Studying the Performance of Unified Particle Swarm Optimization on the Single Machine Total Weighted Tardiness Problem

  • K. E. Parsopoulos
  • M. N. Vrahatis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4304)


Swarm Intelligence algorithms have proved to be very effective in solving problems on many aspects of Artificial Intelligence. This paper constitutes a first study of the recently proposed Unified Particle Swarm Optimization algorithm on scheduling problems. More specifically, the Single Machine Total Weighted Tardiness problem is considered, and tackled through a scheme that combines Unified Particle Swarm Optimization and the Smallest Position Value technique for the derivation of job sequences from real–valued particles. Experiments on well–known benchmark problems are conducted with promising results, which are reported and discussed.


Particle Swarm Optimization Algorithm Swarm Intelligence Variable Neighborhood Search Swarm Intelligence Algorithm Exploitation Ability 
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  1. 1.
    Pinedo, M.: Scheduling: Theory, Algorithms and Systems. Prentice Hall, Englewood Cliffs (1995)MATHGoogle Scholar
  2. 2.
    Johnson, D.S., Garey, M.R.: Computers and Intractability: A Guide to the Theory of NP–Completeness. W.H. Freeman & Co., Englewood Cliffs (1979)MATHGoogle Scholar
  3. 3.
    Lenstra, J.K., Rinnooy Kan, H.G., Brucker, P.: Complexity of machine scheduling problem. In Studies in Integer Programming. Annals of Discrete Mathematics, vol. 1, pp. 343–362. North–Holland, Amsterdam (1977)Google Scholar
  4. 4.
    Abdul-Razaq, T.S., Potts, C.N., Van Wassenhove, L.N.: A survey of algorithms for the single machine total weighted tardiness scheduling problem. Discrete Applied Mathematics 26, 235–253 (1990)CrossRefMathSciNetMATHGoogle Scholar
  5. 5.
    Potts, C.N., Van Wassenhove, L.N.: Single machine tardiness sequencing heuristics. IIE Transactions 23, 346–354 (1991)CrossRefGoogle Scholar
  6. 6.
    Crauwels, H.A.J., Potts, C.N., Van Wassenhove, L.N.: Local search heuristics for the single machine total weighted tardiness scheduling problem. INFORMS Journal on Computing 10(3), 341–350 (1998)CrossRefMathSciNetMATHGoogle Scholar
  7. 7.
    den Besten, M., Stützle, T., Dorigo, M.: Ant colony optimization for the total weighted tardiness problem. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 611–620. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  8. 8.
    Saldam, A., Ahmad, I., Al-Madani, S.: Particle swarm optimization for task assignment problem. Microprocessors and Microsystems 26, 363–371 (2002)CrossRefGoogle Scholar
  9. 9.
    Fatih Tasgetiren, M., Sevkli, M., Liang, Y.C., Gencyilmaz, G.: Particle swarm optimization algorithm for single machine total weighted tardiness problem. In: Proc. 2004 IEEE Congress on Evolutionary Computation, pp. 1412–1419 (2004)Google Scholar
  10. 10.
    Mladenovic, N., Hansen, P.: Variable neighborhood search. Computers and Operations Research 24, 563–571 (1997)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Parsopoulos, K.E., Vrahatis, M.N.: UPSO: A unified particle swarm optimization scheme. In: Proc. Int. Conf. Comput. Meth. Sci. Engin (ICCMSE 2004). Lecture Series on Computer and Computational Sciences, vol. 1, pp. 868–873. VSP International Science Publishers, Zeist (2004)Google Scholar
  12. 12.
    Parsopoulos, K.E., Vrahatis, M.N.: Unified particle swarm optimization for tackling operations research problems. In: Proc. IEEE 2005 Swarm Intelligence Symposium, Pasadena (CA), USA, pp. 53–59 (2005)Google Scholar
  13. 13.
    Parsopoulos, K.E., Vrahatis, M.N.: Unified particle swarm optimization in dynamic environments. In: Rothlauf, F., Branke, J., Cagnoni, S., Corne, D.W., Drechsler, R., Jin, Y., Machado, P., Marchiori, E., Romero, J., Smith, G.D., Squillero, G. (eds.) EvoWorkshops 2005. LNCS, vol. 3449, pp. 590–599. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Parsopoulos, K.E., Vrahatis, M.N.: Unified particle swarm optimization for solving constrained engineering optimization problems. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005. LNCS, vol. 3612, pp. 582–591. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    Parsopoulos, K.E., Vrahatis, M.N.: Parameter selection and adaptation in unified particle swarm optimization (Mathematical and Computer Modelling) (to appear)Google Scholar
  16. 16.
    Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kaufmann, San Francisco (2001)Google Scholar
  17. 17.
    Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proc. IEEE Int. Conf. Neural Networks, vol. IV, pp. 1942–1948. IEEE Service Center, Los Alamitos (1995)CrossRefGoogle Scholar
  18. 18.
    Bonabeau, E., Dorigo, M., Théraulaz, G.: Swarm Intelligence: From Natural to Artificial Swarm Intelligence. Oxford University Press, New York (1999)MATHGoogle Scholar
  19. 19.
    Bonabeau, E., Meyer, C.: Swarm intelligence: A whole new way to think about business. Harvard Business Review 79(5), 106–114 (2001)Google Scholar
  20. 20.
    Engelbrecht, A.P.: Fundamentals of Computational Swarm Intelligence. Wiley, Chichester (2006)Google Scholar
  21. 21.
    Kennedy, J.: Bare bones particle swarms. In: Proc. IEEE Swarm Intelligence Symposium, pp. 80–87. IEEE Press, Indianapolis (2003)Google Scholar
  22. 22.
    Mendes, R., Kennedy, J., Neves, J.: The fully informed particle swarm: Simpler, maybe better. IEEE Trans. Evol. Comput. 8(3), 204–210 (2004)CrossRefGoogle Scholar
  23. 23.
    Li, X.: Adaptively choosing neighborhood bests using species in a particle swarm optimizer for multimodal function optimization. In: Deb, K., et al. (eds.) GECCO 2004. LNCS, vol. 3102, pp. 105–116. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  24. 24.
    Clerc, M., Kennedy, J.: The particle swarm–explosion, stability, and convergence in a multidimensional complex space. IEEE Trans. Evol. Comput. 6(1), 58–73 (2002)CrossRefGoogle Scholar
  25. 25.
    Trelea, I.C.: The particle swarm optimization algorithm: Convergence analysis and parameter selection. Information Processing Letters 85, 317–325 (2003)CrossRefMathSciNetMATHGoogle Scholar
  26. 26.
    Matyas, J.: Random optimization. Automatization and Remote Control 26, 244–251 (1965)MathSciNetMATHGoogle Scholar
  27. 27.
    Parsopoulos, K.E., Vrahatis, M.N.: Recent approaches to global optimization problems through particle swarm optimization. Natural Computing 1(2–3), 235–306 (2002)CrossRefMathSciNetMATHGoogle Scholar
  28. 28.
    Shi, Y., Eberhart, R.C.: A modified particle swarm optimizer. In: Proc. IEEE CEC 1998, pp. 69–73. IEEE Service Center, Los Alamitos (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • K. E. Parsopoulos
    • 1
    • 2
  • M. N. Vrahatis
    • 1
    • 2
  1. 1.Computational Intelligence Laboratory (CI Lab), Department of MathematicsUniversity of PatrasPatrasGreece
  2. 2.University of Patras Artificial Intelligence Research Center (UPAIRC)University of PatrasPatrasGreece

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