Skip to main content
SpringerLink
Log in

Solving flow shop scheduling problems by quantum differential evolutionary algorithm

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

This paper proposed a novel quantum differential evolutionary algorithm (QDEA) based on the basic quantum-inspired evolutionary algorithm (QEA) for permutation flow shop scheduling problem (PFSP). In this QDEA, the quantum chromosomes are encoded and decoded by using the quantum rotating angle and a simple strategy named largest rotating angle value rule to determine job sequence based on job’s quantum information is proposed for the representation of PFSP, firstly. Then, we merge the advantages of differential evolution strategy, variable neighborhood search and QEA by adopting the differential evolution to perform the updating of quantum gate and variable neighborhood search to raise the performance of the local search. We adopted QDEA to minimize the makespan, total flowtime and the maximum lateness of jobs and make the simulations. The results and comparisons with other algorithms based on famous benchmarks demonstrated the effectiveness of the proposed QDEA. Another contribution of this paper is to report new absolute values of total flowtime and maximum lateness for various benchmark problem sets.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Garey M, Johnson D, Sethi R (1976) The complexity of flowshop and jobshop scheduling. Math Oper Res 24(1):117–129

    Article  MathSciNet  Google Scholar 

  2. Nawaz M, Enscore E Jr, Ham I (1983) A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem. OMEGA 11:91–95

    Article  Google Scholar 

  3. Kalczynski PJ, Kaznburowski J (2007) On the NEH heuristic for minimizing the makespan in permutation flow shops. OMEGA 35:53–60

    Article  Google Scholar 

  4. Murata T, Ishibuchi H, Tanaka H (1996) Genetic algorithms for flowshop scheduling problems. Comput Ind Eng 30(4):1061–1071

    Article  Google Scholar 

  5. Reeves CR, Yamada T (1998) Genetic algorithms, path relinking and the flowshop sequencing problem. Evol Comput 6:45–60

    Article  Google Scholar 

  6. Iyer SK, Saxena B (2004) Improved genetic algorithm for the permutation flowshop scheduling problem. Comput Oper Res 34(4):593–606

    Article  MathSciNet  Google Scholar 

  7. Doyen A, Engin O, Ozkan C (2003) A new artificial immune system approach to solve permutation flow shop scheduling problems. Tukish Symposium on Artificial Immune System and Neural Networks TAINN’03.

  8. Nowicki E, Smutnicki C (1996) A fast tabu search algorithm for the permutation flow-shop problem. Eur J Oper Res 91:160–175

    Article  MATH  Google Scholar 

  9. Grabowski J, Wodecki M (2004) A very fast tabu search algorithm for the permutation flow shop problem with makespan criterion. Comput Oper Res 31:1891–1909

    Article  MATH  MathSciNet  Google Scholar 

  10. Osman IH, Potts CN (1989) Simulated annealing for permutation flow-shop scheduling. OMEGA 17:551–557

    Article  Google Scholar 

  11. Ishibuchi H, Misaki S, Tanaka H (1995) Modified simulated annealing algorithms for the flow shop sequencing problem. Eur J Oper Res 81(2):388–398

    Article  MATH  Google Scholar 

  12. Merkle D, Middendorf M (2001) A new approach to solve permutation scheduling problems with ant colony optimization. Lect Notes Comput Sci 2037:484–494

    Article  Google Scholar 

  13. Yinga K-C, Liao C-J (2004) An ant colony system for permutation flow-shop sequencing. Comput Oper Res 31(5):791–801

    Article  Google Scholar 

  14. Rameshkumar K, Suresh RK, Mohanasundaram KM (2005) Discrete particle swarm optimization (DPSO) algorithm for permutation flowshop scheduling to minimize makespan. Adv Nat Comp 3612:572–581

    Article  Google Scholar 

  15. Jarboui B, Ibrahim S, Siarry P, Rebai A (2008) A combinatorial particle swarm optimisation for solving permutation flowshop problems. Comput Ind Eng 54(3):526–538

    Article  Google Scholar 

  16. Stützle T (1998) Applying iterated local search to the permutation flow shop problem. Technical report, AIDA-98-04, FG Intellektik, TU Darmstadt

