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A Characterization of the Performance of Ordering Methods in TTRP with Fuzzy Coefficients in the Capacity Constraints

  • Isis Torres-Pérez
  • Carlos Cruz
  • Alejandro Rosete-Suárez
  • José Luis VerdegayEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 611)

Abstract

Recently, the Truck and Trailer Routing Problem (TTRP) has been tackled with uncertainty in the coefficients of constrains. In order to solve this problem it is necessary to use methods for comparison fuzzy numbers. The problem of ordering fuzzy quantities has been addressed by many authors and there are many indices to perform this task. However, it is impossible to give a final answer to the question on what ranking method is the best in this problem. In this paper we focus our attention on a model to characterize TTRP instances. We use a data mining algorithm to derive a decision tree that determined the best method for comparison based on the characteristics of the TTRP problem to be solved.

Keywords

Fuzzy optimization Truck and Trailer Routing Problem (TTRP) Fuzzy coefficients Fuzzy constraints Ranking function Decision tree 

Notes

Acknowledgments

This work was supported by the projects TIN2014-55024-P from the Spanish Ministry of Economy and Competitiveness, and P11-TIC-8001 from the Andalusian Government (including FEDER funds).

References

  1. 1.
    Baykasoglu, A., Tolunay, G.: A review and classification of fuzzy mathematical programs. J. Intell. Fuzzy Syst. 19(3), 205–229 (2008)zbMATHGoogle Scholar
  2. 2.
    Tanaka, H., Ichihashi, H., Asai, K.: A formulation of fuzzy linear programming problems based on comparison of fuzzy numbers. Control Cybernet. 13, 185–194 (1984)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Delgado, M., Verdegay, J.L., Vila, M.A.: A general model for fuzzy linear programming. Fuzzy Sets Syst. 29(1), 21–29 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Wang, X., Kerre, E.: Fuzzy Logic Foundations and Industrial Applications. Part I, Springer, US, International Series in Intelligent Technologies, cap. On the Classification and the Dependencies of the Ordering Methods Advances in Intelligent Systems Research, vol. 8, pp. 73–90 (1996)Google Scholar
  5. 5.
    Yager, R.R.: Ranking fuzzy subsets over the unit interval. In: Proceeding 1978 CDC, pp. 1435–1437. IEEE Conference, New York (1978)Google Scholar
  6. 6.
    Adamo, J.M.: Fuzzy decision trees. Fuzzy Sets Syst. 4, 207–219 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Yager, R.R.: On choosing between fuzzy subsets. Kybernetes 9, 151–154 (1980)CrossRefzbMATHGoogle Scholar
  8. 8.
    Yager, R.R.: A procedure for ordering fuzzy subsets of the unit interval. Inf. Sci. 24, 143–161 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Chang, W.: Ranking of fuzzy utilities with triangular membership functions. In: Proceeding of International Conference on Policy Analysis and Systems, pp. 263–272 (1981)Google Scholar
  10. 10.
    Jain, R.: A procedure for multiple-aspect decision making using fuzzy set. Int. J. Syst. Sci. 8(1), 1–7 (1977)CrossRefzbMATHGoogle Scholar
  11. 11.
    Chen, S.: Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets Syst. 17, 113–129 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Kim, K., Park, K.S.: Ranking fuzzy numbers with index of optimism. Fuzzy Sets Syst. 35(2), 143–150 (1990)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Dubois, D., Prade, H.: Ranking fuzzy numbers in the setting of possibility theory. Inf. Sci. 30(3), 183–224 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Nakahara, Y.: User oriented ranking criteria and its application to fuzzy mathematical programming problems. Fuzzy Sets Syst. 94, 275–286 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Brunelli, M., Mezeib, J.: How different are ranking methods for fuzzy numbers? A numerical study. Int. J. Approximate Reasoning 54(4), 627–639 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Chao, I.-M.: A tabu search method for the truck and trailer routing problem. Comput. Oper. Res. 29(1), 33–51 (2002)CrossRefzbMATHGoogle Scholar
