Heuristic Methods for Solving the Traveling Salesman Problem (TSP): A Comparative Study

The Traveling Salesman Problem (TSP) is an important NP-Hard combinatorial problem worth studying in Computer Science, Mathematical Optimization, and Operations Research. Heuristic methods are often employed in looking for a nearly-optimized solution for TSP. Common heuristic methods for solving the TSP are the Genetic Algorithm (GA), Ant Colony Optimization (ACO), Simulated Annealing (SA), and the Lin-Kernighan-Helsgaun (LKH) algorithm. Recent studies have combined the Reinforcement Learning (RL) methods with LKH to boost performance. However, little is known about the performance differences between the many heuristic methods given. Also, little is understood about the impact of the TSP landscape on the performance of the heuristic methods. In this paper, five heuristic methods of GA, ACO, SA, LKH, VSR-LKH are discussed. We employed four types of landscape instances from the TSPLIB to perform an empirical analysis of the five heuristics. For the TSP landscape instances tested, we find that the loss and convergence speed of the algorithms is not directly related to the dimension of the TSP instances but the landscape of the TSP instances instead.