## 3 Proposed Algorithm
### Sine Cosine Algorithm  
In recent years, the SCA, a new metaheuristic method, has been proposed. SCA repeats certain random steps by selecting sine or cosine functions to discover the global optimum. Strong randomness patterns have been observed in SCA's search patterns. [PERSON] created SCA, a stochastic population-based optimisation metaheuristic technique. A system's parameters can be optimised by following a method or mathematical procedure to find the optimum values possible in the search space. SCA is a population-based algorithm that operates in two phases--exploration and exploitation--and starts with a set of random solutions. As part of the exploration phase, the algorithm generates a set of results that include unusually high-rate random outcomes, allowing it to identify potential places in the search space. The algorithm primarily highlights the incremental variations in random solutions during the exploitation phase [42]. The shifting positions for both phases are represented by the equation below.  
\[X_{i,j}^{t+1}=X_{i,t}+r_{1}^{t}\times\sin r_{2,j}\times\left|r_{3,j}Q_{d,j}^{ t}-X_{i,j}^{t}\right| \tag{57}\]  
\[X_{i,j}^{t+1}=X_{j,t}+r_{1}^{t}\times\cos r_{2,j}\times\left|r_{3,j}Q_{d,j}^{ t}-X_{i,j}^{t}\right| \tag{58}\]  
Equations (57) and (58) are combined to be applied as follows.  
\[X_{i,j}^{t+1}=\left\{\begin{aligned} & X_{i,t}+r_{1}^{t}\times\sin r_{2,j} \times\left|r_{3,j}Q_{d,j}^{t}-X_{i,j}^{t}\right|,\ r_{4,j}<0.5\\ & X_{j,t}+r_{1}^{t}\times\cos r_{2,j}\times\left|r_{3,j}Q_{d,j}^{ t}-X_{i,j}^{t}\right|,\ r_{4,j}\geq 0.5\end{aligned}\right. \tag{59}\]  
where \(t\) is the current iteration; \(Q_{d,j}^{t}\) is the target location in the \(j\)th dimension; \(X_{i,t}\) is the current solution at the \(t\)th iteration; and the random variables \(r_{1}^{t}\), \(r_{2,j}\), and \(r_{3,j}\) are all present. \(r_{4,j}\) is a random number between 0 and 1, and \(\mid\mid\) displays an absolute value.  
SCA has four main parameters--\(r_{1}^{t}\), \(r_{2,j}\), \(r_{3,j}\), and \(r_{4,j}\)--as shown by the aforementioned equations. The parameter \(r_{1}\) determines the subsequent location regions (or movement direction), which may be inside or outside the region between the solution and the destination. The parameter \(r_{2,j}\) specifies how far the movement should extend in either direction from the target. The value of the parameter \(r_{3}\) determines random weights for the destination to stochastically emphasise or deemphasise the role of the destination in determining the distance. The parameter \(r_{4}\) then alternates equally between the sine and cosine parts of  
Figure 6: EPSCA flowchart.  
Equation (59). The SCA algorithm creates a balance between exploitation and exploration by adjusting the sine and cosine ranges using Equation (60), which is written as follows:  
\[r_{1}^{t}=\mathrm{a}-\mathrm{t}\frac{a}{T} \tag{60}\]  
where \(T\) is the maximum number of iterations, \(a\) is a constant number, and \(t\) is the current iteration. Figure 7 provides a two-dimensional illustration of the effects of sine and cosine on Equations (57) and (58), which can be expanded to higher dimensions. The patterns of these equations allow a solution to reposition and guarantee exploitation of a region between two results, and they specify a domain between two results in a specified search domain. To regulate the exploration in a specific search domain, the optimisation approach should look outside the area that contains subsequent destinations. Figure 8 illustrates the cosine sine functions obtained when changing the amplitude range. Whether a location is within or outside is determined by the random integer \(r_{2,j}\), whose range is (0, 2) [42]. Figure 9 depicts the SCA flowchart.  
Figure 7: Sine and cosine effects on the forthcoming locality in Equations (57) and (58).