In this paper, we introduce the Chaotic Dynamic Cat Swarm Optimization (CHDCSO) algorithm, an enhanced variant of the traditional Cat Swarm Optimization (CSO), to address the Traveling Salesman Problem (TSP). By integrating chaotic dynamics using logistic chaotic maps, the proposed algorithm aims to improve the balance between exploration and exploitation phases, thereby enhancing the global search capability and robustness of the optimization process. Detailed experimental analysis is conducted on various TSP datasets, comparing the performance of CHDCSO against established optimization techniques, including Particle Swarm Optimization (PSO), Differential Evolution (DDE), Transit Search, Random Optimization Algorithm (ROA), and Random Search Algorithm (RSA). The results demonstrate that the CHDCSO algorithm consistently outperforms these traditional methods in terms of convergence speed and solution quality. This study underscores the potential of chaotic dynamics in optimizing complex problems and highlights the CHDCSO algorithm’s efficacy in achieving superior optimization outcomes.