  17. Ruiz R, Stützle T (2007) A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem. Eur J Oper Res 177(3):2033–2049

    Article  MATH  Google Scholar 

  18. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82

    Article  Google Scholar 

  19. Zheng D, Wang L (2003) An effective hybrid heuristic for flow shop scheduling. Int J Adv Manuf Technol 21(1):38–44

    Article  Google Scholar 

  20. Wang L, Zhang L, Zheng Da-Zhong (2006) An effective hybrid genetic algorithm for flow shop scheduling with limited buffers. Comput Oper Res 33(10):2960–2971

    Article  MATH  MathSciNet  Google Scholar 

  21. Liu Z, Wang S (2006) Hybrid Particle Swarm Optimization for Permutation Flow Shop Scheduling. Intelligent Control and Automation, 2006. WCICA 2006. The Sixth World Congress on. 1, pp. 3245–3249

  22. Chandrasekaran, S. Ponnambalam, S.G..Suresh, R.K. Vijayakumar (2006) A Hybrid Discrete Particle Swarm Optimization Algorithm to Solve Flow Shop Scheduling Problems. Cybernetics and Intelligent Systems, 2006 IEEE Conference on, pp.1–6.

  23. Tavakkoli-Moghaddama R, Rahimi-Vaheda A, Mirzaei AH (2007) A hybrid multi-objective immune algorithm for a flow shop scheduling problem with bi-objectives: weighted mean completion time and weighted mean tardiness. Inf Sci 177(22):5072–5090

    Article  Google Scholar 

  24. Andreas AC, Nearchou C (2004) A novel metaheuristic approach for the flow shop scheduling problem. Eng Appl Artif Intell 17(3):289–300

    Article  Google Scholar 

  25. Talbi E-G, Rahoual M, Mabed MH, Dhaenens C (2001) A hybrid evolutionary approach for multicriteria optimization problems: application to the flow shop. Lect Notes Comput Sci 1993:416–428

    Article  Google Scholar 

  26. Ponnambalam SG, Jagannathan H, Kataria M, Gadicherla A (2009) A TSP-GA multi-objective algorithm for flow-shop scheduling. Int J Adv Manuf Technol 23(11–12):909–915

    Google Scholar 

  27. Han K-H (2000) Genetic quantum algorithm and its application to combinatorial optimization problem. In: IEEE Proc. Of the 2000 Congress on Evolutionary Computation, San Diego, USA IEEE Press

  28. KH Han, KH Park, CH Lee, JH Kim Parallel quantum-inspired genetic algorithm for combinatorial optimization problem。Evolutionary Computation, 2001. Proceedings of the 2001.

  29. KH Han, JH Kim, On setting the parameters of quantum-inspired evolutionary algorithm for practical application Evolutionary Computation, 2003. CEC’03. The 2003 Congress on 2003.

  30. Han K-H, Kim J-H. Quantum-inspired Evolutionary Algorithm for a Class of Combinatorial Optimization. IEEE Trans on Evolutionary Computation, 2002.

  31. Han K-H, Kim J-H. Quantum-inspired Evolutionary Algorithms with a New Termination Criterion H,Gate and Two-Phase Scheme. IEEE Trans on Evolutionary Computation 2004.

  32. Wang Ling, Wu Hao, and Zheng Da-Zhong (2005) A quantum-inspired genetic algorithm for scheduling problems. Lecture Notes in Computer Science, v 3612, n PART III. Advances in Natural Computation: First International Conference, ICNC 2005. Proceedings, pp. 417–423.

  33. Wang L, Wu H, Tang F, Zheng DZ (2005) A hybrid quantum-inspired genetic algorithm for flow shop scheduling. Lect Notes Comput Sci 3645:636–644

    Article  Google Scholar 

  34. Li Bin-Bin and Wang Ling (2006) A hybrid quantum-inspired genetic algorithm for multi-objective scheduling. Lecture Notes in Computer Science, v 4113 LNCS—I, International Conference on Intelligent Computing, ICIC 2006, Proceedings, pp. 511–522.

