## 5 Development of the Execution of the Proposed Algorithm
### Analysis of the Hybrid Modified Sine Cosine Algorithm Cuckoo Search Algorithm (HMSCACSA) Results  
The analysis of the HMSCACSA is presented in this section. The general concept is the utilization of the CSA and SCA, followed by the development of the emerging hybrid variant to create a new transformation as an alternative to the negative result through a one-to-one idea. This innovation indicates an effective enhancement of the SCA to create a stable investigation and utilization of the overall iterative search procedure. Furthermore, it also leads to a prompt gathering among diverse individuals until they develop a similarity to the global optimal individual at a fast rate. When the best global individual is confined in the local optima, other individuals would be drawn to the local optima, leading to premature convergence of the SCA. Through the LHS modification to the SCA, a set of random solutions from the function SCA is created by a random population using boundary numbers. Besides, the numbered boundary of all variables is based on the upper and lower number entered by the users to obtain the random population of X global optimum. The initialization function was replaced by the LHS procedure to develop a Latin hypercube sample of size N and a new value of X, which was equally administered on the unit square. During this process, the exploitation phases of SCA were gradually changed in the random solutions, while lower random variations were found compared to the variations in the investigation process. Through this process, the placement of solutions was updated to enable the search of space and to determine the optimal fitness values of the best index cuckoo nest using the solutions. These processes were reserved to update the ideal nest location and gain a new position. In the IEEE CEC 2014 [28] benchmark set, the F1 to F3 test functions were unimodal, while the F4 to F16 test functions were multimodal. Figure 5 shows that the proposed HMSCACSA exhibited the fastest convergence in two out of six test functions, namely, the F5 and F7 test functions. In the majority of the evaluations, the convergence exhibited a higher performance through the proposed HMSCACSA in comparison with the adjusted and original SCA. This enhancement was led by the characteristics of \begin{table}
\begin{tabular}{c c c} \hline \hline
**Function** & **Dim** & **Range** \\ \hline \(F_{1}(x)=\sum_{i}^{n}x_{i}^{2}\) & 20 & (–100,100) \\ \(F_{2}(x)=\sum_{i=1}^{n}\left|x_{i}\right|\) & \(+\prod_{i=1}^{n}\left|x_{i}\right|\) & 20 & (–10,10) \\ \(F_{3}(x)=\sum_{i=1}^{n}\left(\sum_{j=1}^{n}x_{j}\right)^{2}\) & 20 & (–100,100) \\ \(F_{4}(x)=max[x_{i}].1\leq i\leq n]\) & 20 & (–100,100) \\ \(F_{5}(x)=\sum_{i=1}^{n-1}\left[\begin{array}{c}100\left(x_{i+1}-x_{i}^{2} \right)^{2}\\ +(x_{i}-1)^{2}\end{array}\right]\) & 20 & (–30,30) \\ \(F_{6}(x)=\sum_{i=1}^{n}\left(\left[x_{i}+0.5\right]\right)^{2}\) & 20 & (–100,100) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Description of classical benchmark mathematical functions. MSCA hybridization with CSA, as the SCA has internal memory to retain the potential solutions and converge on a global optimization [26]. The MSCA comprises exploration capabilities to facilitate the access of optimum resolutions using LHS, while HMSCACSA consists of operators (sine, cosine, and Levy flight) to enhance the diversity of the population and its resistance to the local optima. Figure 6 presents the convergence curves obtained using the MSCA, HMSCACSA, PSOABC, PSOGWO and PSOGSA, which are presented in blue, green, cyan, black, and magenta smoothed lines, respectively. The performance graph approach is illustrated in a curvilinear way through an optimum focus point. The HMSCACSA was further compared with three existing metaheuristic hybrid algorithms--PSOGSA, PSOGWO, and PSOABC--using the F5 test function with a population of 30 and 20 dimensions and 1500 iterations.