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A genetic algorithm embedded with a concise chromosome representation for distributed and flexible job-shop scheduling problems

Author

Listed:
  • Po-Hsiang Lu

    (National Chiao Tung University)

  • Muh-Cherng Wu

    (National Chiao Tung University)

  • Hao Tan

    (National Chiao Tung University)

  • Yong-Han Peng

    (National Chiao Tung University)

  • Chen-Fu Chen

    (National Chiao Tung University)

Abstract

This paper proposes a genetic algorithm $$GA\_JS$$ G A _ J S for solving distributed and flexible job-shop scheduling (DFJS) problems. A DFJS problem involves three scheduling decisions: (1) job-to-cell assignment, (2) operation-sequencing, and (3) operation-to-machine assignment. Therefore, solving a DFJS problem is essentially a 3-dimensional solution space search problem; each dimension represents a type of decision. The $$GA\_JS$$ G A _ J S algorithm is developed by proposing a new and concise chromosome representation $${\varvec{S}}_{{\varvec{JOB}}}$$ S J O B , which models a 3-dimensional scheduling solution by a 1-dimensional scheme (i.e., a sequence of all jobs to be scheduled). That is, the chromosome space is 1-dimensional (1D) and the solution space is 3-dimensional (3D). In $$GA\_JS$$ G A _ J S , we develop a 1D-to-3D decoding method to convert a 1D chromosome into a 3D solution. In addition, given a 3D solution, we use a refinement method to improve the scheduling performance and subsequently use a 3D-to-1D encoding method to convert the refined 3D solution into a 1D chromosome. The 1D-to-3D decoding method is designed to obtain a “good” 3D solution which tends to be load-balanced. In contrast, the refinement and 3D-to-1D encoding methods of a 3D solution provides a novel way (rather than by genetic operators) to generate new chromosomes, which are herein called shadow chromosomes. Numerical experiments indicate that $$GA\_JS$$ G A _ J S outperforms the IGA developed by De Giovanni and Pezzella (Eur J Oper Res 200:395–408, 2010), which is the up-to-date best-performing genetic algorithm in solving DFJS problems.

Suggested Citation

  • Po-Hsiang Lu & Muh-Cherng Wu & Hao Tan & Yong-Han Peng & Chen-Fu Chen, 2018. "A genetic algorithm embedded with a concise chromosome representation for distributed and flexible job-shop scheduling problems," Journal of Intelligent Manufacturing, Springer, vol. 29(1), pages 19-34, January.
  • Handle: RePEc:spr:joinma:v:29:y:2018:i:1:d:10.1007_s10845-015-1083-z
    DOI: 10.1007/s10845-015-1083-z
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    References listed on IDEAS

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    1. De Giovanni, L. & Pezzella, F., 2010. "An Improved Genetic Algorithm for the Distributed and Flexible Job-shop Scheduling problem," European Journal of Operational Research, Elsevier, vol. 200(2), pages 395-408, January.
    2. Kacem, Imed & Hammadi, Slim & Borne, Pierre, 2002. "Pareto-optimality approach for flexible job-shop scheduling problems: hybridization of evolutionary algorithms and fuzzy logic," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 60(3), pages 245-276.
    3. Stéphane Dauzère-Pérès & Jan Paulli, 1997. "An integrated approach for modeling and solving the general multiprocessor job-shop scheduling problem using tabu search," Annals of Operations Research, Springer, vol. 70(0), pages 281-306, April.
    4. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
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