Metaheuristics for Finding Shortest Hamiltonian Path between Iranian Cities Using Sequential DOE Approach for Parameters Tuning

A Hamiltonian path is a path in an undirected graph, which visits each node exactly once and returns to the starting node. Finding such paths in graphs is the Hamiltonian path problem, which is NP-complete. In this paper, for the first time, a comparative study on metaheuristic algorithms for finding the shortest Hamiltonian path for 1071 Iranian cities is conducted. These are the main cities of Iran based on socialeconomic characteristics. For solving this problem, four hybrid efficient and effective metaheuristics, consisting of simulated annealing, ant colony optimization, genetic algorithm, and tabu search algorithms, are combined with the local search methods. The algorithms’ parameters are tuned by sequential design of experiments (DOE) approach, and the most appropriate values for the parameters are adjusted. To evaluate the proposed algorithms, the standard problems with different sizes are used. The performance of the proposed algorithms is analyzed by the quality of solution and CPU time measures. The results are compared based on efficiency and effectiveness of the algorithms.