Hungarian Algorithm using Haar Tuples to Solve Fuzzy Travelling Salesman Problem

  • Authors

    • S. Dhanasekar
    • Saroj Kumar Dash
    • S. Hariharan
    2018-10-02
    https://doi.org/10.14419/ijet.v7i4.10.20941
  • 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. [1] L.A. Zadeh, “Fuzzy setsâ€, 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 MOTSPâ€, J. Heuristics, Vol.6, (2000), pp:419-431.

      [3] A. Jaszkiewicz, “Genetic local search for multi-objective combinatorial optimizationâ€, 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 analysisâ€, 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 programmingâ€, 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 optimizationâ€, Lecture Notes in Economics and Mathematical Systems, 535, Springer, Berlin, (2004), pp:177--199.

      [8] A. Rehmat, H. Saeed, M.S. Cheema, “Fuzzy multi-objective linear programming approach for travelling salesman problemâ€, 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 parametersâ€, International Journal of Applied Science and Engineering, Vol.10, No.3, (2012), pp:155-170.

      [10] S. Dhanasekar, S. Hariharan, P. Sekar, “Classical Travelling Salesman Problem (TSP) based approach to solve fuzzy TSP using Yager’s rankingâ€, “International journal of Computer Applications (IJCA)â€, Vol.74, No.13, (2013), pp:1-4.

      [11] Abha Singhal and Priyanka Pandy, “Travelling Salesman Problems by Dynamic Programming Algorithmâ€, International Journal of Scientific 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 waveletâ€, Applied Mathematical Sciences, Vol.8, No.160, (2014), pp:7951-7958.

      S. Dhanasekar, S. Hariharan, P. Sekar, “Haar Hungarian algorithm to solve fuzzy assignment problemâ€, 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 & Technology, 7(4.10), 380-382. https://doi.org/10.14419/ijet.v7i4.10.20941

    Received date: 2018-10-04

    Accepted date: 2018-10-04

    Published date: 2018-10-02