A Hybrid Particle Swarm Optimization Algorithm for the Permutation Flowshop Scheduling Problem

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 31)

Abstract

This paper introduces a new hybrid algorithmic nature inspired approach based on Particle Swarm Optimization, for successfully solving one of the most computationally complex problems, the Permutation Flowshop Scheduling Problem. The Permutation Flowshop Scheduling Problem (PFSP) belongs to the class of combinatorial optimization problems characterized as NP-hard and, thus, heuristic and metaheuristic techniques have been used in order to find high quality solutions in reasonable computational time. The proposed algorithm for the solution of the PFSP, the Hybrid Particle Swarm Optimization (HybPSO), combines a Particle Swarm Optimization (PSO) Algorithm, the Variable Neighborhood Search (VNS) Strategy and a Path Relinking (PR) Strategy. In order to test the effectiveness and the efficiency of the proposed method we use a set of benchmark instances of different sizes.

Key words

Permutation flowshop scheduling problem Particle swarm optimization Variable neighborhood search Path relinking 

References

  1. 1.
    Banks, A., Vincent, J., Anyakoha, C.: A review of particle swarm optimization. Part I: background and development. Nat. Comput. 6(4), 467–484 (2007)MathSciNetMATHGoogle Scholar
  2. 2.
    Banks, A., Vincent, J., Anyakoha, C.: A review of particle swarm optimization. Part II: hybridisation, combinatorial, multicriteria and constrained optimization, and indicative applications. Nat. Comput. 7, 109–124 (2008)Google Scholar
  3. 3.
    Chen, S.H., Chang, P.C., Cheng, T.C.E., Zhang, Q.: A Self-guided genetic algorithm for permutation flowshop scheduling problems. Comp. Oper. Res. 39, 1450–1457 (2012)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Clerc, M., Kennedy, J.: The particle swarm: explosion, stability and convergence in a multi-dimensional complex space. IEEE Trans. Evol. Comput. 6, 58–73 (2002)CrossRefGoogle Scholar
  5. 5.
    Dueck, G., Scheurer, T.: Threshold accepting: A general purpose optimization algorithm appearing superior to simulated annealing. J. Comput. Phys. 90, 161–175 (1990)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Gajpal, Y., Rajendran, C.: An ant-colony optimization algorithm for minimizing the completion-time variance of jobs in flowshops. Int. J. Prod. Econ. 101(2), 259–272 (2006)CrossRefGoogle Scholar
  7. 7.
    Garey, M.R., Johnson, D.S., Sethi, R.: The complexity of flowshop and jobshop scheduling. Math. Oper. Res. 1, 117–129 (1976)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Glover, F., M. Laguna, M., Marti, R.: Scatter search and path relinking: advances and applications. In: Glover, F., Kochenberger, G.A. (eds.) Handbook of Metaheuristics, pp. 1–36. Kluwer, Boston (2003)Google Scholar
  9. 9.
    Grabowski, J., Wodecki, M.: A very fast tabu search algorithm for the permutation flow shop problem with makespan criterion. Comp. Oper. Res. 31, 1891–1909 (2004)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Gupta, J.N.D., Stafford, E.F., Jr.: Flowshop scheduling research after five decades. Eur. J. Oper. Res. 169, 699–711 (2006)MATHCrossRefGoogle Scholar
  11. 11.
    Hansen, P., Mladenovic, N.: Variable neighborhood search: principles and applications. Eur. J. Oper. Res. 130, 449–467 (2001)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Jarboui, B., Ibrahim, S., Siarry, P., Rebai, A.: A combinatorial particle swarm optimisation for solving permutation flow shop problems. Comp. Ind. Eng. 54, 526–538 (2008)CrossRefGoogle Scholar
  13. 13.
    Johnson, S.: Optimal two-and-three stage production schedules with setup times included. Naval Res. Logist. Q. 1, 61–68 (1954)CrossRefGoogle Scholar
  14. 14.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of 1995 IEEE International Conference on Neural Networks, vol. 4, Perth, WA and the paper ISBN: 0-7803-2768-3 pp. 1942–1948 (1995)Google Scholar
  15. 15.
    Lian, Z., Gu, X., Jiao, B.: A similar particle swarm optimization algorithm for permutation flowshop scheduling to minimize makespan. Appl. Math. Comput. 175(1), 773–785 (2006)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Liao, C.J., Tseng, C.T., Luarn P.: A discrete version of particle swarm optimization for flowshop scheduling problems. Comp. Oper. Res. 34, 3099–3111 (2007)MATHCrossRefGoogle Scholar
  17. 17.
