## 3 Proposed Modified Sine Cosine Algorithm (MSCA)
### Adjustment of Sine Cosine Algorithm (SCA) Using Latin Hypercube Sampling (LHS)  
The SCA is a recently developed optimization strategy. Researchers have developed an interest in solving optimization problems because of their flexibility and simplicity. LHS has proven its validity results with large deviations in the context of built estimators and is a well-known sampling technique for variance reduction, as discussed in [44; 45; 46]. This method has been extensively applied due to its simple implementation and beneficial features. Specifically, only one sample in LHS is chosen in every column or row for every sub-hypercube [45], with \(n\) (initial sample size) points and \(d\) random variables denoted as \(X_{n\times d}=\left[x_{1}^{T},x_{2}^{T},\ldots x_{n}^{T}\right]^{T}\), where each row \(X_{i}=\left[x_{1},x_{2},\ldots x_{id}\right]\) represents a sample point as generated in [45]. To improve the SCA using LHS, it can be treated as space filling criteria to search the best combination of the sample matrix \(X_{n\times d}\). This sample provides a maximum and minimum number of search agents (population), \(N\). Different sampling algorithms using LHS in the SCA are slightly better than the original sample in terms of efficiency. This is because the proposed algorithm was optimized each time in the sample points. As an extension algorithm of LHS, the performance of MSCA is slightly superior compared to traditional SCA sampling. Figure 2 shows the random sample value of the SCA with and without LHS, and this example had a sample size of \(n=30\). The use of random points in the hypercube intervals (random LHS) relied upon the selection of the initial design in LHS. LHS increases the efficiency of these sampling strategies through the development of new algorithms based on the combination of innovative space-filling criteria and specialized optimization schemes. Algorithm 1 illustrates the pseudocode of the MSCA algorithm. The identification of the MSCA process initially led to a new category of random resolutions. Following the random initialization is the measurement of a category of random resolutions through the fitness function, which is the aim of the placement of location. When the fitness function of the initial population is evaluated, the most ideal resolutions would be regarded as those to be applied to identify the next resolutions. The targeted resolution was reached by MSCA through some iterations (generations). The update of the cosine and sine functions was made when the iteration counter increased. When the optimal solution (destination) for the particular domain of issue was achieved and the termination requirements were fulfilled, the algorithm ended. In this case, it was assumed that the set of SCA resolutions from LHS sampling in Equations (1) and (2) are the replacement of the new solution of \(X\). Following that, the calculation was updated in a certain range (\(r\) value). The efficiency of LHS samples into the SCA resulted in the fastest convergence of MSCA, which reflects the decreasing number of iterations (Figure 3). The aim of the proposed  
Figure 2: The random sample value of the Sine Cosine Algorithm (SCA) with and without Latin Hypercube Sampling (LHS). algorithm is to generate an additional sample matrix and optimize the matrix by exchanging the elements within the column. It is also demonstrated that the proposed algorithm exhibited good performance in efficiency and convergence compared to the traditional extension algorithms.