Applied Intelligence

, Volume 49, Issue 2, pp 791–803 | Cite as

Quantum-inspired cuckoo co-search algorithm for no-wait flow shop scheduling

  • Haihong Zhu
  • Xuemei QiEmail author
  • Fulong Chen
  • Xin He
  • Linfeng Chen
  • Ziyang Zhang


Minimizing the makespan in no-wait flow shop scheduling problem (NWFSP) is widely applied in various industries. However, it is a NP-hard problem. A novel quantum-inspired cuckoo co-search (QCCS) algorithm is proposed to solve this problem. The QCCS algorithm consists of the following three phases: 1) Quantum representation of solution. 2) A quantum-inspired cuckoo search-differential evolution (QCS-DE) search. 3) Local neighborhood search (LNS) algorithm. Meanwhile, the convergence property of the QCCS algorithm is analyzed theoretically. The Taguchi experiments are further designed for the calibration of parameters. The QCCS algorithm was performed on Rec and Car benchmark instances and compared with the state-of-the-art algorithms, including GA-VNS, HGA, TS-PSO, TMIIG, where the superiority of the proposed algorithm is verified by numerical analyses. In addition, the in-depth statistical analysis demonstrates the effectiveness of the proposed algorithm. The numerical results verify that the proposed algorithm has strong optimization ability and can effectively solve the NWFSP with small and medium scale.


Quantum-inspired cuckoo Co-search Differential evolution No-wait flow shop scheduling Makespan 



The authors would like to thank the reviewers for their useful comments and suggestions for this paper. This work was supported by the National Natural Science Foundation of China(61672039, 61572036), the University Natural Science Foundation Project of Anhui Province (1808085QF191) and the University Natural Science Research Project of Anhui Province (KJ2016A272).


