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New approaches in metaheuristics to solve the fixed charge transportation problem in a fuzzy environment

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Abstract

Fixed charge transportation problem (FCTP) is a primary and important problem which attracts researchers in the last decade. Recently, solution approaches typically metaheuristics are in focus. Therefore, metaheuristics have been developed to solve such a nondeterministic polynomial-time hard (NP-hard) problem. Since the real world is a complicated system and we could not formulate it as an exact problem, therefore it is necessary to describe an approximate and a fuzzy model. In this paper, both fixed costs and variable costs are considered as the fuzzy numbers. Three well-known algorithms that included a single point-based and two population-based metaheuristics are developed. Besides, a new population-based algorithm that has not been used in the previous works is developed: whale optimization algorithm (WOA). Contrary to previous works, this paper proposes new approaches in solution algorithms using both spanning tree-based Prüfer number and priority-based representation. Also, Taguchi method is used to guarantee the proper performance of algorithms and calibration of parameters. In addition, several problems with different sizes are generated to assess the capability of the algorithms and commercial software according to the real-world case.

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References

  1. Hirsch WM, Dantzig GB (1968) The fixed charge problem. Naval research logistics quarterly 15:413–424

    Article  MathSciNet  MATH  Google Scholar 

  2. Clover F, Klingman D, Phillips NV (1992) Network models in optimization and their applications in practice. Wiley, New York

    Google Scholar 

  3. Klose A (2008) Algorithms for solving single-sink fixed-charge transportation problem. Comput Oper Res 35:2079–2092

    Article  MathSciNet  MATH  Google Scholar 

  4. Adlakha V, Kowalski K (2003) A simple heuristic for solving small fixed-charge transportation problems. Omega Int J Manag Sci 31:205–211

    Article  Google Scholar 

  5. Jawahar N, Balaji N (2011) A genetic algorithm based heuristic to the multi-period fixed charge distribution problem. Appl Soft Comput 12:682–699

    Article  Google Scholar 

  6. Juman ZAMS, Hoque MA (2015) An efficient heuristic to obtain a better initial feasible solution to the transportation problem. Appl Soft Comput 34:813–826

  7. Holmberg K, Joborn M, Melin K (2008) Lagrangian based heuristics for the multi-commodity network flow problem with fixed costs on paths. Eur J Oper Res 188(1):101–108

  8. Gottlieb J, Paulmann L (1998) Genetic algorithms for the fixed charge transportation problem. In Proceedings of IEEE international conference on evolutionary computation. Anchorage pp 330–335

  9. Sun M, Aronson JE, Mckeown PG, Drinka D (1998) A tabu search heuristic procedure for the fixe charge transportation problem. Eur J Oper Res 106:441–456

    Article  MATH  Google Scholar 

  10. Gen M, Cheng R (2000) Genetic algorithms and engineering optimization. Wiley, NY

    Google Scholar 

  11. Prüfer H (1918) Neuer bewis eines saizes uber permutationen. Arch Math Phys 27:742–744

    Google Scholar 

  12. Dossey J, Otto A, Spence L, Eynden C (1993) Discrete mathematics. Harper Collins, New York

    Google Scholar 

  13. Zhou G, Gen M (1997) A note on genetic algorithm for degree-constrained spanning tree problem. Networks 30:91–95

    Article  MATH  Google Scholar 

  14. Syarif A, Gen M (2003b) Double spanning tree-based genetic algorithm for two stage transportation problem. International Journal of Knowledge-based Engineering Systems 7:214–221

    Google Scholar 

  15. Gen M, Cheng R (1997) Genetic algorithms and engineering design. Wiley, NY

    Google Scholar 

  16. Syarif A, Gen M (2003c) Hybrid genetic algorithm for production/distribution system in supply chain. International Journal of Smart Engineering System Design 5:289–298

    Article  MATH  Google Scholar 

  17. Gen M, Syarif A (2005) Hybrid genetic algorithm for multi-time period production/distribution planning. Comput Ind Eng 48:799–809