  35. Bean JC (1994) Genetics and random keys for sequencing and optimization. ORSA J Comput 6(2):154–160

    MATH  Google Scholar 

  36. Storn R, Price K (1999) Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces. Technical Report TR-95-012, ICSI.

  37. Storn R, Price K (1997) Differential evolution—a simple evolution strategy for fast optimization. Dr. Dobb’s J 78:18–24

    Google Scholar 

  38. Pan QK, Tasgetiren MF, Liang YC (2008) A discrete differential evolution algorithm for the permutation flowshop scheduling problem. Comput Ind Eng 55(4):795–816

    Article  Google Scholar 

  39. Qian B, Wang L, Rong Hu, Wang W-L, Huang De-Xian, Wang X (2008) A hybrid differential evolution method for permutation flow-shop scheduling. Int J Adv Manuf Technol 38(5–6):757–777

    Article  Google Scholar 

  40. Hansen P, Mladenovic N (2003) A tutorial on variable neighborhood search. GERAD and Mathematical Institute, SANU

    Google Scholar 

  41. Ong YS, Lim MH, Zhu N (2006) Classification of adaptive memetic algorithms: a comparative study. IEEE Transact Sys, Man and Cyb-B: Cyb 36:141–152

    Article  Google Scholar 

  42. Hart W E, Krasnogor N, Smith J E. ( 2004) Recent advances in memetic algorithms. Springer: Heidelberg.

  43. Carlier J (1978) Ordonnancements a contraintes disjonctives. Rech Opér 12(4):333–350

    MATH  MathSciNet  Google Scholar 

  44. Reeves CR (1995) A genetic algorithm for flowshop sequencing. Comp Ope Res 22(1):5–13

    Article  MATH  Google Scholar 

  45. Heller J (1960) Some numerical experiments for an MxJ flow shop and its decision-theoretical aspects. Oper Res 8:178–184

    Article  MATH  MathSciNet  Google Scholar 

  46. Taillard E (1993) Benchmarks for basic scheduling problems. Eur J Oper Res 64(2):278–285

    Article  MATH  Google Scholar 

  47. Demirkol E, Mehta S, Uzsoy R (1998) Benchmarks for shop scheduling problems. Eur J Oper Res 109:137–141

    Article  MATH  Google Scholar 

  48. Tasgetiren MF, Liang YC, Sevkli M, Gencyilmaz G. (2004) Particle swarm optimization algorithm for makespan and maximum lateness minimization in permutation flowshop sequencing problem. In: Proceedings of the fourth international symposium on intelligent manufacturing systems. Turkey: Sakarya. pp. 431–41.

  49. Liao C-J, Tseng C-T, Luarn P (2007) A discrete version of particle swarm optimization for flowshop scheduling problems. Comput Oper Res 34(10):3099–3111

    Article  MATH  Google Scholar 

  50. Liu J, Reeves CR (2001) Constructive and composite heuristic solutions to the scheduling P//ΣCi problem. Eur J Oper Res 132:439–452

    Article  MATH  MathSciNet  Google Scholar 

  51. Rajendran C, Ziegler H (2004) Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs. Eur J Oper Res 155:426–438

    Article  MATH  MathSciNet  Google Scholar 

  52. Rajendran C, Ziegler H (2005) Two ant-colony algorithms for minimizing total flowtime in permutation flowshops. Comput Ind Eng 48(4):789–797

    Article  Google Scholar 

  53. Rajendran C, Chaudhuri D (1991) A flowshop scheduling algorithm to minimize maximum lateness. J Oper Res Soc Jpn 34:28–45

    MATH  Google Scholar 

  54. Laha D, Sarin SC (2009) A heuristic to minimize total flow time in permutation flow shop. Omega 37(3):734–739

    Article  Google Scholar 

  55. Framinan JM, Leisten R (2003) An efficient constructive heuristic for flowtime minimisation in permutation flow shops. Omega 31(4):311–317

    Article  Google Scholar 

  56. Rad SF, Ruiz R, Boroojerdian N (2009) New high performing heuristics for minimizing makespan in permutation flowshops. Omega 37(2):331–345

    Article  Google Scholar 

  57. Zhang C, Sun J (2009) An alternate two phases particle swarm optimization algorithm for flow shop scheduling problem. Expert Systems Appl 36(3):5162–5167

    Article  Google Scholar 

  58. Changsheng Zhang, Jiaxu Ning and Dantong Ouyang (2009) A hybrid alternate two phases particle swarm optimization algorithm for flow shop scheduling problem. Comp Ind Eng (in press)

  59. Rajkumar R, Shahabudeen P (2009) Scheduling jobs on flowshop environment applying simulated annealing algorithm. Int Jour Serv Op Info 4(3):212–231

