74 International Journal of Applied Metaheuristic Computing, 2(2), 74-92, April-June 2011
Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
Keywords: Design of Experiments, Hamiltonian Path, Iranian Cities, MetaheuristicAlgorithms, Traveling
Salesman Problem
DIMMA-Implemented
Metaheuristics for Finding
Shortest Hamiltonian Path
Between Iranian Cities Using
Sequential DOE Approach
for Parameters Tuning
Masoud Yaghini, Iran University of Science and Technology, Iran
Mohsen Momeni, Iran University of Science and Technology, Iran
Mohammadreza Sarmadi, Iran University of Science and Technology, Iran
ABSTRACT
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 frst time, a comparative study on metaheuristic algorithms for fnding the shortest Hamiltonian
path for 1071 Iranian cities is conducted. These are the main cities of Iran based on social-economic charac-
teristics. For solving this problem, four hybrid effcient 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 algo-
rithms, 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 effciency
and effectiveness of the algorithms.
1. INTRODUCTION
The shortest Hamiltonian path is a well-known
and important combinatorial optimization
problem. The goal of Traveling Salesman
Problem (TSP) is to find the shortest path that
visits each city in a given list exactly once and
then returns to the starting city. The distances
between n cities are stored in a distance matrix
D with elements d
ij
where i, j = 1, 2, ..., n and
DOI: 10.4018/jamc.2011040104