Advertisement

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
Article
  • 15 Downloads

Abstract

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.

Keywords

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

Notes

Acknowledgements

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.

References

  1. 1.
    Pan QK, Ruiz R (2012) An estimation of distribution algorithm for lot-streaming flow shop problems with setup times. Omega 40(2):166–180CrossRefGoogle Scholar
  2. 2.
    Ruiz-Torres AJ, Ho JC, Ablanedo-Rosas JH (2011) Makespan and workstation utilization minimization in a flowshop with operations flexibility. Omega 39(3):273–282CrossRefGoogle Scholar
  3. 3.
    Ronconi DP, Henriques LRS (2009) Some heuristic algorithms for total tardiness minimization in a flowshop with blocking. Omega 37(2):272–281CrossRefGoogle Scholar
  4. 4.
    Gong H, Tang L, Duin CW (2010) A two-stage flow shop scheduling problem on a batching machine and a discrete machine with blocking and shared setup times. Comput Oper Res 37(5):960–969CrossRefzbMATHGoogle Scholar
  5. 5.
    Hall NG, Sriskandarajah C (1996) A survey of machine scheduling problems with blocking and no-wait in process. Oper Res 44(3):510–525MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Sethi SP, Sriskandarajah C, Sorger G, Blazewicz J, Kubiak W (1992) Sequencing of parts and robot moves in a robotic cell. Int J Flex Manuf Syst 4(3–4):331–358CrossRefGoogle Scholar
  7. 7.
    Ribas I, Companys R (2015) Efficient heuristic algorithms for the blocking flow shop scheduling problem with total flow time minimization. Comput Ind Eng 87:30–39CrossRefGoogle Scholar
  8. 8.
    Mccormick ST, Pinedo M, Wolf B, Wolf B (1989) Sequencing in an assembly line with blocking to minimize cycle time. Oper Res 37(6):925–935CrossRefzbMATHGoogle Scholar
  9. 9.
    Fernandez-Viagas V, Leisten R, Framinan JM (2016) A computational evaluation of constructive and improvement heuristics for the blocking flow shop to minimise total flowtime. Expert Syst Appl 61:290–301CrossRefGoogle Scholar
  10. 10.
    Pan QK, Wang L (2011) Effective heuristics for the blocking flowshop scheduling problem with makespan minimization. Omega 40(2):218–229CrossRefGoogle Scholar
  11. 11.
    Ribas I, Companys R, Tort-Martorell X (2015) An efficient discrete artificial bee Colony algorithm for the blocking flow shop problem with total flowtime minimization. Expert Syst Appl 42(15–16):6155–6167CrossRefGoogle Scholar
  12. 12.
    Nouha N, Talel L (2015) A particle swarm optimization metaheuristic for the blocking flow shop scheduling problem: Total tardiness minimization. Multi-agent systems and agreement technologies. Springer: 145–153Google Scholar
  13. 13.
    Riahi V, Khorramizadeh M, Newton MAH, Sattar A (2017) Scatter search for mixed blocking flowshop scheduling. Expert Syst Appl 79(C):20–32CrossRefGoogle Scholar
  14. 14.
    Pan QK, Wang L, Sang HY, Li JQ, Liu M (2013) A high performing memetic algorithm for the Flowshop scheduling problem with blocking. IEEE Trans Auto Sci Eng 10(3):741–756CrossRefGoogle Scholar
  15. 15.
    Lin SW, Ying KC (2013) Minimizing makespan in a blocking flowshop using a revised artificial immune system algorithm. Omega 41(2):383–389CrossRefGoogle Scholar
  16. 16.
    Wang C, Song S, Gupta JND, Wu C (2012) A three-phase algorithm for flowshop scheduling with blocking to minimize makespan. Comput Oper Res 39(11):2880–2887MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Wang L, Pan QK, Tasgetiren MF (2011) A hybrid harmony search algorithm for the blocking permutation flow shop scheduling problem. Comput Ind Eng 61(1):76–83CrossRefGoogle Scholar
  18. 18.
    Moslehi G, Khorasanian D (2013) Optimizing blocking flow shop scheduling problem with total completion time criterion. Comput Oper Res 40(7):1874–1883MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Ying KC, Lin SW (2017) Minimizing Makespan in distributed blocking Flowshops using hybrid iterated greedy algorithms. IEEE Access PP (99):1–1Google Scholar
  20. 20.
    Tasgetiren MF, Kizilay D, Pan QK, Suganthan PN (2017) Iterated greedy algorithms for the blocking flowshop scheduling problem with makespan criterion. Comput Oper Res 77(C):111–126MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Han Y, Gong D, Li J, Zhang Y (2016) Solving the blocking flow shop scheduling problem with makespan using a modified fruit fly optimisation algorithm. Int J Prod Res 54(22):6782–6797CrossRefGoogle Scholar
