Skip to main content
SpringerLink
Log in

Weighted preferences in evolutionary multi-objective optimization

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

Evolutionary algorithms have been widely used to tackle multi-objective optimization problems. Incorporating preference information into the search of evolutionary algorithms for multi-objective optimization is of great importance as it allows one to focus on interesting regions in the objective space. Zitzler et al. have shown how to use a weight distribution function on the objective space to incorporate preference information into hypervolume-based algorithms. We show that this weighted information can easily be used in other popular EMO algorithms as well. Our results for NSGA-II and SPEA2 show that this yields similar results to the hypervolume approach and requires less computational effort.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Allmendinger R, Li X, Branke J (2008) Reference point-based particle swarm optimization using a steady-state approach. In: Proc. simulated evolution and learning (SEAL ’08). Lecture Notes in Computer Science, vol 5361, pp 200–209

  2. Auger A, Bader J, Brockhoff D, Zitzler E (2009) Articulating user preferences in many-objective problems by sampling the weighted hypervolume. In: Proc. 11th annual conference on genetic and evolutionary computation, pp 555–562

  3. Beume N, Naujoks B, Emmerich MTM (2007) SMS-EMOA: multiobjective selection based on dominated hypervolume. Eur J Oper Res 181:1653–1669

    Article  MATH  Google Scholar 

  4. Bringmann K, Friedrich T (2010) Approximating the volume of unions and intersections of high-dimensional geometric objects. Comput Geom Theory Appl 43:601–610

    Article  MathSciNet  MATH  Google Scholar 

  5. Coello Coello CA, Van Veldhuizen DA, Lamont GB (2002) Evolutionary algorithms for solving multi-objective problems. Kluwer Academic Publishers, New York

    Book  MATH  Google Scholar 

  6. Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, Chichester

    MATH  Google Scholar 

  7. Deb K, Agrawal S, Pratap A, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  8. Deb K, Sundar J (2006) Reference point based multi-objective optimization using evolutionary algorithms. In: Proc. 8th annual conference on genetic and evolutionary computation conference (GECCO ’06), pp 635–642

  9. Friedrich T, Kroeger T, Neumann F (2011) Weighted preferences in evolutionary multi-objective optimization. In: Wang D, Reynolds M (eds) Australasian conference on artificial intelligence. Lecture Notes in Computer Science, volume 7106, pp 291–300. Springer

  10. Ho S-l, Yang S, Ni G (2008) Incorporating a priori preferences in a vector pso algorithm to find arbitrary fractions of the pareto front of multiobjective design problems. IEEE Trans Magn 44:1038–1041

    Article  Google Scholar 

  11. Hu Q, Xu L, Goodman ED (2009) Non-even spread NSGA-II and its application to conflicting multi-objective compatible control. In: Proc. genetic and evolutionary computation conference summit (GEC ’09), pp 223–230

  12. Huband S, Barone L, While L, Hingston P (2005) A scalable multi-objective test problem toolkit. In: Evolutionary multi-criterion optimization, pp 280–295. Springer

  13. Igel C, Hansen N, Roth S (2007) Covariance matrix adaptation for multi-objective optimization. Evol Comput 15:1–28

    Article  Google Scholar 

  14. Suttorp T, Hansen N, Igel C (2009) Efficient covariance matrix update for variable metric evolution strategies. Mach Learn 75:167–197

    Article  Google Scholar 

  15. Thiele L, Miettinen K, Korhonen PJ, Luque JM (2009) A preference-based evolutionary algorithm for multi-objective optimization. Evol Comput 17(3):411–436

    Article  Google Scholar 

  16. Wickramasinghe UK, Li X (2008) Integrating user preferences with particle swarms for multi-objective optimization. In: Proc. 10th annual conference on genetic and evolutionary computation, pp 745–752

  17. Wickramasinghe UK, Li X (2009) Using a distance metric to guide pso algorithms for many-objective optimization. In: Proc. 11th annual conference on genetic and evolutionary computation, pp 667–674

  18. Zitzler E, Brockhoff D, Thiele L (2007) The hypervolume indicator revisited: on the design of Pareto-compliant indicators via weighted integration. In: Proc. fourth international conference on evolutionary multi-criterion optimization (EMO ’07). LNCS, vol 4403, pp 862–876. Springer

  19. Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195

    Article  Google Scholar 

  20. Zitzler E, Laumanns M, Thiele L (2002) SPEA2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Proc. evolutionary methods for design, optimisation and control with application to industrial problems (EUROGEN 2001), pp 95–100

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Tobias Friedrich

  2. School of Computer Science, The University of Adelaide, Adelaide, Australia

    Trent Kroeger & Frank Neumann

Authors
  1. