## 4 Proposed Snake Optimizer
### Pseudocode and Operational Flow
Although this study uses fixed values for the constants \(c_{1}\), \(c_{2}\), and \(c_{3}\), which control aspects of food quantity scaling, exploration movement, and exploitation intensity, respectively, their influence on the algorithm's behavior is significant. The constant \(c_{1}\) modulates the transition between exploration and exploitation by shaping the exponential decay of food availability; higher values can lead to earlier exploitation onset. The parameter \(c_{2}\) controls the step size during exploration, affecting the diversity of the search, while \(c_{3}\) determines the aggression of movements toward optimal solutions in the exploitation phase. Preliminary tests suggest that increasing \(c_{2}\) slightly improves exploration breadth but may delay convergence, while higher \(c_{3}\) accelerates convergence but risks premature convergence. A full sensitivity analysis of these parameters will be considered in future work to further optimize performance. ### On the Scalability Evaluation with More than 30 Bands

To further evaluate the scalability and robustness of SO, we extended the simulation scenarios to include more than 20 frequency bands (denoted as Scenario 4). These expanded experiments help assess the optimizer's performance under increased spectrum complexity, which naturally introduces a larger search space and a higher probability of interference. In Scenario 4, the number of available bands was increased to 30. As anticipated, the optimizer required slightly more iterations to converge, and the final fitness values were modestly lower than in less complex scenarios due to the increased allocation challenges. Nevertheless, spectrum utilization efficiency remained high, and the collision rate was consistently low, demonstrating the algorithm's adaptability to more demanding spectrum environments. To address runtime performance, the average raw execution time for each run in Scenario 4 was approximately 1.8 s for 30 iterations, 2.9 s for 50 iterations, and 5.6 s for 100 iterations. All simulations were performed on a system with an Intel Core i7 (3 rd Gen), 8 GB RAM, and 6 MB L3 cache. These runtimes confirm the practicality of the Snake Optimizer even in dense spectrum settings. The results from Scenario 4 affirm the SO's ability to sustain strong performance metrics in more complex allocation environments. Despite the increased number of bands, the algorithm continued to deliver efficient and collision-aware spectrum usage, highlighting its suitability for dynamic and high-density cognitive radio networks. ### Scalability Comparison in High-Band Scenario (30 Bands)

To further evaluate the scalability and robustness of SO, we conducted experiments under Scenario 4, which involves 30 frequency bands that is a setup representing a highly complex and dense spectrum environment. The performance of SO was compared with four widely adopted optimization techniques: PSO, GA, ABC, and Q-Learning. Table 4 presents a comparative summary of key performance indicators, including convergence speed, spectrum utilization, and interference resilience. As shown in Table 4, SO demonstrates superior performance across all evaluation metrics. It achieved the highest mean fitness and spectral capacity, reflecting more effective spectrum allocation. Furthermore, SO converged faster than all compared methods, requiring fewer iterations on average. The spectrum utilization efficiency was highest for SO, accompanied by the lowest observed collision rate, indicating its robustness in managing interference. While PSO and ABC delivered competitive results, they exhibited slower convergence and marginally higher collision rates. GA performed slightly worse in terms of stability and overall efficiency. Q-Learning showed limited scalability in this complex environment, with the highest collision rate and the slowest convergence. These results confirm that SO is highly scalable and well-suited for dynamic, large-scale cognitive radio scenarios.