## 6 Evaluated Algorithms  
A diverse array of optimization algorithms have been chosen (See Table 3) to provide a comprehensive comparison across various metaheuristic approaches. This selection is motivated by the need to evaluate the effectiveness, versatility, and robustness of different optimization techniques across a range of problem domains. The algorithms selected span several decades of development, beginning with foundational methods like the Genetic Algorithm (GA) introduced in the 1960s and the Simulated Annealing (SA) algorithm from the early 1980s, both of which have become standard benchmarks in the field of optimization. These classical algorithms have been widely studied and provide a solid reference point for evaluating newer methods. Our selection also includes some of the most influential and widely used swarm intelligence algorithms such as Particle Swarm Optimization (PSO), Grey Wolf Optimizer \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Dimensionality (\(D\)) & 10 \\ Search Range & \([-100,100]^{D}\) \\ Rotation & Applied to all rotated functions \\ Shift & Applied to all shifted functions \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Instance parameter Settings. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Population Size & 30 \\ Maximum Function Evaluations & 1000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Algorithm parameter. (GWO), and Whale Optimization Algorithm (WOA), which have demonstrated remarkable performance in solving complex optimization problems. These algorithms have been chosen not only for their proven efficacy but also for their varying strategies in exploring and exploiting the search space, thereby providing insights into how different mechanisms influence the optimization process. In addition to these, we have included several recent and innovative algorithms such as the Synergistic Swarm Optimization Algorithm (SSOA), Filled Lizard Optimization (FLO), Four Vector Optimizer (FVIM), and Chinese Pangolin Optimizer (CPO). These algorithms represent the latest advancements in metaheuristic optimization, incorporating novel mechanisms and hybrid strategies that potentially offer improved performance and faster convergence rates. By including these cutting-edge techniques, we aim to assess whether they can outperform or complement the established methods in terms of solution quality, computational efficiency, and adaptability to different problem landscapes. Furthermore, we have integrated a variety of nature-inspired algorithms like the Success History Intelligent Optimizer (SHIO), Remora Optimization Algorithm (ROA), and Sooty Tern Optimization Algorithm (STOA), each inspired by different biological and ecological phenomena. These algorithms introduce unique heuristics and search patterns that contribute to the diversity of approaches in our comparison. The Zebra Optimization Algorithm (ZOA), Dingo Optimization Algorithm (DOA), and Aquila Optimizer (AO) add further variety by bringing in concepts from animal behavior and ecological systems, which are particularly interesting for their balance between exploration and exploitation. By covering a wide range of algorithmic strategies, from evolutionary algorithms, swarm intelligence, and hybrid methods to algorithms based on ecological and animal behavior, we ensure that our comparative analysis is not only thorough but also reflective of the current state-of-the-art in optimization research. This diverse selection allows us to examine the performance of each algorithm under various scenarios, thereby identifying the most suitable techniques for different types of optimization problems. Additionally, by comparing these algorithms against both classical and contemporary benchmarks, we aim to provide valuable insights into their relative strengths and weaknesses, contributing to the ongoing development and refinement of optimization algorithms.