  22. 22.
    Tasgetiren MF, Pan QK, Kizilay D, Suer G (2015) A populated local search with differential evolution for blocking flowshop scheduling problem. IEEE Congress on Evolutionary Computation (CEC): 2789–2796Google Scholar
  23. 23.
    Tasgetiren M, Pan QK, Kizilay D, Gao K (2016) A variable block insertion heuristic for the blocking Flowshop scheduling problem with Total flowtime criterion. Algorithms 9(4):71MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Shao Z, Pi D, Shao W (2018) A multi-objective discrete invasive weed optimization for multi-objective blocking flow-shop scheduling problem. Expert Syst Appl 113:77–99CrossRefGoogle Scholar
  25. 25.
    Shao Z, Pi D, Shao W (2017) Self-adaptive discrete invasive weed optimization for the blocking flow-shop scheduling problem to minimize total tardiness. Comput Ind Eng 111:331–351CrossRefGoogle Scholar
  26. 26.
    Nouri N, Ladhari T (2015) Minimizing regular objectives for blocking permutation flow shop scheduling: heuristic approaches. 441–448Google Scholar
  27. 27.
    Toumi S, Jarboui B, Eddaly M, Rebai (2013) A solving blocking flowshop scheduling problem with branch and bound algorithm. International Conference on Advanced Logistics and Transport: 411–416Google Scholar
  28. 28.
    Khorasanian D, Moslehi G (2012) An iterated greedy algorithm for solving the blocking flow shop scheduling problem with Total flow time criteria. Int J Indust Eng 23(4):301–308Google Scholar
  29. 29.
    Yang X-S (2018) Mathematical analysis of nature-inspired algorithms. Nature-inspired algorithms and applied optimization. Springer: 1–25Google Scholar
  30. 30.
    Kennedy J, Eberhart RC (1995) Particle swarm optimization. IEEE Int Conf Neural Netw 4:1942–1948Google Scholar
  31. 31.
    Storn R, Price K (1997) Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Zhao F, Qin S, Zhang Y, Ma W, Zhang C, Song H (2019) A two-stage differential biogeography-based optimization algorithm and its performance analysis. Expert Syst Appl 115:329–345CrossRefGoogle Scholar
  33. 33.
    Zhao F, Liu Y, Zhang C, Wang J (2015) A self-adaptive harmony PSO search algorithm and its performance analysis. Expert Syst Appl 42(21):7436–7455CrossRefGoogle Scholar
  34. 34.
    Zhao F, Liu Y, Zhang Y, Ma W, Zhang C (2017) A hybrid harmony search algorithm with efficient job sequence scheme and variable neighborhood search for the permutation flow shop scheduling problems. Eng Appl Artif Intell 65:178–199CrossRefGoogle Scholar
  35. 35.
    Zhao F, Shao Z, Wang J, Zhang C (2017) A hybrid differential evolution and estimation of distribution algorithm based on neighbourhood search for job shop scheduling problems. Int J Prod Res 54(4):1–22Google Scholar
  36. 36.
    Meng Z, Pan JS, Kong L (2018) Parameters with adaptive learning mechanism (PALM) for the enhancement of differential evolution. Knowl-Based Syst 141:92–112CrossRefGoogle Scholar
  37. 37.
    Meng Z, Pan JS, Xu H (2016) QUasi-affine TRansformation evolutionary (QUATRE) algorithm: a cooperative swarm based algorithm for global optimization. Knowl-Based Syst 109:104–121CrossRefGoogle Scholar
  38. 38.
    Rao RV (2016) Jaya: a simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int J Ind Eng Comput 7:19–34Google Scholar
  39. 39.
    Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248CrossRefzbMATHGoogle Scholar
  40. 40.
    Rashedi E, Rashedi E, Nezamabadi-pour H (2018) A comprehensive survey on gravitational search algorithm. Swarm Evol Comput 41:141–158CrossRefzbMATHGoogle Scholar
  41. 41.
    Zhao F, Xue F, Zhang Y, Ma W, Zhang C, Song H (2018) A hybrid algorithm based on self-adaptive gravitational search algorithm and differential evolution. Expert Syst Appl 113:515–530CrossRefGoogle Scholar
  42. 42.
    Choudhary A, Gupta I, Singh V, Jana PK (2018) A GSA based hybrid algorithm for bi-objective workflow scheduling in cloud computing. Futur Gener Comput Syst 83:14–26CrossRefGoogle Scholar
  43. 43.
    Lee T, Loong Y, Moslemipour (2017) G gravitational search algorithm optimization for bi-objective flow shop scheduling using weighted dispatching rules. 2017 7th IEEE International Conference on Control System, Computing and Engineering (ICCSCE) IEEE: 127–132Google Scholar