  17. 17.
    Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-completeness. W. H. Freeman, San Francisco (1979)zbMATHGoogle Scholar
  18. 18.
    Drexl, M.: A Branch-and-price algorithm for the truck-and-trailer routing problem. Technical report, Deutsche Post Endowed Chair of Optimization of Distribution Networks (2006)Google Scholar
  19. 19.
    Scheuerer, S.: A tabu search heuristic for the truck and trailer routing problem. Comput. Oper. Res. 33(4), 894–909 (2006)CrossRefzbMATHGoogle Scholar
  20. 20.
    Lin, S.-W., Yu, V.F., Chou, S.Y.: Solving the truck and trailer routing problem based on a simulated annealing heuristic. Computers & Operation Research. 36(5), 1683–1692 (2009)CrossRefzbMATHGoogle Scholar
  21. 21.
    Villegas, J.G., Prins, C., Prodhon, C., Medaglia, A.L., Velasco, N.: A grasp with evolutionary path relinking for the truck and trailer routing problem. Comput. Oper. Res. 38(9), 1319–1334 (2011)CrossRefzbMATHGoogle Scholar
  22. 22.
    Derigs, U., Pullmann, M., Vogel, U.: Truck and trailer routing - problems, heuristics and computational experience. Comput. Oper. Res. 40(2), 536–546 (2013)CrossRefGoogle Scholar
  23. 23.
    Mirmohammadsadeghi, S., Ahmed, S., Nadirah, E.: Application of memetic algorithm to solve truck and trailer routing problems. In: Proceedings of the 2014 International Conference on Industrial Engineering and Operations Management, Bali, pp. 747–755 (2014)Google Scholar
  24. 24.
    Villegas, J.G., Prins, C., Prodhon, C., Medaglia, A.L., Velasco, N.: A matheuristic for the truck and trailer routing problem. Eur. J. Oper. Res. 230(2), 231–244 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Torres, I., Rosete, A., Cruz, C., Verdegay, J.: Fuzzy constraints in the truck and trailer routing problem. In: Proceedings of the Fourth International Workshop on Knowledge Discovery, Management and Decision Support (EUREKA-2013), Mazatln, pp. 71–78 (2013)Google Scholar
  26. 26.
    Torres, I., Cruz, C., Verdegay, J.: Solving the truck and trailer routing problem with fuzzy constraints. Int. J. Comput. Intell. Syst. 8(4), 713–724 (2015)CrossRefGoogle Scholar
  27. 27.
    Torres, I., Rosete, A., Cruz, C., Verdegay, J.: Truck and Trailer Routing Problem under fuzzy environment. In: Proceedings of the 16th World Congress of the International Fuzzy Systems Association (IFSA) and 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), Gijón, pp. 1189–1194 (2015)Google Scholar
  28. 28.
    Fajardo, J., Masegosa, A., Pelta, D.: Algorithm portfolio based scheme for dynamic optimization problems. Int. J. Comput. Intell. Syst. 8(4), 667–689 (2015)CrossRefGoogle Scholar
  29. 29.
    Friedman, M.: A comparison of alternative tests of significance for the problem of m rankings. Ann. Math. Stat. 11(40), 86–92 (1940)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Shaffer, J.: Modified sequentially rejective multiple test procedures. J. Am. Stat. Assoc. 81(395), 826–831 (1986)CrossRefzbMATHGoogle Scholar
  31. 31.
    Holm, S.: A simple sequentially rejective multiple test procedure. Scand. J. Stat. 6(2), 65–70 (1979)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Isis Torres-Pérez
    • 1
  • Carlos Cruz
    • 2
  • Alejandro Rosete-Suárez
    • 1
  • José Luis Verdegay
    • 2
    Email author
  1. 1.Instituto Superior Politécnico José Antonio EcheverríaHavanaCuba
  2. 2.University of GranadaGranadaSpain

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