    Google Scholar 

  60. Rajkumar R, Shahabudeen P (2009) An improved genetic algorithm for the flowshop scheduling problem. Int J Prod Res 47(1):233–249

    Article  MATH  Google Scholar 

  61. Zobolas GI, Tarantilisa CD, Ioannoua G (2009) Minimizing makespan in permutation flow shop scheduling problems using a hybrid metaheuristic algorithm. Comput Oper Res 36(4):1249–1267

    Article  MATH  MathSciNet  Google Scholar 

  62. Qian B, Wang L, Huang DX, Wang X (2009) An effective hybrid DE-based algorithm for flow shop scheduling with limited buffers. Int J Prod Res 47(1):1–24

    Article  MathSciNet  Google Scholar 

  63. Tseng L-Y, Lin Y-T (2009) A hybrid genetic local search algorithm for the permutation flowshop scheduling problem. Eur J Oper Res 198(1):84–92

    Article  MATH  Google Scholar 

  64. Laha D, Chakraborty UK (2009) An efficient hybrid heuristic for makespan minimization in permutation flow shop scheduling. Int J Adv Manuf Technol 44(5–6):559–569

    Article  Google Scholar 

  65. Kuo I-Hong, Horng S-J, Kao T-W, Lin T-L, Lee C-L, Terano T, Pan Y (2009) An efficient flow-shop scheduling algorithm based on a hybrid particle swarm optimization model. Expert Systems Appl 36(2):7027–7032

    Article  Google Scholar 

  66. Lian Z, Gu X, Jiao B (2008) A novel particle swarm optimization algorithm for permutation flow-shop scheduling to minimize makespan. Chaos, Solitons Fractals 35:851–861

    Article  MATH  Google Scholar 

  67. Zhang Y, Li X, Wang Q (2009) Hybrid genetic algorithm for permutation flowshop scheduling problems with total flowtime minimization. Eur J Oper Res 196(3):869–876

    Article  MATH  Google Scholar 

  68. PC Chang, WH Huang, CJ Ting, LC Wu, CM Lai (2009) A Hybrid Genetic-Immune Algorithm with Improved Offsprings and Elitist Antigen for Flow-shop Scheduling Problems. 11th IEEE International Conference on High Performance Computing and Communications.

  69. Bożejko W (2009) Solving the flow shop problem by parallel programming. J Parallel Distrib Comput 69(5):470–481

    Article  Google Scholar 

  70. Vallada E, Ruiz R (2009) Cooperative metaheuristics for the permutation flowshop scheduling problem. Eur J Oper Res 193(2):365–376

    Article  MATH  Google Scholar 

  71. Bai D, Tang L (2009) New heuristics for flow shop problem to minimize makespan. J Oper Res Soc (in press)

  72. Naderi B, Tavakkoli-Moghaddam R, Khalili M (2009) Electromagnetism-like mechanism and simulated annealing algorithms for flowshop scheduling problems minimizing the total weighted tardiness and makespan. Knowledge-Based Systems (in press).

  73. Li X, Wang Q, Cheng Wu (2009) Efficient composite heuristics for total flowtime minimization in permutation flow shops. Omega 37(1):155–164

    Article  Google Scholar 

  74. Sheibani K (2009) A fuzzy greedy heuristic for permutation flow-shop scheduling. J Oper Res Soc (in press)

  75. Chin-Chia Wu and Wen-Chiung Lee (2009) A note on the total completion time problem in a permutation flowshop with a learning effect. Eur J Oper Res 192(1):343–347

    Article  Google Scholar 

  76. Rahimi-Vahed A, Dangchi M, Rafiei H, Salimi E (2009) A novel hybrid multi-objective shuffled frog-leaping algorithm for a bi-criteria permutation flow shop scheduling problem. Int J Adv Manuf Technol 41(11–12):1227–1239

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial and Information Systems Engineering, Ashikaga Institute of Technology, 268-1, Omae cho, Ashikaga, Tochigi, Japan, 326-8558

    Tianmin Zheng & Mitsuo Yamashiro

Authors
  1. Tianmin Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mitsuo Yamashiro
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tianmin Zheng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zheng, T., Yamashiro, M. Solving flow shop scheduling problems by quantum differential evolutionary algorithm. Int J Adv Manuf Technol 49, 643–662 (2010). https://doi.org/10.1007/s00170-009-2438-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-009-2438-4

Keywords

Search

Navigation