Travelling Salesman Problem: An Empirical Comparison Between ACO, PSO, ABC, FA and GA

  • Kinjal ChaudhariEmail author
  • Ankit Thakkar
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 906)


Travelling salesman problem (TSP) is one of the optimization problems which has been studied with a large number of heuristic and metaheuristic algorithms, wherein swarm and evolutionary algorithms have provided effective solutions to TSP even with a large number of cities. In this paper, our objective is to solve some of the benchmark TSPs using ant colony optimization (ACO), particle swarm optimization (PSO), artificial bee colony (ABC), firefly algorithm (FA) and genetic algorithm (GA). The empirical comparisons of the experimental outcomes show that ACO and GA outperform to ABC, PSO and FA for the given TSP.




  1. 1.
    Blum, C., & Li, X. (2008). Swarm intelligence in optimization. In Swarm intelligence (pp. 43–85). Berlin: Springer.Google Scholar
  2. 2.
    Beni, G., & Wang, J. (1993). Swarm intelligence in cellular robotic systems. In Robots and biological systems: Towards a new bionics? (pp. 703–712). Berlin: Springer.Google Scholar
  3. 3.
    Dorigo, M., & Birattari, M. (2011). Ant colony optimization. In Encyclopedia of machine learning (pp. 36–39). Berlin: Springer.Google Scholar
  4. 4.
    Poli, R., Kennedy, J., & Blackwell, T. (2007). Particle swarm optimization. Swarm Intelligence, 1(1), 33–57.CrossRefGoogle Scholar
  5. 5.
    Tereshko, V., & Loengarov, A. (2005). Collective decision making in honey-bee foraging dynamics. Computing and Information Systems, 9(3), 1.Google Scholar
  6. 6.
    Yang, X.-S. (2010). Firefly algorithm, stochastic test functions and design optimisation. International Journal of Bio-Inspired Computation, 2(2), 78–84.CrossRefGoogle Scholar
  7. 7.
    Hoffman, K. L., Padberg, M., & Rinaldi, G. (2013). Traveling salesman problem. In Encyclopedia of operations research and management science (pp. 1573–1578). Berlin: Springer.Google Scholar
  8. 8.
    Holland, J. H. (1975). Adaptation in natural and artificial systems. In An introductory analysis with application to biology, control, and artificial intelligence (pp. 439–444). Ann Arbor, MI: University of Michigan Press.Google Scholar
  9. 9.
    Blum, C., & Roli, A. (2003). Metaheuristics in combinatorial optimization: Overview and conceptual comparison. ACM Computing Surveys (CSUR), 35(3), 268–308.CrossRefGoogle Scholar
  10. 10.
    Balas, E., & Toth, P. (1983). Branch and bound methods for the traveling salesman problem. Technical Report, Carnegie-Mellon Univ, Pittsburgh, PA, Management Sciences Research Group.Google Scholar
  11. 11.
    Held, M., & Karp, R. M. (1971). The traveling-salesman problem and minimum spanning trees: Part II. Mathematical Programming, 1(1), 6–25.MathSciNetCrossRefGoogle Scholar
  12. 12.
    Win, Z. (1995). 14-state in Burma.Google Scholar
  13. 13.
    Groetschel, R. (1995). Juenger, 29 cities in Bavaria, geographical distances.Google Scholar
  14. 14.
    Padberg, R. (1995). 48 capitals of the US.Google Scholar
  15. 15.
    Dorigo, M., Maniezzo, V., & Colorni, A. (1996). Ant system: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics. Part B (Cybernetics), 26(1), 29–41.Google Scholar
  16. 16.
    Fang, L., Chen, P., & Liu, S. (2007). Particle swarm optimization with simulated annealing for tsp. In Proceedings of the 6th WSEAS International Conference on Artificial Intelligence, Knowledge Engineering and Data Bases (pp. 206–210).Google Scholar
  17. 17.
    Kennedy, J., & Eberhart, R. C. (1997). A discrete binary version of the particle swarm algorithm. In 1997 IEEE International Conference on Systems, Man, and Cybernetics, 1997. Computational Cybernetics and Simulation (Vol. 5, pp. 4104–4108). New York: IEEE.Google Scholar
  18. 18.
    Wang, K.-P., Huang, L., Zhou, C.-G., & Pang, W. (2003). Particle swarm optimization for traveling salesman problem. In 2003 International Conference on Machine Learning and Cybernetics (Vol. 3, pp. 1583–1585). New York: IEEE.Google Scholar
  19. 19.
    Karaboga, D., & Akay, B. (2009). A comparative study of artificial bee colony algorithm. Applied Mathematics and Computation, 214(1), 108–132.MathSciNetCrossRefGoogle Scholar
  20. 20.
    Karaboga, D., & Basturk, B. (2007). Artificial bee colony (abc) optimization algorithm for solving constrained optimization problems. In International Fuzzy Systems Association World Congress (pp. 789–798). Berlin: Springer.Google Scholar
  21. 21.
    Łukasik, S., & Żak, S. (2009). Firefly algorithm for continuous constrained optimization tasks. In International Conference on Computational Collective Intelligence (pp. 97–106). Berlin: Springer.Google Scholar
  22. 22.
    Kumbharana, S. N., & Pandey, G. M. (2013). Solving travelling salesman problem using firefly algorithm. International Journal for Research in Science & Advanced Technologies, 2(2), 53–57.Google Scholar
  23. 23.
    Razali, N. M., Geraghty, J., et al. (2011). Genetic algorithm performance with different selection strategies in solving tsp. In Proceedings of the World Congress on Engineering (Vol. 2, pp. 1134–1139). International Association of Engineers, Hong Kong.Google Scholar
  24. 24.
    Dorigo, M., Birattari, M., & Stutzle, T. (2006). Artificial ants as a computational intelligence technique. IEEE Computational Intelligence Magazine, 1, 28–39.CrossRefGoogle Scholar
  25. 25.
    Yonggang, C., Fengjie, Y., & Jigui, S. (2006). A new particle swam optimization algorithm. Journal of Jilin University, 24(2), 181–183.Google Scholar
  26. 26.
    Farahani, S. M., Abshouri, A., Nasiri, B., & Meybodi, M. (2011). A Gaussian firefly algorithm. International Journal of Machine Learning and Computing, 1(5), 448.CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Institute of TechnologyNirma UniversityAhmedabadIndia

Personalised recommendations