  44. 44.
    Narang N (2018) Hydro-thermal generation scheduling using integrated gravitational search algorithm and predator–prey optimization technique. Neural Comput & Applic 30(2):519–538CrossRefGoogle Scholar
  45. 45.
    Özyön S, Yaşar C (2018) Gravitational search algorithm applied to fixed head hydrothermal power system with transmission line security constraints. Energy 155:392–407CrossRefGoogle Scholar
  46. 46.
    Pelusi D, Mascella R, Tallini L, Nayak J, Naik B, Abraham A (2018) Neural network and fuzzy system for the tuning of gravitational search algorithm parameters. Expert Syst Appl 102:234–244CrossRefGoogle Scholar
  47. 47.
    Mittal H, Saraswat M (2018) An optimum multi-level image thresholding segmentation using non-local means 2D histogram and exponential Kbest gravitational search algorithm. Eng Appl Artif Intell 71:226–235CrossRefGoogle Scholar
  48. 48.
    Taillard E (1993) Benchmarks for basic scheduling problems. Eur J Oper Res 64(2):278–285MathSciNetCrossRefzbMATHGoogle Scholar
  49. 49.
    Graham RL, Lawler EL, Lenstra JK, Kan AHGR (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discrete Math 5(1):287–326MathSciNetCrossRefzbMATHGoogle Scholar
  50. 50.
    Li X, Wang Q, Wu C (2009) Efficient composite heuristics for total flowtime minimization in permutation flow shops. Omega 37(1):155–164CrossRefGoogle Scholar
  51. 51.
    Han Y-Y, Quan-Ke L, Qing J, Cao NN, Liang JJ (2013) Effective hybrid discrete artificial bee colony algorithms for the total;flowtime minimization in the blocking flowshop problem. Int J Adv Manuf Technol 67(1–4):397–414CrossRefGoogle Scholar
  52. 52.
    Wu B, Qian C, Ni W, Fan S (2012) Hybrid harmony search and artificial bee colony algorithm for global optimization problems. Comput Math Applic 64(8):2621–2634MathSciNetCrossRefzbMATHGoogle Scholar
  53. 53.
    Nawaz M, Jr EEE, Ham I (1983) A heuristic algorithm for the m -machine, n -job flow-shop sequencing problem. Omega 11(1):91–95CrossRefGoogle Scholar
  54. 54.
    Wang X, Tang L (2012) A discrete particle swarm optimization algorithm with self-adaptive diversity control for the permutation flowshop problem with blocking. Appl Soft Comput J 12(2):652–662CrossRefGoogle Scholar
  55. 55.
    Glover F, Laguna M (1998) Tabu search. Handbook of combinatorial optimization. Springer: 2093–2229Google Scholar
  56. 56.
    Mladenović N, Hansen P (1997) Variable neighborhood search. Comput Oper Res 24(11):1097–1100.  https://doi.org/10.1016/S0305-0548(97)00031-2 MathSciNetCrossRefzbMATHGoogle Scholar
  57. 57.
    Ribas I, Companys R, Tort-Martorell X (2017) Efficient heuristics for the parallel blocking flow shop scheduling problem. Expert Syst Appl 74:41–54CrossRefGoogle Scholar
  58. 58.
    Zhao F, Liu H, Zhang Y, Ma W, Zhang C (2018) A discrete water wave optimization algorithm for no-wait flow shop scheduling problem. Expert Syst Appl 91:347–363CrossRefGoogle Scholar
  59. 59.
    He J, Yao X (2001) Drift analysis and average time complexity of evolutionary algorithms. Artif Intell 127(1):57–85MathSciNetCrossRefzbMATHGoogle Scholar
  60. 60.
    Goryajnov VV (1996) Evolutionary families of analytic functions and time-nonhomogeneous Markov branching processes. Dokl Math 53 (2)Google Scholar
  61. 61.
    Sudholt D (2010) General lower bounds for the running time of evolutionary algorithms. International conference on parallel problem solving from nature. Springer: 124–133Google Scholar
  62. 62.
    Montgomery DC (2006) Design and analysis of experiments. Technometrics 48(1):158–158Google Scholar
  63. 63.
    Lebbar G, Barkany AE, Jabri A, Abbassi IE (2018) Hybrid metaheuristics for solving the blocking Flowshop scheduling problem. Int J Eng Res Afr 36:124–136CrossRefGoogle Scholar
  64. 64.
    Zhang G, Xing K, Cao F (2018) Discrete differential evolution algorithm for distributed blocking flowshop scheduling with makespan criterion. Eng Appl Artif Intell 76:96–107CrossRefGoogle Scholar
  65. 65.
    Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms' behaviour: a case study on the CEC'2005 special session on real parameter optimization. J Heuristics 15(6):617–644CrossRefzbMATHGoogle Scholar

Copyright information

© 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

Personalised recommendations