Many-Objective Particle Swarm Optimization by Gradual Leader Selection

  • Mario Köppen
  • Kaori Yoshida
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4431)


Many-objective optimization refers to multi-objective optimization problems with a number of objectives considerably larger than two or three. This papers contributes to the use of Particle Swarm Optimization (PSO) for the handling of such many-objective optimization problems. Multi-objective PSO approaches typically rely on the employment of a so-called set of leaders that generalizes the global best particle used in the standard PSO algorithm. The exponentially decreasing probability of finding non-dominated points in search spaces with increasing number of objectives poses a problem for the selection from this set of leaders, and renders multi-objective PSOs easily unusable. Gradual Pareto dominance relation can be used to overcome this problem. The approach will be studied by means of the problem to minimize the Euclidian distances to a number of points, where each distance to the points is considered an independent objective. The Pareto set of this problem is the convex closure of the set of points. The conducted experiments demonstrate the usefulness of the proposed approach and also show the higher resemblance of the proposed PSO variation with the standard PSO.


Pareto Front Objective Vector Pareto Dominance Standard Particle Swarm Optimization Global Good Particle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alvarez-Benitez, J.E., Everson, R.M., Fieldsend, J.E.: A MOPSO Algorithm Based Exclusively on Pareto Dominance Concepts. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 459–473. Springer, Heidelberg (2005)Google Scholar
  2. 2.
    Coello Coello, C.A., Salazar Lechuga, M.: MOPSO: A Proposal for Multiple Objective Particle Swarm Optimization. In: Congress on Evolutionary Computation (CEC’2002), May 2002, vol. 2, pp. 1051–1056. IEEE Service Center, Piscataway (2002)Google Scholar
  3. 3.
    Coello Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic Publishers, New York (May 2002)zbMATHGoogle Scholar
  4. 4.
    Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001)zbMATHGoogle Scholar
  5. 5.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Multi-Objective Optimization Test Problems. In: Congress on Evolutionary Computation (CEC’2002), May 2002, vol. 1, pp. 825–830. IEEE Service Center, Piscataway (2002)Google Scholar
  6. 6.
    Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kaufmann Publishers, San Francisco (2001)Google Scholar
  7. 7.
    Köppen, M., Vicente-Garcia, R., Nickolay, B.: Fuzzy-pareto-dominance and its application in evolutionary multi-objective optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 399–412. Springer, Heidelberg (2005)Google Scholar
  8. 8.
    Köppen, M., Vicente Garcia, R., Nickolay, B.: The pareto-box problem for the modelling of evolutionary multi-objective optimization. In: Adaptive and Natural Computing Algorithms, Proceedings of the ICANNGA 2005, Coimbra, Portugal, pp. 194–197 (2005)Google Scholar
  9. 9.
    Köppen, M., Vicente Garcia, R.: A fuzzy scheme for the ranking of multivariate data and its application. In: Proceedings of the 2004 Annual Meeting of the NAFIPS (CD-ROM), Banff, Alberta, Canada, pp. 140–145. NAFIPS (2004)Google Scholar
  10. 10.
    Reyes Sierra, M., Coello Coello, C.A.: Multi-objective particle swarm optimizers: A survey of the state-of-the-art. International Journal of Computational Intelligence Research 2(3), 287–308 (2006)MathSciNetGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Mario Köppen
    • 1
  • Kaori Yoshida
    • 1
  1. 1.Kyushu Institute of Technology, Dept. Artificial Intelligence, 680-4, Kawazu, Iizuka, Fukuoka 820-8502Japan

Personalised recommendations