Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지
DOI QR코드

DOI QR Code

FUZZY TRANSPORTATION PROBLEM WITH ADDITIONAL CONSTRAINT IN DIFFERENT ENVIRONMENTS

  • BUVANESHWARI, T.K. (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology) ;
  • ANURADHA, D. (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology)
  • 투고 : 2021.10.05
  • 심사 : 2022.04.08
  • 발행 : 2022.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this research, we presented the type 2 fuzzy transportation problem with additional constraints and solved by our proposed genetic algorithm model, and the results are verified using the softwares, genetic algorithm tool in Matlab and Lingo. The goal of our approach is to minimize the cost in solving a transportation problem with an additional constraint (TPAC) using the genetic algorithm (GA) based type 2 fuzzy parameter. We reduced the type 2 fuzzy set (T2FS) into a type 1 fuzzy set (T1FS) using a critical value-based reduction method (CVRM). Also, we use the centroid method (CM) to obtain the corresponding crisp value for this reduced fuzzy set. To achieve the best solution, GA is applied to TPAC in type 2 fuzzy parameters. A real-life situation is considered to illustrate the method.

키워드

참고문헌

  1. M.A. Albadr, S. Tiun, M. Ayob, F. AL-Dhief, Genetic Algorithm Based on Natural Selection Theory for Optimization Problems, Symmetry 12 (2020), 1758. https://doi.org/10.3390/sym12111758
  2. J. Chen, P. Gui, T. Ding, S. Na, Y. Zhou, Optimization of transportation routing problem for fresh food by improved ant colony algorithm based on tabu search, Sustain 11 (2019), 6584. https://doi.org/10.3390/su11236584
  3. A. Das, U.K. Bera, B. Das, A solid transportation problem with mixed constraint in different environment, Journal of Applied Analysis and Computation 6 (2016), 179-95.
  4. A. Das, U.K. Bera, M. Maiti, Defuzzification of trapezoidal type-2 fuzzy variables and its application to solid transportation problem, J. Intell. Fuzzy Syst. 30 (2016), 2431-2445. https://doi.org/10.3233/IFS-152013
  5. D. Dutta, A.S. Murthy, Fuzzy transportation problem with additional restrictions, ARPN J. Eng. Appl. Sci. 5 (2010), 36-40. https://doi.org/10.3923/jeasci.2010.36.44
  6. K.B. Hale, New Methods in Mathematical Programming-The Solid Transportation Problem, Oper. Res. 10 (1962), 448-463. https://doi.org/10.1287/opre.10.4.448
  7. K.B. Haley, A.J. Smith, Transportation Problems with Additional Restrictions, J. R. Stat. Soc. Ser. C (Applied Stat). 15 (1966), 116-127.
  8. F.L. Hitchcock, The Distribution of a Product from Several Sources to Numerous Localities, J. Math. Phys. 20 (1941), 224-230. https://doi.org/10.1002/sapm1941201224
  9. J.H. Holland, Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence, U Michigan Press, 1992.
  10. S.H. Jana, B. Jana, Application of fuzzy programming techniques to solve solid transportation problem with additional constraints, Oper. Res. Decis. 30 (2020), 67-84.
  11. K. Jebari, M. Madiafi, Selection Methods for Genetic Algorithms, International Journal of Emerging Sciences 3 (2013), 333-344.
  12. S. Jose, C. Vijayalakshmi, Design and Analysis of Multi-Objective Optimization Problem Using Evolutionary Algorithms, Procedia Computer Science 172 (2020), 896-899. https://doi.org/10.1016/j.procs.2020.05.129
  13. B.O. Koopman, The optimum distribution of effort, J. Oper. Res. soceity Am. 1 (1953), 52-63.
  14. A. Kumar, S.S. Appadoo, P. Kaur, Mehar approach for solving dual-hesitant fuzzy transportation problem with restrictions, Sadhana-Acad. Proc. Eng. Sci. 45 (2020), 1-9.
  15. R. Kumar, R. Gupta, O. Karthiyayini, R.S. Kuntal, G.A. Vatsala, Fuzzified Multi-Objective Transportation Problem :A Real Coded Genetic Algorithm approach to the Compromised near-to-Optimal solution, International Conference on Advanced Technologies in Intelligent Control, Environment, Computing and Communication Engineering, (2019), 80-84.
  16. P. Kundu, S. Kar, M. Maiti, Fixed charge transportation problem with type-2 fuzzy variables, Inf. Sci. (Ny). 255 (2014), 170-186. https://doi.org/10.1016/j.ins.2013.08.005
  17. I. Kucukoqlu, N. Ozturk, Simulated Annealing Approach for Transportation Problem of Cross-docking Network Design, Procedia-Soc. Behav. Sci. 109 (2014), 1180-1184. https://doi.org/10.1016/j.sbspro.2013.12.608
  18. Lin, Feng-Tse, Solving the transportation problem with fuzzy coefficients using genetic algorithms, 2009 IEEE international conference on fuzzy systems, (2009), 1468-1473.
  19. J. Mendel, R. John, Type-2 fuzzy sets made easy, IEEE Trans. fuzzy Syst. 10 (2002), 117-127. https://doi.org/10.1109/91.995115
  20. Misevicius, Alfonsas and Dovile Verene, A Hybrid Genetic-Hierarchical Algorithm for the Quadratic Assignment Problem, Entropy 23 (2021), 108. https://doi.org/10.3390/e23010108
  21. P. Pandian, D. Anuradha, Floating Point Method for Solving Transportation Problems with Additional Constraints, International Mathematical Forum 6 (2011), 1983-1992.
  22. T. Pasa, The genetic algorithm for solving the non-linear transportation problem, Rev. Air Force Acad. 16 (2018), 37-44. https://doi.org/10.19062/1842-9238.2018.16.2.4
  23. R. Qin, Y.K. Liu, Z.Q. Liu, Methods of critical value reduction for type-2 fuzzy variables and their applications, J. Comput. Appl. Math. 235 (2011), 1454-1481. https://doi.org/10.1016/j.cam.2010.08.031
  24. Saul I. Gass, On Solving the Transportation Problem, Journal of the Operational Research Society 41 (1990), 291-297. https://doi.org/10.2307/2583799
  25. A. Serban, The use of the genetic algorithms for optimizing public transport schedules in congested urban areas, IOP Conference Series: Materials Science and Engineering 1037 (2021), 012062. https://doi.org/10.1088/1757-899X/1037/1/012062
  26. V.E. Sobana, D. Anuradha, Multi-objective Unbalanced Solid Assignment Problem with Triangular Type-2 Fuzzy Parameter, Journal of Xi'an University of Architecture & Technology 12 (2020), 4518-4527.