A discrete gravitational search algorithm for the blocking flow shop problem with total flow time minimization

  • Fuqing ZhaoEmail author
  • Feilong Xue
  • Yi Zhang
  • Weimin Ma
  • Chuck Zhang
  • Houbin Song


The blocking flow shop problem (BFSP) is one of the key models in the flow shop scheduling problem in the manufacturing systems. Gravitational Search Algorithm (GSA) is an algorithm based on the population for solving various optimization problems. However, GSA is scarcely applied to solve the BFSP as it is designed to solve the continuous problems. In this paper, a Discrete Gravitational Search Algorithm (DGSA) is presented for solving the BFSP with the total flow time minimization. A new variable profile fitting (VPF) combined with NEH heuristic, named VPF _ NEH(n), is introduced for balancing the quality and the diversity of the initial population to configure the DGSA. The three operators including the variable neighborhood operators (VNO), the path relinking and the plus operator are implemented during the location updating of the candidates. The objective of the operation is to prevent the premature convergence of the population and to balance the exploration and exploitation in the process of optimization. The expected runtime of the DGSA is analyzed by the level-based theorem. The simulated results indicate that the effectiveness and superiority of the DGSA.


Gravitational search algorithm Blocking flow shop problem Total flow time Constructive heuristic Variable neighborhood search 



This work was financially supported by the National Natural Science Foundation of China under grant numbers 61663023. It was also supported by the Key Research Programs of Science and Technology Commission Foundation of Gansu Province (2017GS10817), Lanzhou Science Bureau project (2018-rc-98), Zhejiang Provincial Natural Science Foundation (LGJ19E050001), Wenzhou Public Welfare Science and Technology project (G20170016), respectively.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Computer and Communication TechnologyLanzhou University of TechnologyLanzhouChina
  2. 2.School of Mechnical EngineeringXijin UniversityXi’anChina
  3. 3.School of Economics and ManagementTongji UniversityShanghaiChina
  4. 4.H. Milton Stewart School of Industrial & Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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