## 3 Proposed Methodology
### Phase 5: Application of the Opposition Nelder-Mead Algorithm
If the generated number is less than or equal to the specified mutation rate, then add the mutation amount to the current value of the variable to obtain the mutated value. 3. Repeat steps 1 and 2 for all individuals in the population. The standard deviation parameter plays a crucial role in Gaussian mutation. A smaller standard deviation leads to smaller random perturbations, resulting in finer exploration and a higher likelihood of converging to a local optimum. Conversely, a larger standard deviation allows for larger random perturbations, promoting broader exploration and the potential to escape local optima. Gaussian mutation enables the exploration of the continuous search space in genetic algorithms by introducing random perturbations to the individuals. It provides a way to balance exploration and exploitation, aiding the algorithm's ability to search for optimal or near-optimal solutions in continuous domains. ### Time Complexity of the Proposed Methodology

In this section, we delve into the time complexity of the proposed methodology. The efficiency of the methodology is intricately tied to its various phases, namely Phase 2, Phase 3, Phase 4, Phase 5, and Phase 6. The time complexity analysis of each stage provides valuable insights into the overall performance of the methodology. By understanding the time complexities of these individual stages, we gain a comprehensive understanding of how the methodology scales with larger dimensions or more complex problems. Through this examination, we can assess the computational demands and make informed decisions regarding the feasibility and efficiency of implementing the proposed methodology in real-world scenarios. Table 1 provides a comprehensive summary of the time complexity associated with each phase of the proposed methodology. Finally, by computing the complexities of all phases, we can determine the global complexity of the methodology. It is worth mentioning that the time complexity of a function evaluation is \(\mathcal{O}(n^{2})\). \begin{table}
\begin{tabular}{l l} \hline \hline  & **Phase** & **Time Complexity** \\ \hline Phase 2 & \(\mathcal{O}(n^{3})\) \\ \hline Phase 3 & \(\mathcal{O}(n^{3})\) \\ \hline Phase 4 & \(\mathcal{O}(n^{3})\) \\ \hline Phase 5 & \(\mathcal{O}(n^{3})\) \\ \hline Phase 6 & \(\mathcal{O}(n^{3})\) \\ \hline
**Methodology’s time complexity** & \(\mathcal{O}(n^{3})\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Time complexity of the proposed methodology. ## 4 Experimental Results and Discussion

The workstation utilized for conducting the experimental study is equipped with a well-suited hardware and software configuration to support the required tasks. The workstation runs on a Windows 11 Home operating system, providing a user-friendly interface and compatibility with a wide range of software applications. The hardware configuration features an Intel(R) Core(TM) i7-9750H CPU, with a base frequency of 2.60 GHz and a maximum turbo frequency of 4.50 GHz. This high-performance processor ensures the efficient execution of computational tasks and data processing. Additionally, the workstation includes 16.0 GB of RAM, enabling the handling of complex calculations with ease. The software suite installed on the workstation consists of Matlab R2020b, a powerful programming language and environment for numerical computing and algorithm development. Furthermore, the IBM SPSS Statistics 26 software is also installed on the workstation, providing a comprehensive platform for statistical analysis and conducting various statistical tests. This combination of hardware and software configurations offers a robust and capable environment for conducting the experimental study, effectively facilitating data analysis, statistical modeling, and computational tasks.