    Article  Google Scholar 

  18. Syarif A, Yun YS, Gen M (2002) Study on multi-stage logistics chain network: a spanning tree based genetic algorithm. Comput Ind Eng 43:299–314

    Article  Google Scholar 

  19. Jo JB, Li Y, Gen M (2007) Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Comput Ind Eng 53:290–298

    Article  Google Scholar 

  20. Syarif A, Gen M (2003a) Solving exclusionary side constrained transportation problem by using a hybrid spanning tree-based genetic algorithm. International Journal of Intelligent Manufacturing 14:389–399

    Article  Google Scholar 

  21. Zhou G, Gen M (1999) Genetic algorithm approach on multi-criteria minimum spanning tree problem. Eur J Oper Res 114:141–152

    Article  MATH  Google Scholar 

  22. Gen M, Altiparmak F, Lin L (2006) A genetic algorithm for two-stage transportation problem using priority-based encoding. Journal of Operational Research 28:337–354

    MathSciNet  MATH  Google Scholar 

  23. Lotfi MM, Tavakkoli-Moghaddam R (2013) A genetic algorithm using priority-based encoding with new operators for fixed charge transportation problems. Appl Soft Comput 13:2711–2726

    Article  Google Scholar 

  24. Hajiaghaei-Keshteli M, Molla-Alizadeh-Zavardehi S, Tavakkoli-Moghaddam R (2010) Addressing a nonlinear fixed-charge transportation problem using a spanning tree-based genetic algorithm. Comput Ind Eng 59(2010):259–271

    Article  Google Scholar 

  25. El-Sherbiny MM, Alhamali RM (2012) A hybrid particle swarm algorithm with artificial immune learning for solving the fixed charge transportation problem. Comput Ind Eng 64(2013):610–620

    Google Scholar 

  26. Xie F, Jia R (2012) Nonlinear fixed charge transportation problem by minimum cost flow-based genetic algorithm. Comput Ind Eng 63:763–778

    Article  Google Scholar 

  27. Altassan KM, El-Sherbiny MM, Abid AD (2014) Artificial immune algorithm for solving fixed charge transportation problem. Applied Mathematics and Information Sciences 2:751–759

    Article  Google Scholar 

  28. Jawahara N, Balajib AN (2009) A genetic algorithm for the two-stage supply chain distribution problem associated with a fixed charge. Eur J Oper Res 194:496–537

    Article  Google Scholar 

  29. Hajiaghaei-Keshteli M, Aminnayeri M (2014) Solving the integrated scheduling of production and rail transportation problem by Keshtel algorithm. Appl Soft Comput 25:184–203

    Article  Google Scholar 

  30. Hajiaghaei-Keshteli M, Aminnayeri M, Fatemi Ghomi SMT (2014) Integrated scheduling of production and rail transportation. Comput Ind Eng 74:240–256

    Article  Google Scholar 

  31. Molla-Alizadeh-Zavardehi S, Sadi Nezhad S, Tavakkoli-Moghaddam R, Yazdani M (2013) Solving a fuzzy fixed charge solid transportation problem by metaheuristics. Math Comput Model 57:1543–1558

    Article  MathSciNet  Google Scholar 

  32. Pramanik S, Janab DK, Mondala SK, Maiti M (2015) A fixed-charge transportation problem in two-stage supply chain network in Gaussian type-2 fuzzy environments. Inf Sci 325:190–214

    Article  MathSciNet  Google Scholar 

  33. Ebrahimnejad A (2016) New method for solving fuzzy transportation problems with LR flat fuzzy numbers. Inf Sci 357:108–124

    Article  Google Scholar 

  34. Waiel F, El-Wahed A (2001) A multi-objective transportation problem under fuzziness. Fuzzy Sets Syst 117:27–33

    Article  MathSciNet  MATH  Google Scholar 

  35. Gao SP, Liu SY (2004) Two-phase fuzzy algorithms for multi-objective transportation problem. The Journal of Fuzzy Mathematics 12:147–155

