Using the Expanded IWO Algorithm to Solve the Traveling Salesman Problem

Daniel Kostrzewa, Henryk Josiński

Abstract

The Invasive Weed Optimization algorithm (IWO) is an optimization metaheuristic inspired by dynamic growth of weeds colony. The authors of the present paper have expanded the strategy of the search space exploration of the IWO algorithm introducing a hybrid method along with a concept of the family selection applied in the phase of creating individuals. The goal of the project was to evaluate the expanded IWO version (exIWO) as well as the original IWO by testing their usefulness for solving some test instances of the traveling salesman problem (TSP) taken from the TSPLIB collection which allows to compare the experimental results with outcomes reported in the literature. The results produced by other heuristic algorithms as well as the methods based on the self-organizing maps served as the reference points.

References

  1. Angéniol, B., de la Croix Vaubois, G., Le Texier, J.Y., 1988. Self-organizing feature maps and the travelling salesman problem. In Neural Networks 1(4). Elsevier.
  2. Aras, N., Oommen, B.J., Altinel, I.K., 1999. Kohonen network incorporating explicit statistics and its application to the travelling salesman problem. In Neural Networks 12(9). Elsevier.
  3. Bai, Y., Zhang, W., Jin, Z., 2006. A new self-organizing maps strategy for solving the traveling salesman problem. In Chaos, Solitons & Fractals. Elsevier.
  4. Burke, L.I., Damany, P., 1992. The guilty net for the traveling salesman problem. In Computers & Operations Research 19(3-4). Elsevier.
  5. DePuy, G.W., Moraga, R.J., Whitehouse G.E., 2005. Meta-RaPS: a simple and effective approach for solving the traveling salesman problem. In Transportation Research Part E. Elsevier.
  6. DePuy, G.W., Moraga, R.J., Whitehouse G.E., 2002. Using the Meta-RaPS approach to solve combinatorial problems. In Proceedings of the 2002 Industrial Engineering Research Conference.
  7. Fort, J.C., 1988. Solving combinatorial problem via selforganizing process: An application of the Kohonen algorithm to the traveling salesman problem. In Biological Cybernetics 59(1). Springer.
  8. Golden, B.L., Stewart, W.R., 1985. Empirical analysis of heuristics. In Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B., 1985. The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. John Wiley & Sons.
  9. Herdy, M., 1991. Application of the Evolution Strategy to Discrete Optimization Problems. In Lecture Notes in Computer Science 496. Springer.
  10. Hueter, G.J., 1988. Solution to the travelling salesman problem with an adaptive ring. In Proceedings of the IEEE International Conference on Neural Networks.
  11. Kostrzewa, D., Josinski, H., 2011. Verification of the Search Space Exploration Strategy Based on the Solutions of the Join Ordering Problem. In Advances in Intelligent and Soft Computing. Springer.
  12. Krasnogor, N., Moscato, P., Norman, M.G., 1995. A new hybrid heuristic for large geometric traveling salesman problems based on the Delaunay triangulation. In Anales del XXVII Simposio Brasileiro de Pesquisa Operacional.
  13. Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B., 1985. The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. John Wiley & Sons.
  14. Mak, K.T., Morton, A.J., 1993. A modified Lin-Kernighan traveling salesman heuristic. In Operations Research Letters 13(3). Elsevier.
  15. Mallahzadeh, A. R., Oraizi, H., Davoodi-Rad, Z., 2008. Application of the Invasive Weed Optimization Technique for Antenna Configurations. In Progress in Electromagnetics Research.
  16. Mehrabian, R., Lucas, C., 2006. A novel numerical optimization algorithm inspired from weed colonization. In Ecological Informatics 1(4), Elsevier.
  17. Michalewicz, Z., Fogel, D. B., 2004. How to Solve It: Modern Heuristics. Springer.
  18. Padberg, M., Rinaldi, G., 1991. A branch-and-cut algorithm for the solution of large-scale traveling salesman problems. In SIAM Review 33(1).
  19. Rego, C., 1998. Relaxed tours and path ejections for the traveling salesman problem. In European Journal of Operational Research 106(2-3). Elsevier.
  20. Reinelt, G., 1991. TSPLIB - traveling salesman problem library. In ORSA Journal on Computing 3(4).
  21. Renaud, J., Boctor, F.F., Laporte, G., 1996. A fast composite heuristic for the symmetric traveling salesman problem. In INFORMS Journal on Computing 8(2).
  22. Sahraei-Ardakani, M., Roshanaei, M., Rahimi-Kian, A., Lucas C., 2008. A Study of Electricity Market Dynamics Using Invasive Weed Colonization Optimization. IEEE Symposium on Computational Intelligence and Games.
  23. Sepehri Rad, H., Lucas, C., 2007. A Recommender System based on Invasive Weed Optimization Algorithm. IEEE Congress on Evolutionary Computation.
  24. Tao, G., Michalewicz, Z., 1998. Inver-over Operator for the TSP. In Lecture Notes In Computer Science 1498. Springer.
  25. Vieira, F.C., Neto, A.D.D., Costa, J.A.F., 2003. An efficient approach to the travelling salesman problem using self-organizing maps. In International Journal of Neural Systems 13(2).
Download


Paper Citation


in Harvard Style

Kostrzewa D. and Josiński H. (2013). Using the Expanded IWO Algorithm to Solve the Traveling Salesman Problem . In Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-8565-39-6, pages 451-456. DOI: 10.5220/0004224204510456


in Bibtex Style

@conference{icaart13,
author={Daniel Kostrzewa and Henryk Josiński},
title={Using the Expanded IWO Algorithm to Solve the Traveling Salesman Problem},
booktitle={Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},
year={2013},
pages={451-456},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004224204510456},
isbn={978-989-8565-39-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - Using the Expanded IWO Algorithm to Solve the Traveling Salesman Problem
SN - 978-989-8565-39-6
AU - Kostrzewa D.
AU - Josiński H.
PY - 2013
SP - 451
EP - 456
DO - 10.5220/0004224204510456