Research Article

Classical Travelling Salesman Problem (TSP) based Approach to Solve Fuzzy TSP using Yager’s Ranking

by  S. Dhanasekar, S. Hariharan, P. Sekar
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 74 - Issue 13
Published: July 2013
Authors: S. Dhanasekar, S. Hariharan, P. Sekar
10.5120/12942-9921
PDF

S. Dhanasekar, S. Hariharan, P. Sekar . Classical Travelling Salesman Problem (TSP) based Approach to Solve Fuzzy TSP using Yager’s Ranking. International Journal of Computer Applications. 74, 13 (July 2013), 1-4. DOI=10.5120/12942-9921 

                        @article{ 10.5120/12942-9921,
                        author  = { S. Dhanasekar,S. Hariharan,P. Sekar },
                        title   = { Classical Travelling Salesman Problem (TSP) based Approach to Solve Fuzzy TSP using Yager’s Ranking },
                        journal = { International Journal of Computer Applications },
                        year    = { 2013 },
                        volume  = { 74 },
                        number  = { 13 },
                        pages   = { 1-4 },
                        doi     = { 10.5120/12942-9921 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2013
                        %A S. Dhanasekar
                        %A S. Hariharan
                        %A P. Sekar
                        %T Classical Travelling Salesman Problem (TSP) based Approach to Solve Fuzzy TSP using Yager’s Ranking%T 
                        %J International Journal of Computer Applications
                        %V 74
                        %N 13
                        %P 1-4
                        %R 10.5120/12942-9921
                        %I Foundation of Computer Science (FCS), NY, USA
Abstract

Travelling salesman problem (TSP) is a classical and most widely studied problem in both operation research and computer science. If in the TSP the cost or time or distance is not certain then it is said to be Fuzzy TSP. We propose a new algorithm to solve the fuzzy TSP and also implemented the same and the results are discussed.

References
  • Bellman RE, Zadeh LA . 1970. Decision-making in a fuzzy environment, Manage. Sci. , 17: 141-164.
  • Hannan EL 1981. Linear programming with multiple fuzzy goals. Fuzzy Sets Syst. , 6: 235-248
  • Hansen MP 2000. Use of substitute Scalarizing Functions to guide Local Search based Heuristics: The case of MOTSP, J. Heuristics, 6: 419-431
  • Jaszkiewicz A 2002. Genetic Local Search for Multiple Objectives Combinatorial Optimization. Eur. J. Oper. Res. , 137(1): 50-71.
  • Yan Z, Zhang L, Kang L, Lin G 2003. A new MOEA for multi-objective TSP and its convergence property analysis. Proceedings of Second International Conference, Springer Verlag, Berlin, pp. 342-354.
  • Angel E, Bampis E, Gourvès, L 2004. Approximating the Pareto curve with Local Search for Bi-Criteria TSP (1, 2) Problem, Theor. Comp. Sci. , 310(1-3): 135-146.
  • Paquete L, Chiarandini M, Stützle T 2004. Pareto Local Optimum Sets in Bi-Objective Traveling Sales man Problem: An Experimental Study. In: Gandibleux X. , Sevaux M. , Sörensen K. and Tkindt V. (Eds. ), Metaheuristics for Multi-objective Optimization. Lect. Notes Ec on. Math. Syst. , Springer Verlag, Berlin, 535: 177-199.
  • Liang TF 2006. Distribution planning decisions using interactive fuzzy multi-objective linear programming. Fuzzy Sets Syst. , 157: 1303-1316.
  • Rehmat A, Saeed H, Cheema MS 2007. Fuzzy Multi-objective Linear Programming Approach for Traveling Salesman Problem. Pak. J. Stat. Oper. Res. , 3(2): 87-98.
  • Javadia B, Saidi-Mehrabad M, Haji A, Mahdavi I, J olai F, Mahdavi-Amiri . N 2008. No-wait flow shop scheduling using fuzzy multi-objective linear programming. J. Franklin Inst. , 345: 452-467.
  • Tavakoli-Moghaddam R, Javadi B, J olai F, Ghodratnama A 2010. The use of a fuzzy multi-objective linear programming for solving a multi-objective single-machine scheduling problem. Appl. Soft Comput. , 10: 919-925.
  • Mukherjee S. and Basu, K. 2010. Application of fuzzy ranking method for solving assignment problems with fuzzy costs. International Journal of Computational and Applied Mathematics, 5: 359-368.
  • Chaudhuri A, De K 2011. Fuzzy multi-objective linear programming for traveling sales man problem. Afr. J. Math. Comp. Sci. Res. , 4(2): 64-70.
  • Majumdar J, Bhunia AK 2011. Genetic algorithm for asymmetric traveling salesman problem with imprecise travel times. J. Comp. Appl. Math. , 235: 3063-3078.
  • Sepideh Fereidouni 2011. Travelling salesman problem by using a fuzzy multi-objective linear programming. African Journal of mathematics and computer science research 4(11) 339-349
  • Amit kumar and Anil gupta, 2012. Assignment and Travelling salesman problems with co-efficient as LR fuzzy parameter. International Journal of applied science and engineering 10(3) 155-170.
  • R. R. Yager, 1981 . A procedure for ordering fuzzy subsets of the unit interval. Information Sciences, 24, 143-161
  • Zadeh LA 1965. Fuzzy Logic and its Applications, Academic Press, New York.
Index Terms
Computer Science
Information Sciences
No index terms available.
Keywords

Fuzzynumbers fuzzy ranking fuzzy assignment problem fuzzy Hungarian method route conditions

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