    MATH  Google Scholar 

  36. Samanta B, Roy TK (2005) Multi-objective entropy transportation model with trapezoidal fuzzy number penalties, sources and destination. J Transp Eng 131:419–428

    Article  Google Scholar 

  37. Omar MS, Samir AA (2003) A parametric study on transportation problem under fuzzy environment. The Journal of Fuzzy Mathematics 11:115–124

    MathSciNet  MATH  Google Scholar 

  38. Chanas S, Kuchta D (1996) A concept of the optimal solution of the transportation problem with fuzzy cost coefficients. Fuzzy Sets and System 82:299–305

    Article  MathSciNet  Google Scholar 

  39. Ojha D, Mondal SK, Maiti M (2009) An entropy based solid transportation problem for general fuzzy costs and time with fuzzy equality. Math Comput Model 50:166–178

    Article  MathSciNet  MATH  Google Scholar 

  40. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  41. Fuzzy logic: an introductory course for engineering students (studies in fuzziness and soft computing) 2015th Edition by Enric Trillas and Luka Eciolaza

  42. Enric Trillas, Luka Eciolaza (2015) Fuzzy Logic. An introductory course for engineering students, 320. Springer.

  43. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–679

    Article  MathSciNet  MATH  Google Scholar 

  44. Kennedy, J and Eberhart, R. (1995). Particle swarm optimization. Proc of IEEE International Conference on Neural Network, Perth, Australia, IEEE Service Center Piscataway, NJ, 1942–1948.

  45. Su YX, Chi R (2015) Multi-objective particle swarm-differential evolution algorithm. Neural Comput Applic: 1–12

  46. Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor

    Google Scholar 

  47. Aličković E, Subasi A (2015) Breast cancer diagnosis using GA feature selection and rotation forest. Neural Comput Applic: 1–11

  48. Mirjalili SA, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Article  Google Scholar 

  49. Taguchi G (1986) Introduction to quality engineering. Asian Productivity Organization/UNIPUB, White Plains

    Google Scholar 

  50. Phadke MS (1989) Quality engineering using robust design. Prentice-Hall, NJ

    Google Scholar 

  51. Naderi B, Zandieh M, Ghoshe Balagh AK, Roshanaei V (2009) An improved simulated annealing for hybrid flowshops with sequence-dependent setup and transportation times to minimize total completion time and total tardiness. Expert Syst Appl 36:9625–9633

    Article  Google Scholar 

  52. Naderi B, Khalili M, Tavakkoli-Moghaddam R (2009) A hybrid artificial immune algorithm for a realistic variant of job shops to minimize the total completion time. Comput Ind Eng 56:1494–1501

    Article  Google Scholar 

  53. Sun M, Aronson JE, Patrick PG, Drinka D (1998) A tabu search heuristic procedure for the fixed charge transportation problem. Eur J Oper Res 106:441456

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Industrial Engineering, University of Science and Technology of Mazandaran, Behshahr, Iran

    Samira Sadeghi-Moghaddam, Mostafa Hajiaghaei-Keshteli & Mehdi Mahmoodjanloo

Authors
  1. Samira Sadeghi-Moghaddam
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  2. Mostafa Hajiaghaei-Keshteli
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  3. Mehdi Mahmoodjanloo
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Correspondence to Mostafa Hajiaghaei-Keshteli.

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The authors whose names are listed immediately below certify that they have no affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licencing arrangements) or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript.

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Sadeghi-Moghaddam, S., Hajiaghaei-Keshteli, M. & Mahmoodjanloo, M. New approaches in metaheuristics to solve the fixed charge transportation problem in a fuzzy environment. Neural Comput & Applic 31 (Suppl 1), 477–497 (2019). https://doi.org/10.1007/s00521-017-3027-3

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