  1. 1.
    Wismer DA (1972) Solution of the flowshop-scheduling problem with no intermediate queues. Oper Res 20:689–697CrossRefzbMATHGoogle Scholar
  2. 2.
    Hall NG, Sriskandarajah C (1996) A survey of machine scheduling problems with blocking and no-wait in process. Oper Res 44:510–525MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Rajendran C (1994) A no-wait flowshop scheduling heuristic to minimize makespan. J Oper Res Soc 45:472–478CrossRefzbMATHGoogle Scholar
  4. 4.
    Gilmore PC, Gomory RE (1964) Sequencing a one state-variable machine: a solvable case of the traveling salesman problem. Oper Res 12:655–679MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Edwin Cheng TC, Wang G, Sriskandarajah C (1999) One-operatorCtwo-machine flowshop scheduling with setup and dismounting times. Comput Oper Res 26:715–730CrossRefzbMATHGoogle Scholar
  6. 6.
    Aldowaisan T, Allahverdi A (2004) New heuristics for m-machine no-wait flowshop to minimize total completion time. Omega 32:345–352CrossRefGoogle Scholar
  7. 7.
    Li P, Li S (2008) Quantum-inspired evolutionary algorithm for continuous space optimization based on Bloch coordinates of qubits. Neurocomputing 72:581–591CrossRefGoogle Scholar
  8. 8.
    Ruiz R, Allahverdi A (2009) New heuristics for no-wait flow shops with a linear combination of makespan and maximum lateness. Int J Prod Res 47:5717–5738CrossRefzbMATHGoogle Scholar
  9. 9.
    Rabiee M, Zandieh M, Jafarian A (2012) Scheduling of a no-wait two-machine flow shop with sequence-dependent setup times and probable rework using robust meta-heuristics. Int J Prod Res 50:7428–7446CrossRefGoogle Scholar
  10. 10.
    Ramezani P, Rabiee M, Jolai F (2015) No-wait flexible flowshop with uniform parallel machines and sequence-dependent setup time: a hybrid meta-heuristic approach. J Intell Manuf 26:731–744CrossRefGoogle Scholar
  11. 11.
    Wang S, Liu M, Chu C (2015) A branch-and-bound algorithm for two-stage no-wait hybrid flow-shop scheduling. Int J Prod Res 53:1143–1167CrossRefGoogle Scholar
  12. 12.
    Lin SW, Ying KC (2015) Optimization of makespan for no-wait flowshop scheduling problems using efficient matheuristics. Omega 64:115–125CrossRefGoogle Scholar
  13. 13.
    Aldowaisan T, Allahverdi A (2012) Minimizing total tardiness in no-wait flowshops. Found Comput Decis Sci 37:149–162MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Sapkal SU, Laha D (2013) A heuristic for no-wait flow shop scheduling. Int J Adv Manuf Technol 68:1327–1338CrossRefGoogle Scholar
  15. 15.
    Ding JY, Song S, Gupta JND et al (2015) An improved iterated greedy algorithm with a Tabu-based reconstruction strategy for the no-wait flowshop scheduling problem. Appl Soft Comput 30:604–613CrossRefGoogle Scholar
  16. 16.
    Röck H (1984) The three-machine no-wait flow shop is NP-complete. Journal of the ACM (JACM) 31:336–345Google Scholar
  17. 17.
    Akrout H et al (2013) New Greedy Randomized Adaptive Search Procedure based on differential evolution algorithm for solving no-wait flowshop scheduling problem. In: International Conference on Advanced Logistics and Transport. IEEE, pp 327–334Google Scholar
  18. 18.
    Laha D, Gupta JND (2016) A Hungarian penalty-based construction algorithm to minimize makespan and total flow time in no-wait flow shops. Comput Ind Eng 98:373–383CrossRefGoogle Scholar
  19. 19.
    Yang XS, Deb S (2014) Cuckoo search: recent advances and applications. Neural Comput & Applic 24:169–174CrossRefGoogle Scholar
  20. 20.
    Qian B, Wang L, Hu R et al (2009) A DE-based approach to no-wait flow-shop scheduling. Computers & Industrial Engineering 57:787–805CrossRefGoogle Scholar
  21. 21.
    Tseng LY, Lin YT (2010) A hybrid genetic algorithm for no-wait flowshop scheduling problem. Int J Prod Econ 128:144–152CrossRefGoogle Scholar
  22. 22.
    Jarboui B, Eddaly M, Siarry P (2011) A hybrid genetic algorithm for solving no-wait flowshop scheduling problems. Int J Adv Manuf Technol 54:1129–1143CrossRefGoogle Scholar
  23. 23.
    Samarghandi H, ElMekkawy TY (2012) A meta-heuristic approach for solving the no-wait flow-shop problem. Int J Prod Res 50:1–14CrossRefGoogle Scholar
  24. 24.
    Davendra D, Zelinka I, Bialic-Davendra M et al (2013) Discrete self-organising migrating algorithm for flow-shop scheduling with no-wait makespan. Math Comput Model 57:100–110MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Yang Xin She, Deb S (2010) Cuckoo Search via Lvy flights. In: Nature & Biologically Inspired Computing. NaBIC 2009. World Congress on IEEE, pp 210–214Google Scholar
  26. 26.
    Han KH, Kim JH (2002) Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Trans Evol Comput 6:580–593MathSciNetCrossRefGoogle Scholar
  27. 27.
    Nezamabadi-pour H (2015) A quantum-inspired gravitational search algorithm for binary encoded optimization problems. Eng Appl Artif Intell 40:62–75CrossRefGoogle Scholar
  28. 28.
    Draa A, Meshoul S, Talbi H et al (2011) A quantum-inspired differential evolution algorithm for solving the N-queens problem. Neural Netw 1:12Google Scholar
  29. 29.
    Carlier Jacques (2011) Ordonnancements contraintes disjonctives. RAIRO - Operations Research 12:333–350MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Reeves C (1995) A genetic algorithm for flowshop sequencing. Computers & operations research 22:5–13CrossRefzbMATHGoogle Scholar
  31. 31.
    Taillard E (1993) Benchmarks for basic scheduling programs. Eur J Oper Res 64:278–285CrossRefzbMATHGoogle Scholar
  32. 32.
    Zheng T, Yamashiro M (2010) Solving flow shop scheduling problems by quantum differential evolutionary algorithm. Int J Adv Manuf Technol 49:643–662CrossRefGoogle Scholar
  33. 33.
    Li P, Li S (2008) Quantum-inspired evolutionary algorithm for continuous space optimization based on Bloch coordinates of qubits. Neurocomputing 72:581–591CrossRefGoogle Scholar
  34. 34.
    Framinan JM, Leisten R (2003) An efficient constructive heuristic for flowtime minimisation in permutation flow shops. Omega 31:311–317CrossRefGoogle Scholar
  35. 35.
    Qi X, Wang H, Zhu H et al (2016) Fast local neighborhood search algorithm for the no-wait flow shop scheduling with total flow time minimization. Int J Prod Res 54:1–16CrossRefGoogle Scholar
  36. 36.
    Ye Honghan, Li W, Miao E (2017) An improved heuristic for no-wait flow shop to minimize makespan. J Manuf Syst 44:273–279CrossRefGoogle Scholar
  37. 37.
    Beyer HG, Schwefel HP (2002) Evolution strategiesCA comprehensive introduction. Nat Comput 1:3–52MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Montgomery D (2005) Design and analysis of experiments. Technometrics 48:158–158Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Haihong Zhu
    • 1
    • 2
  • Xuemei Qi
    • 1
    • 2
    Email author
  • Fulong Chen
    • 1
    • 2
  • Xin He
    • 1
    • 2
  • Linfeng Chen
    • 1
    • 2
  • Ziyang Zhang
    • 1
    • 2
  1. 1.School of Computer and InformationAnhui Normal UniversityWuhuChina
  2. 2.Anhui Provincial Key Laboratory of Network and Information SecurityWuhuChina

Personalised recommendations