Reference Point-Based Particle Swarm Optimization Using a Steady-State Approach

  • Richard Allmendinger
  • Xiaodong Li
  • Jürgen Branke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5361)


Conventional multi-objective Particle Swarm Optimization (PSO) algorithms aim to find a representative set of Pareto-optimal solutions from which the user may choose preferred solutions. For this purpose, most multi-objective PSO algorithms employ computationally expensive comparison procedures such as non-dominated sorting. We propose a PSO algorithm, Reference point-based PSO using a Steady-State approach (RPSO-SS), that finds a preferred set of solutions near user-provided reference points, instead of the entire set of Pareto-optimal solutions. RPSO-SS uses simple replacement strategies within a steady-state environment. The efficacy of RPSO-SS in finding desired regions of solutions is illustrated using some well-known two and three-objective test problems.


Particle Swarm Optimization Algorithm Multiobjective Evolutionary Algorithm Nadir Point Particle Swarm Optimization Variant Personal Good Position 
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.


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  1. 1.
    Clerc, M., Kennedy, J.: The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation 6(1), 58–73 (2002)CrossRefGoogle Scholar
  2. 2.
    Li, X.: A non-dominated sorting particle swarm optimizer for multiobjective optimization. In: Proceedings of Genetic and Evolutionary Computation Conference 2003 (GECCO 2003), pp. 37–48 (2003)Google Scholar
  3. 3.
    Li, X.: Better spread and convergence: Particle swarm multiobjective optimization using the maximin fitness function. In: Deb, K., et al. (eds.) GECCO 2004. LNCS, vol. 3103, pp. 117–128. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Deb, K., Chaudhurid, S., Miettinen, K.: Estimating nadir objective vector quickly using evolutionary approaches. Technical Report No. 2005009, KanGAL, Kanpur India (2005)Google Scholar
  5. 5.
    Corne, D.W., Knowles, J.D.: Techniques for highly multiobjective optimisation: Some nondominated points are better than others. In: Proceedings of Genetic and Evolutionary Computation Conference 2007 (GECCO 2007), pp. 773–780 (2007)Google Scholar
  6. 6.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)CrossRefGoogle Scholar
  7. 7.
    Gembicki, F.W.: Vector optimization for control with performance and parameter sensitivity indices. PhD thesis, Case Western Reserve University, Ohio, USA (1974)Google Scholar
  8. 8.
    Chankong, V., Haimes, Y.Y.: Multiobjective Decision Making Theory and Methodology. Elsevier Science Publishing Co., Amsterdam (1983)zbMATHGoogle Scholar
  9. 9.
    Wierzbicki, A.P.: The use of reference objectives in multiobjective optimisation. Multiple Criteria Decision Making Theory and Applications, 468–486 (1980)Google Scholar
  10. 10.
    Mumford-Valenzuela, C.L.: A simple approach to evolutionary multiobjective optimization. Evolutionary Computation Based Multi-Criteria Optimization: Theoretical Advances and Applications, 55–79 (2004)Google Scholar
  11. 11.
    Coello Coello, C.A.: Handling preferences in evolutionary multiobjective optimization: A survey. In: Proceedings of the 2000 Congress on Evolutionary Computation (CEC 2000), pp. 30–37 (2000)Google Scholar
  12. 12.
    Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science (MHS 1995), pp. 39–43 (1995)Google Scholar
  13. 13.
    Parsopoulos, K.E., Vrahatis, M.N.: Particle swarm optimization method in multiobjective problems. In: Proceedings of the 2002 ACM Symposium on Applied Computing (SAC 2002), pp. 603–607 (2002)Google Scholar
  14. 14.
    Sierra, M.R., Coello Coello, C.A.: Improving PSO-based multi-objective optimization using crowding, mutation and ε-dominance. In: Proceedings of the Third Evolutionary Multi-Criterion Optimization Conference (EMO 2005), pp. 505–519 (2005)Google Scholar
  15. 15.
    Kuhn, H.W., Tucker, A.W.: Nonlinear programming. In: Proceedings of Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 481–492 (1950)Google Scholar
  16. 16.
    Mumford-Valenzuela, C.L.: Simple population replacement strategies for a steady-state multi-objective evolutionary algorithm. In: Proceedings of Genetic and Evolutionary Computation Conference 2004 (GECCO 2004), pp. 1389–1400 (2004)Google Scholar
  17. 17.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation 8(2), 173–195 (2002)CrossRefGoogle Scholar
  18. 18.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. Technical Report No. 112, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH), Zurich, Switzerland (2001)Google Scholar
  19. 19.
    Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach. IEEE Transactions on Evolutionary Computation 3(4), 257–271 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Richard Allmendinger
    • 1
  • Xiaodong Li
    • 2
  • Jürgen Branke
    • 1
  1. 1.Institute AIFBUniversity of KarlsruheKarlsruheGermany
  2. 2.School of Computer Science and Information TechnologyRMIT UniversityMelbourneAustralia

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