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Fuzzy Stage Dependent Travelling Salesman Problem with Networks as Nodes

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Information Systems Architecture and Technology: Proceedings of 36th International Conference on Information Systems Architecture and Technology – ISAT 2015 – Part I

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 429))

Abstract

A new generalisation of the travelling salesman problem is proposed. First of all, the nodes of the problem are allowed to be networks themselves, in which travelling salesman subproblems have to be solved. Then, a stage dependent problem is considered, in which the nodes have different inner travel times parameters in various stages of the travelling salesman route. Such a problem is considered in a fuzzy version, when the travel time parameters may be imprecise and variable, due, for example, to weather or traffic conditions. Corresponding integer linear programming models are formulated. An example is used to illustrate the proposed approach.

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References

  1. Korte, B., Vygen, J.: Combinatorial Optimization, Theory and Algorithms. Algorithms and Combinatorics, 21st edn. Springer, Berlin, Heidelberg, New York, Tokyo, Paris, Milan (2012)

    Google Scholar 

  2. Michalewicz, Z., Fogel, D.B.: How to Solve It: Modern Heuristics. Springer, Berlin, Heidelberg, New York, Tokyo, Paris, Milan (2010)

    Google Scholar 

  3. Orman, A.J., Williams, H.P.: A survey of different integer programming formulations of the travelling salesman problem. In: Kontoghiorghes, E.J., Gatu, C. (eds.) Econometric and Financial Analysis. Advances in Computational Management Science, pp. 93–108. Springer, Berlin, Germany (2006)

    Google Scholar 

  4. Botzheim, J., Földesi P., Kóczy T.L.: Solution for fuzzy road transport traveling salesman problem using eugenic bacterial memetic algorithm. In: Proceedings of IFSA-EUSFLAT, pp. 1667–1672 (2009)

    Google Scholar 

  5. Zadeh, L.A.: A computational approach to fuzzy quantifiers in natural languages. Comput. Math Appl. 9(1), 149–184 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  6. Changdar, C., Mahapatra, G.S., Kumar Pal, R.: An efficient genetic algorithm for multi-objective solid travelling salesman problem under fuzziness. Swarm Evol. Comput. 15(0), 27–37 (2014)

    Google Scholar 

  7. Gupta, A., Kumar, A., Sharma, M.K.: Applications of fuzzy linear programming with generalized LR flat fuzzy parameter. Fuzzy Inf. Eng. 5(4), 475–492 (2013)

    Article  MathSciNet  Google Scholar 

  8. Isleyen, S.K., Kesen, S.E., Baykoç, Ö.F.: From analytical perspective to heuristic approach: travelling salesman problem with discrete fuzzy travel times. Gazi Univ. J. Sci. 22(4), 267–276 (2009)

    Google Scholar 

  9. Cordeau, J., Ghiani, G., Guerriero, E.: Analysis and branch-and-cut algorithm for the time-dependent travelling salesman problem. Transp. Sci. 48(1), 46–58 (2014)

    Article  Google Scholar 

  10. Gouveia, L., Voss, S.: A classification of formulations for the (time-dependent) traveling salesman problem. Eur. J. Oper. Res. 83(1), 69–82 (1995)

    Article  MATH  Google Scholar 

  11. Li, F., Golden, B., Wasil, E.: Solving the time dependent traveling salesman problem (2005)

    Google Scholar 

  12. Bortolan, G., Degani, R.: A review of some methods for ranking fuzzy subsets. Fuzzy Sets Syst. 15(1), 1–19 (1985)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Wroclaw University of Technology, Wroclaw, Poland

    Dorota Kuchta

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  1. Dorota Kuchta
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Correspondence to Dorota Kuchta .

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Editors and Affiliations

  1. Faculty of Computer Science and Manageme, Wrocław University of Technology, Wrocła, Wroclaw, Poland

    Leszek Borzemski

  2. Faculty of Computer Science and Manageme, Wrocław University of Technology, Wrocła, Wroclaw, Poland

    Adam Grzech

  3. Faculty of Computer Science and Manageme, Wrocław University of Technology, Wrocła, Wrocław, Poland

    Jerzy Świątek

  4. Faculty of Computer Science and Manageme, Wrocław University of Technology, Wrocła, Wrocław, Poland

    Zofia Wilimowska

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Kuchta, D. (2016). Fuzzy Stage Dependent Travelling Salesman Problem with Networks as Nodes. In: Borzemski, L., Grzech, A., Świątek, J., Wilimowska, Z. (eds) Information Systems Architecture and Technology: Proceedings of 36th International Conference on Information Systems Architecture and Technology – ISAT 2015 – Part I. Advances in Intelligent Systems and Computing, vol 429. Springer, Cham. https://doi.org/10.1007/978-3-319-28555-9_8

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  • DOI: https://doi.org/10.1007/978-3-319-28555-9_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28553-5

  • Online ISBN: 978-3-319-28555-9

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