## 4 Proposed Methodology
### Cluster Head Selection
#### 4.1.3 Formulation of Fuzzy Criminal Search Ebola Optimization (FCSEO)  
* The Criminal search and Ebola optimization are novel algorithms which apply unique patterns for both exploration and exploitation. Both algorithms have their own advantages in solving the non-constrained statistical functions, but in the case of complex engineering problems, their performance often drops. * The main reason is the exploration-exploitation tradeoff achieved via a constant ratio (neighborhood parameter or best information of the prime suspect). Often the best individual in both the algorithm populations is the individual with the maximum fitness which often becomes trapped in the local minimum. * This is the major reason for premature convergence. These are the problems that affect the algorithm's convergence rate and accuracy, and it is overcome in this work using the FCSEO algorithm. The exploration and exploitation behaviors are controlled here using the fuzzy decision-making strategy. * A new support agent called a virtual individual is defined and included in the navigation process. The search behavior of the algorithm is constantly modeled using the fuzzy strategy based on a threshold value. * The search procedure (optimal cluster head selection and energy minimization) is improved by applying a nine-rule fuzzy policy and speeding up the convergence. * A virtual agent is introduced in the Ebola population to share every individual's experience and also provide a different search direction for the population in each iteration. * In this way, the individual in the population escapes the local minima and identifies some significant region in the search space [31]. The FCSEO algorithm gives equal chances to the individuals in the population to perform both exploration and exploitation in every iteration. Hence the CSO algorithm is used for local search and the Ebola algorithm is used for global search. * The virtual agent (\(B^{V}\)) is mainly induced inside the population instead of using the random interaction between the individuals in the population. According to the fitness function value, the direction of the individual in the population connected with the virtual agent is determined. * The new self-adaptive method formulated is known as the FCSEO algorithm where the search behavior is controlled using a fuzzy decision module. * The working of the FCSEO algorithm is shown in Figure 2 and the algorithm is formulated as shown below:\[B_{j}^{i+1}=B_{j}^{i}+\partial.\psi_{j}.\left(z_{1}^{2}\times G^{*}-B_{j}^{i} \right)+\beta.\overline{\partial}.\psi_{j}(z_{2}^{2}\times B_{j}^{A(i)}-B_{j}^{i}) \tag{21}\]  
Here, \(\overline{\partial}_{i}\) is given as \(1-\partial_{i}\) and  
\[\beta= \begin{cases}1&if\;f\left(B_{j}^{A(i)}\right)<f(B_{j}^{i})\\ -1&if\;f(B_{j}^{A(i)})\geq f(B_{j}^{i})\end{cases}  \tag{22}\]  
The \(j\)th individual in the population is represented as the \(j\)th subscript, \(\partial\) is the fuzzy decision factor, \(\overline{\partial}_{i}\) is the complementary value of \(\partial_{i},z_{1}\) and \(z_{2}\) are the two random numbers in the interval \([0,1]\), \(\psi_{j}\) is the growth rate in the Ebola optimization algorithm, and \(B_{j}^{A(i)}\) is the virtual agent used. The fuzzy tendency factor is mainly used to alter the search behavior of the Ebola and criminal search optimization algorithms. The nine fuzzy rules used in the proposed work illustrate the search behavior of the individual in the algorithm. Figure 2: Formulation of the FCSEO algorithm. A normalized objective function called \(G\) is introduced to ensure fairness in this algorithm and the \(G\) function for the \(j\)th individual in the population is stated below:  
\[G_{j}=\frac{f(B_{j})-f(G*)}{f(B_{worst})-f(G*)+\tau} \tag{23}\]  
In Equation (23), the \(j\)th object in the population is represented as \(B_{j}\), the worst individual in the population is represented as \(B_{worst}\), and the best solution is represented as \(G*\). A positive scalar value called \(\tau\) is used to control the zero-condition divergence.