Comparative Analysis of Metaheuristic Algorithms for Solving The Travelling Salesman Problems

This study presents a comprehensive comparative analysis of nine state-of-the-art metaheuristic optimization algorithms applied to the classical Traveling Salesman Problem (TSP), a fundamental benchmark in ‎combinatorial optimization. The selected algorithms—Ant Colony Optimization (ACO), Lion Algorithm ‎‎(LA), Cuckoo Search (CS), Grey Wolf Optimizer (GWO), Vibrating Particles System (VPS), Social Spider ‎Optimization (SSO), Cat Swarm Optimization (CSO), Bat Algorithm (BA), and Artificial Bee Colony ‎‎(ABC)—are evaluated on three standardized TSPLIB benchmark instances: berlin52, eil76, and pr1002. ‎The evaluation framework encompasses multiple performance metrics, including best-found cost, mean ‎solution quality, standard deviation, and convergence behavior, over 30 independent runs per instance. ‎The results offer empirical insights into each algorithm’s strengths, limitations, and scalability across ‎problem sizes. Notably, ACO, GWO, and CSO demonstrate superior balance between solution accuracy ‎and robustness, making them promising candidates for large-scale combinatorial problems. This work not ‎only provides an up-to-date performance landscape of leading swarm-based and evolutionary metaheuristics but also guides algorithm selection for real-world optimization applications requiring adaptability ‎and computational efficiency‎.