## 5 Development of the Execution of the Proposed Algorithm
### Analysis of the Hybrid Modified Sine Cosine Algorithm Cuckoo Search Algorithm (HMSCACSA) Results
The selection of specific internal parameters should be emphasized due to the significant effect of the optimization algorithm's performance. Notably, the SCA exhibits sensitive parameter values, which could be fine-tuned to improve the capability of exploring optimal solutions in the global search domain. Three main parameters can be considered for tuning to obtain significant performance enhancements: (1) the reasonable value for a search agent (population) should be considered; (2) the convergence curve and problem dimensions must be taken into account in the selection of population values; and (3) the computational time might be compromised by high population values, which might also be redundant in the search process due to the increase in the number of iterations. Finally, four small fraction parameters (\(r_{1},r_{2},r_{3}\) and \(r_{4}\)) in the exploration and exploitation SCA algorithm were used to determine the placements of a new resolution, which may be towards or outwards from the destination points. To successfully solve the optimization using the HMSCACSA technique, five specific samples exhibited promising values to develop a strong potential selection. However, the adjustment of the selection parameters was a challenging task. Furthermore, constant values (nearer to the basic code) would display better results in the optimization of benchmark issues, which had a higher possibility of affecting the identification of a resolution, including the population (number of search agents) and dimension sizes, and the randomly selected parameter (value of investigation or utilization range). The details of the design specifications are presented in Table 6, along with the comparative results simulated by the F5 benchmark test function. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Population & 20, 30, 40, 50, 60 \\ Dimension & 20 \\ Range & 2 \\ Maximum Iterations & 500 \\ Dimension & 20, 30, 40, 50, 60 \\ Population & 60 \\ Range & 2 \\ Maximum Iterations & 500 \\ Range & 1.4, 1.8, 2, 2.2, 2.4 \\ Dimension & 20 \\ Population & 60 \\ Maximum Iterations & 500 \\ Dimension & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Parametric specification of population, dimension and range value for five samples with varied population sizes. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Function** & **PSOABC** & **PSOGWO** & **PSOGSA** & **MSCA** & **HMSCACSA** \\ \hline F1 & 0.0001039 & 0.0001096 & 0.0000915 & 0.0000968 & 0.0000700 \\ F2 & 0.0001039 & 0.0001197 & 0.0000993 & 0.0000967 & 0.0000682 \\ F3 & 0.0000939 & 0.0001126 & 0.0000938 & 0.0000904 & 0.0000665 \\ F4 & 0.0000974 & 0.0001140 & 0.0000947 & 0.000953 & 0 Figure 8 displays the convergence curves using different numbers of search agents (population), which were specified as 20, 30, 40, 50, and 60, with a dimension value of 20. It was found that the increase in population from 20 to 60 led to a higher convergence rate by a maximum of 7.4%. Based on the tuning of the experimental dimensional value, it was found that the low dimension value had the lowest optimal solutions compared to other values shown in Figure 9. The dimension values of the HMSCACSA were set at 20, 30, 40, 50, and 60, with the number of search agents set to 30. As a result, the convergence rate was reduced by a maximum of 37.86%. Four variables were used in the SCA for the tuning of \(r\) variables. In this case, \(r_{1}\) determined the action to be performed by the search agent between investigation and utilization. Although all stochastic algorithms consist of investigation and utilization, the balance of these algorithms is important. \(r_{2}\) determined the distance of the movement of the resolution, while \(r_{3}\) distributed a random weight, and \(r_{4}\) determined the formula to be applied between sine or cosine [51]. The resolutions in every iteration were assessed by the fitness function, while the algorithm distributed the ideal resolution acquired at the point of location.