \ldots,x_{iD})\) represents the location of \(ith\) EPO in the \(D\)-dimension search region; \(x_{j}^{\min}<x_{ij}<x_{j}^{\max}\), \((j=1,2,\ \ldots,\ D)\). \(f\) ( ) denotes the objective function; and \(f(x_{i})\)signifies the objective value of the location \(x_{i}\). \(x_{j}^{\min}\) and \(x_{j}^{\max}\) represent the lower bound and upper bound of the location of emperor penguin in the \(jth\) dimensions, respectively [28]. The belief space of EPO population in the \(tth\) generation is determined as \(s^{t}\) & N\({}_{j}^{t}\), in which \(s^{t}\) implies situational knowledge components. N\({}_{j}^{t}\) denotes normative knowledge that represents the value space data for all parameters in the \(jth\) dimensions and \(tth\) generations. N\({}_{j}^{t}\) represents \(I\), \(L\), \(U\). \(\text{I}_{j}^{t}=[l_{j}^{t},\ u_{j}^{t}]\), whereas \(\text{I}_{j}^{t}\) denotes the interval of normative knowledge in \(jth\) parameter. The lower bound \(l_{j}^{t}\) and upper bound \(u_{j}^{t}\) are initiated based on the value range of parameters provided by the problems [29]. \(L_{j}^{t}\) characterizes the objective value of lower bound \(l_{j}^{j}\) of the \(jth\) dimension and \(U_{j}^{t}\) represent the objective value of upper bound \(u_{j}^{t}\) of the \(jth\) dimension. The acceptance functions are employed for selecting the EPO could directly impact the present belief space. In CEPO, the acceptance functions select the individual in proportion to 20% from the present population space for updating the belief space. Figure 2 illustrates the work flow of algorithm [30]. Situational knowledge \(s^{t}\) could be upgraded with upgrade functions:  
\[s^{t+1}= \begin{cases}x_{best}^{t+1}&\text{if }f\left(x_{best}^{t+1}\right)<f \left(s^{t}\right)\\ s^{t},&\ else,\end{cases}  \tag{5}\]  
where \(x_{best}^{t+1}\) represents the optimum location of EPO population space in the \((t+1)\)th generation [31]. Consider that the \(qth\) cultural individual, an arbitrary parameter \(\theta_{q}\) in the interval of zero and one, is generated. The \(qth\) cultural individual affect the lower bound of normative knowledge in the \(j\)th parameter if \(\theta_{q}<0.5\) is fulfilled. Normative knowledge N\({}_{j}^{t}\) could be upgraded with upgrade functions:  
\[l_{j}^{t+1}= \begin{cases}x_{qj}^{t+1},&if\ x_{qj}^{t+1}\leq l_{j}^{t}\text{ or }f\left(x_{q}^{t+1}\right)<L_{j}^{t}\\ l_{j}^{t},&\ else,\end{cases}  \tag{6}\]  
\[L_{j}^{t+1}= \begin{cases}f\left(x_{q}^{t+1}\right),&if\ x_{qj}^{t+1}\leq l_{j}^ {t}\text{ or }f\left(x_{q}^{t+1}\right)<L_{j}^{t}\\ L_{j}^{t},&\ else.\end{cases} \]  
The qth cultural individual affect the upper bound of normative knowledge in \(jth\) parameter if \(\theta_{q}\geq 0.5\) is fulfilled:  
\[u_{j}^{t+1}= \begin{cases}x_{qj}^{t+1},&if\ x_{qj}^{t+1}\leq u_{j}^{t}\text{ or }f\left(x_{q}^{t+1}\right)<U_{j}^{t}\\ u_{j}^{t},&\ else,\end{cases}  \tag{7}\]  
Figure 2: Workflow of CEPO algorithm. \[U_{j}^{t+1}= \begin{cases}f\left(x_{q}^{t+1}\right),&if\ x_{qj}^{t+1}\leq u_{j}^{t} \ or\ f\left(x_{q}^{t+1}\right)<U_{j}^{t}\\ U_{j}^{t},&else.\end{cases} \]  
Normative and situational knowledges could be employed for guiding EPO population development with the impact functions [32]. In CEPO, an election operator \(\beta\) is generated to affect the evolutional EPO population:  
\[\beta=\frac{\text{Max}_{\text{iteration}}-t}{\text{Max}_{\text{iteration}}} \tag{8}\]  
where \(\text{Max}_{\text{iteration}}\) represents the maximal numbers of iteration. Consider that \(ith\) EPO, an arbitrary parameter \(\lambda_{i}\) in the interval of zero and one is generated [33].