A Novel Encoding Scheme of PSO for Two-Machine Group Scheduling

  • Cheng-Dar Liou
  • Chun-Hung Liu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6145)


This paper investigates the two-machine flow shop group scheduling problem with the transportation times and sequence-dependent setup times considerations. The objective is to minimize the total completion time. In this paper, a novel encoding scheme of PSO for flow shop group scheduling is proposed to effectively solve various instances with group numbers up to 15. Note that the proposed encoding scheme simultaneously determines the sequence of jobs in each group and the sequence of groups. Three different lower bounds are developed to evaluate the performance of the proposed PSO algorithm. Limited numerical results show that the proposed PSO algorithm performs well for all test problems.


Group scheduling Transportation times Sequence-dependent Setup times PSO 


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  1. 1.
    Garey, M.D., Johnson, D.S., Sethi, R.: The complexity of flowshop and jobshop scheduling. Math. Oper. Res. 1(2), 117–129 (1976)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Schaller, J.E., Gupta, J.N.D., Vakharia, A.J.: Scheduling a flowline manufacturing cell with sequence dependent family setup times. Eur. J. Oper. Res. 125, 324–339 (2000)zbMATHCrossRefGoogle Scholar
  3. 3.
    Logendran, R., Salmasi, N., Sriskandarajah, C.: Two-machine group scheduling problems in discrete parts manufacturing with sequence-dependent setups. Comp. Oper. Res. 33, 158–180 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, Piscataway, NJ, pp. 1942–1948 (1995)Google Scholar
  5. 5.
    Maggu, P.L., Das, G.: On sequencing problem with transportation times of jobs. Pure A. Math. 12, 1–6 (1980)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Yang, D.L., Chern, M.S.: Two-machine flowshop group scheduling problem. Comp. Oper. Res. 27, 975–985 (1999)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Bean, J.C.: Genetic algorithms and random keys for sequencing and optimization. ORSA J. Comp. 6(2), 154–160 (1994)zbMATHGoogle Scholar
  8. 8.
    Liu, B., Wang, L., Jin, Y.H.: An effective hybrid PSO-based algorithm for flow shop scheduling with limited buffers. Comp. Oper. Res. 35(9), 2791–2806 (2008)zbMATHCrossRefGoogle Scholar
  9. 9.
    Nasser, S., Rasaratnam, L., Mohammad, R.S.: Total flow time minimization in a flowshop sequence-dependent group scheduling problem. Comp. Oper. Res. 37(1), 199–212 (2010)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Cheng-Dar Liou
    • 1
  • Chun-Hung Liu
    • 1
  1. 1.Department of Business AdministrationNational Formosa UniversityHuweiTaiwan, ROC

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