Particle Swarm Optimisation for Open Shop Problems with Fuzzy Durations

  • Juan José Palacios
  • Inés González-Rodríguez
  • Camino R. Vela
  • Jorge Puente
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6686)


In this paper we confront a variation of the open shop problem where task durations are allowed to be uncertain and where uncertainty is modelled using fuzzy numbers. We propose a particle swarm optimization (PSO) approach to minimise the expected makespan using priorities to represent particle position, as well as a decoding algorithm to generate schedules in a subset of possibly active ones. Finally, the performance of the PSO is tested on several benchmark problems, modified so as to have fuzzy durations, compared with a memetic algorithm from the literature.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Andresen, M., Bräsel, H., Mörig, M., Tusch, J., Werner, F., Willenius, P.: Simulated annealing and genetic algorithms for minimizing mean flow time in an open shop. Mathematical and Computer Modelling 48, 1279–1293 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Blum, C.: Beam-ACO—hybridizing ant colony optimization with beam search: an application to open shop scheduling. Computers & Operations Research 32(6), 1565–1591 (2005)CrossRefzbMATHGoogle Scholar
  3. 3.
    Brucker, P., Hunrink, J., Jurisch, B., Wöstmann, B.: A branch & bound algorithm for the open-shop problem. Discrete Applied Mathematics 76, 43–59 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Dubois, D., Fargier, H., Fortemps, P.: Fuzzy scheduling: Modelling flexible constraints vs. coping with incomplete knowledge. European Journal of Operational Research 147, 231–252 (2003)CrossRefzbMATHGoogle Scholar
  5. 5.
    Fortemps, P.: Jobshop scheduling with imprecise durations: a fuzzy approach. IEEE Transactions of Fuzzy Systems 7, 557–569 (1997)CrossRefGoogle Scholar
  6. 6.
    Giffler, B., Thompson, G.L.: Algorithms for solving production scheduling problems. Operations Research 8, 487–503 (1960)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Gonçalves, J., Mendes, J., de M, R.M.: A hybrid genetic algorithm for the job shop scheduling problem. European Journal of Operational Research 167, 77–95 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    González, M.A., Sierra, M., Vela, C.R., Varela, R.: Genetic algorithms hybridized with greedy algorithms and local search over the spaces of active and semi-active schedules. In: Marín, R., Onaindía, E., Bugarín, A., Santos, J. (eds.) CAEPIA 2005. LNCS (LNAI), vol. 4177, pp. 231–240. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    González-Rodríguez, I., Puente, J., Vela, C.R.: Sensitivity analysis for the job shop problem with uncertain durations and flexible due dates. In: Mira, J., Álvarez, J.R. (eds.) IWINAC 2007. LNCS, vol. 4527, pp. 538–547. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. 10.
    González-Rodríguez, I., Palacios, J.J., Vela, C.R., Puente, J.: Heuristic local search for fuzzy open shop scheduling. In: Proceedings IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2010, pp. 1858–1865. IEEE, Los Alamitos (2010)Google Scholar
  11. 11.
    González Rodríguez, I., Puente, J., Vela, C.R., Varela, R.: Semantics of schedules for the fuzzy job shop problem. IEEE Transactions on Systems, Man and Cybernetics, Part A 38(3), 655–666 (2008)CrossRefGoogle Scholar
  12. 12.
    Guéret, C., Prins, C.: Classical and new heuristics for the open-shop problem: A computational evaluation. European Journal of Operational Research 107, 306–314 (1998)CrossRefzbMATHGoogle Scholar
  13. 13.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: IEEE International Conference on Neural Networks, pp. 1942–1948. IEEE Press, New Jersey (1995)Google Scholar
  14. 14.
    Konno, T., Ishii, H.: An open shop scheduling problem with fuzzy allowable time and fuzzy resource constraint. Fuzzy Sets and Systems 109, 141–147 (2000)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Lei, D.: Pareto archive particle swarm optimization for multi-objective fuzzy job shop scheduling problems. International Journal of Advanced Manufacturing Technology 37, 157–165 (2008)CrossRefGoogle Scholar
  16. 16.
    Liaw, C.F.: A tabu search algorithm for the open shop scheduling problem. Computers and Operations Research 26, 109–126 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Liu, B., Liu, Y.K.: Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems 10, 445–450 (2002)CrossRefGoogle Scholar
  18. 18.
    Palacios, J.J., Puente, J., Vela, C.R., González-Rodríguez, I.: A genetic algorithm for the open shop problem with uncertain durations. In: Mira, J., Ferrández, J.M., Álvarez, J.R., de la Paz, F., Toledo, F.J. (eds.) IWINAC 2009. LNCS, vol. 5601, pp. 255–264. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Pinedo, M.L.: Scheduling. Theory, Algorithms, and Systems, 3rd edn. Springer, Heidelberg (2008)zbMATHGoogle Scholar
  20. 20.
    Puente, J., Diez, H., Varela, R., Vela, C., Hidalgo, L.: Heuristic Rules and Genetic Algorithms for Open Shop Scheduling Problem. In: Conejo, R., Urretavizcaya, M., Pérez-de-la-Cruz, J.-L. (eds.) CAEPIA/TTIA 2003. LNCS (LNAI), vol. 3040, pp. 394–403. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  21. 21.
    Puente, J., Vela, C.R., González-Rodríguez, I.: Fast local search for fuzzy job shop scheduling. In: Proceedings of ECAI 2010, pp. 739–744. IOS Press, Amsterdam (2010)Google Scholar
  22. 22.
    Sha, D.Y., Cheng-Yu, H.: A modified parameterized active schedule generation algorithm for the job shop scheduling problem. In: Proceedings of the 36th International Conference on Computers and Industrial Engineering, ICCIE 2006, pp. 702–712 (2006)Google Scholar
  23. 23.
    Sha, D.Y., Cheng-Yu, H.: A new particle swarm optimization for the open shop scheduling problem. Computers & Operations Research 35, 3243–3261 (2008)CrossRefzbMATHGoogle Scholar
  24. 24.
    Tavakkoli-Moghaddam, R., Safei, N., Kah, M.: Accessing feasible space in a generalized job shop scheduling problem with the fuzzy processing times: a fuzzy-neural approach. Journal of the Operational Research Society 59, 431–442 (2008)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Juan José Palacios
    • 1
  • Inés González-Rodríguez
    • 2
  • Camino R. Vela
    • 1
  • Jorge Puente
    • 1
  1. 1.A.I. Centre and Department of Computer ScienceUniversity of OviedoSpain
  2. 2.Department of Mathematics, Statistics and ComputingUniversity of CantabriaSpain

Personalised recommendations