## 4 Proposed Snake Optimizer
### Pseudocode and Operational Flow
Additionally, we acknowledge that the scenarios evaluated in this study, although sufficient for demonstrating the core behavior of the SO-based framework, remain simplified compared to real-world CRN deployments. To address this, we plan to explore larger-scale simulations (e.g., involving more than 50 channels and users) and evaluate the framework on publicly available or real-world CRN datasets, where possible, in future work. This will help validate the scalability and practical relevance of the proposed method in more complex and dynamic spectrum environments. ### Limitations

While the proposed SO demonstrates high spectrum utilization efficiency, low collision rates, and strong convergence behavior across the three test scenarios, it is important to acknowledge its limitations. The experimental setup involves relatively small-scale or \"toy\" CRN configurations with moderate numbers of users and channels. Consequently, the computational cost of SO, due to its population, based nature, and multiple fitness evaluations per iteration, is higher than that of simpler meta-heuristics such as PSO, especially as the problem dimensionality increases. Moreover, the current implementation of SO is sequential, which may limit its real-time applicability in large-scale or latency-sensitive CRN environments. Future work will focus on optimizing performance by integrating parallel computation strategies (e.g., multi-threaded or GPU-based evaluations). Additionally, we plan to explore hybrid methods that combine SO with deep reinforcement learning techniques to improve scalability, decision-making speed, and adaptability in more dynamic and complex CRN scenarios. ## 6 Conclusions

In this study, we explored the application of SO, a novel meta-heuristic algorithm inspired by the natural behaviors of snakes, for optimizing resource allocation in CRNs. Through a series of experiments across three distinct scenarios, each varying in the number of SUs, PUs, and available frequency bands, we demonstrated the optimizer's effectivenessin achieving high spectrum utilization efficiency, minimizing collision rates, and maximizing spectral capacity. The results indicate that SO consistently converges to near-optimal solutions, with performance improving as the number of iterations increases. Specifically, the optimizer achieved higher mean final fitness values, greater spectrum utilization efficiencies, and lower collision rates as the iteration count increased from 30 to 100. This trend was observed across all three scenarios, regardless of the network configuration, highlighting the robustness and adaptability of SO. In Scenario 1, with 10 SUs, 5 PUs, and 15 frequency bands, the optimizer achieved a maximum mean final fitness value of 14.50 after 100 iterations, with a spectrum utilization efficiency of 96.67% and a minimal collision rate of 0.05. Similarly, in Scenario 2, with 8 SUs, 4 PUs, and 12 bands, the optimizer reached a final fitness value of 11.80, achieving a spectrum utilization efficiency of 98.33% and a collision rate of just 0.03. In the more complex Scenario 3, with 12 SUs, 6 PUs, and 20 bands, the optimizer excelled by attaining a mean final fitness value of 19.80, with a spectrum utilization efficiency of 99.00% and an exceptionally low collision rate of 0.02. These findings underscore the potential of SO as a powerful tool for dynamic resource allocation in CRNs. Its ability to balance exploration and exploitation allows it to adapt effectively to varying network conditions, ensuring optimal performance in terms of spectrum management. The consistent improvement in results with increased iterations further suggests that SO can be fine-tuned to meet the specific demands of different CRN scenarios, making it a versatile solution for future wireless communication systems. Future work could focus on enhancing SO by integrating additional learning mechanisms, such as reinforcement learning, to further improve its adaptability and decision-making capabilities in real-time environments.