## 5 Experimental Analysis of the Cybersecurity Optimizer
### Description of the CEC2022 Benchmark Functions F1 to F12  
The CEC2022 benchmark functions, as outlined in Table 1, provide a comprehensive suite of test problems designed to evaluate the performance of optimization algorithms across a variety of problem landscapes. These functions encompass different types, including unimodal, multimodal, hybrid, and composition functions, each aimed at testing specific aspects of an optimizer's performance [53]. Unimodal functions assess an algorithm's exploitation capability, while multimodal functions test its exploration potential in avoiding local optima. Hybrid and composition functions, which combine features from the other categories, offer complex landscapes that challenge an algorithm's ability to balance exploration and exploitation dynamically. These benchmark functions are widely used by researchers to evaluate the efficiency, robustness, and adaptability of both novel and established optimization techniques in controlled yet challenging scenarios. The functions F1 to F12 used in this study are part of the widely recognized benchmark suite from the 2022 IEEE Congress on Evolutionary Computation (CEC2022). These benchmark functions are specifically crafted to rigorously assess the performance of optimization algorithms by presenting them with a wide range of problem types, each possessing unique characteristics. Each function represents a distinct class of optimization problems, differing in terms of modality, separability, and the inclusion of noise, thereby making them highly suitable for evaluating algorithms under varying and challenging conditions. \begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Category** & **Function Description** & **f\({}_{\text{min}}\)** \\ \hline F1 & Unimodal & Shifted and Fully Rotated Zakharov Function & 300 \\ \hline F2 & & Shifted and Fully Rotated Rosenbrock’s Function & 400 \\ \hline F3 & & Shifted and Fully Rotated Expanded Schaffer’s f6 Function & 600 \\ \hline F4 & & Shifted and Fully Rotated Non-Continuous Restrigin/’s Function & 800 \\ \hline F5 & & Shifted and Fully Rotated Levy Function & 900 \\ \hline F6 & & Hybrid Function 1 (N = 3) & 1800 \\ \hline F7 & Hybrid & Hybrid Function 2 (N = 6) & 2000 \\ \hline F8 & & Hybrid Function 3 (N = 5) & 2200 \\ \hline F9 & & Composition function 1 (N = 5) & 2300 \\ \hline F10 & & Composition function 2 (N = 4) & 2400 \\ \hline F11 & & Composition function 3 (N = 5) & 2600 \\ \hline F12 & & Composition function 4 (N = 6) & 2700 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Benchmark functions utilized in the 2022 IEEE Congress on Evolutionary Computation (CEC2022) [54]. The Unimodal Function F1, referred to as the Shifted and Fully Rotated Zakharov Function, represents a unimodal problem, characterized by a single global optimum. This function is designed to evaluate the exploitation capabilities of optimization algorithms, as they must efficiently converge to the global optimum without becoming trapped in local minima. The complexity of this function is heightened by the shifting and rotating of the search space, which hinders the algorithms from easily identifying the optimal search direction. The Multimodal Functions F2 to F5 represent optimization problems characterized by the presence of multiple local optima in the search space. These functions are designed to assess the exploration capabilities of algorithms, specifically their ability to avoid premature convergence to local optima and successfully locate the global optimum. F2 is the Shifted and Fully Rotated Rosenbrock's Function, a non-separable function that contains a narrow valley leading to the global minimum, thus requiring algorithms with strong search capabilities. F3, the Shifted and Fully Rotated Expanded Schaffer's f6 Function, is known for its sharp peaks and ridges, making it particularly challenging for algorithms to traverse the search space effectively.