    Lichtblau, D.: Discrete optimization using Mathematica. In: Callaos, N., Ebisuzaki, T., Starr, B., Abe, J.M., Lichtblau, D. (eds.) Proceedings of World Multi-Conference on Systemics, Cybernetics and Informatics (SCI 2002). International Institute of Informatics and Systemics, vol. 16, pp. 169–174 Orlando, Florida, USA (2002)Google Scholar
  18. 18.
    Liu, B., Wang, L., Jin, Y.H.: An effective PSO-based memetic algorithm for flow shop scheduling. IEEE Trans. Syst. Man Cybern. B Cybern. 37(1), 18–27 (2007)CrossRefGoogle Scholar
  19. 19.
    Liu, Y.F., Liu, S.Y.: A hybrid discrete artificial bee colony algorithm for permutation flowshop scheduling problem. Appl. Soft Comput. (2011) doi:10.1016/j.asoc.2011.10.024Google Scholar
  20. 20.
    Lourenco, H.R., Martin, O., St\(\ddot{u}\)tzle, T.: Iterated local search. In: Handbook of Metaheuristics, vol. 57. Operations Research and Management Science, pp. 321–353. Kluwer, Boston (2002)Google Scholar
  21. 21.
    Nowicki, E., Smutnicki, C.: A fast tabu search algorithm for the permutation flow-shop problem. Eur. J. Oper. Res. 91, 160–175 (1996)MATHCrossRefGoogle Scholar
  22. 22.
    Pan, Q.K., Tasgetiren, M.F., Liang, Y.C.: A discrete differential evolution algorithm for the permutation flowshop scheduling problem. Comp. Ind. Eng. 55, 795–816 (2008)CrossRefGoogle Scholar
  23. 23.
    Pinedo, M.: Scheduling. Theory, Algorithms, and Systems. Prentice Hall, Englewood Cliffs (1995)Google Scholar
  24. 24.
    Poli, R., Kennedy, J., Blackwell, T.: Particle swarm optimization. An overview. Swarm Intell. 1, 33–57 (2007)CrossRefGoogle Scholar
  25. 25.
    Rajendran, C., Ziegler, H.: Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs. Eur. J. Oper. Res. 155(2), 426–438 (2004)MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Rajendran, C., Ziegler, H.: Two ant-colony algorithms for minimizing total flowtime in permutation flowshops. Comp. Ind. Eng. 48(4), 789–797 (2005)CrossRefGoogle Scholar
  27. 27.
    Rinnooy Kan, A.H.G.: Machine Scheduling Problems: Classification, Complexity, and Computations. Nijhoff, The Hague (1976)Google Scholar
  28. 28.
    Ruiz, R., Maroto, C.: A comprehensive review and evaluation of permutation flowshop heuristics. Eur. J. Oper. Res. 165, 479–494 (2005)MathSciNetMATHCrossRefGoogle Scholar
  29. 29.
    Ruiz, R., St\(\ddot{u}\)tzle, T.: A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem. Eur. J. Oper. Res. 177, 2033–2049 (2007)Google Scholar
  30. 30.
    Ruiz, R., Maroto, C., Alcaraz, J.: Two new robust genetic algorithms for the flowshop scheduling problem. Omega 34, 461–476 (2006)CrossRefGoogle Scholar
  31. 31.
    Taillard, E.: Benchmarks for basic scheduling problems. Eur. J. Oper. Res. 64, 278–285 (1993)MATHCrossRefGoogle Scholar
  32. 32.
    Tasgetiren, M., Liang, Y., Sevkli, M., Gencyilmaz, G.: A particle swarm optimization algorithm for makespan and total flow time minimization in the permutation flowshop sequencing problem. Eur. J. Oper. Res. 177, 1930–1947 (2007)MATHCrossRefGoogle Scholar
  33. 33.
    Tseng, L.Y., Lin, Y.T.: A hybrid genetic local search algorithm for the permutation flowshop scheduling problem. Eur. J. Oper. Res. 198, 84–92 (2009)MATHCrossRefGoogle Scholar
  34. 34.
    Tseng, L.Y., Lin, Y.T.: A genetic local search algorithm for minimizing total flowtime in the permutation flowshop scheduling problem. Int. J. Prod. Econ. 127, 121–128 (2010)CrossRefGoogle Scholar
  35. 35.
    Vallada, E., Ruiz, R.: Cooperative metaheuristics for the permutation flowshop scheduling problem. Eur. J. Oper. Res. 193, 365–376 (2009)MATHCrossRefGoogle Scholar
  36. 36.
    Ying, K.C., Liao, C.J.: An ant colony system for permutation flow-shop sequencing. Comp. Oper. Res. 31, 791–801 (2004)MATHCrossRefGoogle Scholar
  37. 37.
    Zhang, C., Sun, J., Zhu, X., Yang, Q.: An improved particle swarm optimization algorithm for flowshop scheduling problem. Inform. Process. Lett. 108, 204–209 (2008)MathSciNetCrossRefGoogle Scholar
  38. 38.
    Zhang, C., Ning, J., Ouyang, D.: A hybrid alternate two phases particle swarm optimization algorithm for flow shop scheduling problem. Comp. Ind. Eng. 58, 1–11 (2010)CrossRefGoogle Scholar
  39. 39.
    Zobolas, G.I., Tarantilis, C.D., Ioannou, G.: Minimizing makespan in permutation flow shop scheduling problems using a hybrid metaheuristic algorithm. Comp. Oper. Res. 36, 1249–1267 (2009)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Technical University of Crete, Department of Production Engineering and ManagementIndustrial Systems Control LaboratoryChaniaGreece

Personalised recommendations