Performance Evaluation of Heuristic and Meta-Heuristic Algorithms on Large-Scale Travelling Salesman Problem Instances

The Travelling Salesman Problem (TSP) is a well known method for the optimisation problem that asks you to find the shortest route that visits each city in a set exactly once and then goes back to the starting point. Owing to its classification as an NP-hard problem, generating optimal solutions for large instances remains computationally challenging. To address this, researchers have frequently applied heuristic and metaheuristic algorithms to obtain near-optimal solutions within reasonable time constraints. This study looks at how well a few heuristic methods work, like Nearest Neighbour, Farthest Insertion, and Minimum Spanning Tree (MST) Approximation. It also looks at how well some metaheuristic methods work, like Simulated Annealing (SA), Genetic Algorithm (GA), and Ant Colony Optimisation (ACO). Heuristic methods are generally faster and require fewer computational resources but may compromise solution quality. In contrast, metaheuristic algorithms tend to achieve better accuracy, particularly in large problem instances, albeit with higher computational demands. The comparative analysis was conducted on TSP datasets comprising 50, 100, 200, and 1000 cities. The results show that the MST Approximation algorithm works well for smaller problems and takes a reasonable amount of time to compute. But it doesn’t work as well for larger datasets when it comes to accuracy. On the other hand, ACO demonstrates strong performance across all test cases by consistently producing near-optimal solutions, especially in large-scale problems, but at the cost of increased computational effort. The standard benchmark dataset TSPLIB-eil51, kroA100, kroA200, and pr1002 has been taken into consideration to validate the results. This validation ensures consistency and comparability and offers practical insights into selecting appropriate solution strategies for the TSP based on the trade-offs between speed, accuracy, and available computational resources.