Neural Computing and Applications

, Volume 31, Supplement 1, pp 477–497 | Cite as

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

  • Samira Sadeghi-Moghaddam
  • Mostafa Hajiaghaei-KeshteliEmail author
  • Mehdi Mahmoodjanloo
Original Article


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.


Fixed charge transportation problem Metaheuristic Prüfer number Spanning tree Fuzzy Priority based 


Compliance with ethical standards

Conflicts of interest statement

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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Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  1. 1.Department of Industrial EngineeringUniversity of Science and Technology of MazandaranBehshahrIran

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