Hungarian Algorithm using Haar Tuples to Solve Fuzzy Travelling Salesman Problem

  • Authors

    • S. Dhanasekar
    • Saroj Kumar Dash
    • S. Hariharan
    https://doi.org/10.14419/ijet.v7i4.10.20941

    Received date: October 4, 2018

    Accepted date: October 4, 2018

    Published date: October 2, 2018

  • Triangular fuzzy number, Trapezoidal fuzzy number, Fuzzy arithmetic operations, Fuzzy number, Fuzzy ranking techniques, Fuzzy Travelling Salesman problems, Haar Wavelet, Optimal solution.
  • Abstract

    Travelling salesman problem(TSP) deals with visiting all the given cities and return back to the starting city with the minimum travelling distance or minimum travelling cost where each city is visited exactly once. The TSP problem is a special kind of an assignment model that excludes sub tours.  In this paper we used Haar Hungarian algorithm approach [13] to solve a Fuzzy Travelling Salesman Problem (FTSP) and Numerical examples are given to validate the proposed algorithm.

  • References

    1. L.A. Zadeh, “Fuzzy sets”, Information Control, Vol.8, (1965), pp:338-353.
    2. M.P. Hansen, “Use of substitute scalarizing functions to guide local search based heuristics: The case of MOTSP”, J. Heuristics, Vol.6, (2000), pp:419-431.
    3. A. Jaszkiewicz, “Genetic local search for multi-objective combinato-rial optimization”, European Journal of Operational Research, Vol.137, (2002), pp:50-71.
    4. Z. Yan, L. Zhang, L. Kang, G. Lin, “A new MOEA for multi-objective TSP and its convergence property analysis”, Proceedings of Second International Conference, Springer Verlag, Berlin, (2003), pp:342-354.
    5. F. Sepideh, “Travelling salesman problem by using a fuzzy multi-objective linear programming”, African Journal of Mathematics and Computer Science Research, Vol.4, No.11, (2003), pp:339-349.
    6. E. Angel, E. Bampis, L. Gourvs, “Approximating the Pareto curve with local search for the bicriteria TSP(1,2) problem, Theoretical Computer Science, Vol.310, (2004), pp:135--146.
    7. L. Paraquete, M. Chiarandini, T. Stytzle, “Pareto local optimum sets in the biobjective travelling salesman problem : an experimental study. Metaheuristics for multiobjective optimization”, Lecture Notes in Economics and Mathematical Systems, 535, Springer, Ber-lin, (2004), pp:177--199.
    8. A. Rehmat, H. Saeed, M.S. Cheema, “Fuzzy multi-objective linear programming approach for travelling salesman problem”, Pakistan Journal of Statistics Operation Research , Vol.3, No.2, (2007), pp:87-98.
    9. Amitkumar and Anilgupta., “ Assignment and Travelling salesman problems with co.eff as LR fuzzy parameters”, International Jour-nal of Applied Science and Engineering, Vol.10, No.3, (2012), pp:155-170.
    10. S. Dhanasekar, S. Hariharan, P. Sekar, “Classical Travelling Sales-man Problem (TSP) based approach to solve fuzzy TSP using Ya-ger’s ranking”, “International journal of Computer Applications (IJCA)”, Vol.74, No.13, (2013), pp:1-4.
    11. Abha Singhal and Priyanka Pandy, “Travelling Salesman Problems by Dynamic Programming Algorithm”, International Journal of Sci-entific Engineering and Applied Science, Vol.2, (2016), pp:263-267.
    12. S. Dhanasekar, S. Hariharan, P. Sekar, “Ranking of Generalized trapezoidal fuzzy numbers using Haar wavelet”, Applied Mathemat-ical Sciences, Vol.8, No.160, (2014), pp:7951-7958.
    13. S. Dhanasekar, S. Hariharan, P. Sekar, “Haar Hungarian algorithm to solve fuzzy assignment problem”, International Journal of Pure and Apllied Mathematics, Vol.113, No.7, (2017), pp:58-66.
  • Downloads

  • How to Cite

    Dhanasekar, S., Kumar Dash, S., & Hariharan, S. (2018). Hungarian Algorithm using Haar Tuples to Solve Fuzzy Travelling Salesman Problem. International Journal of Engineering and Technology, 7(4.10), 380-382. https://doi.org/10.14419/ijet.v7i4.10.20941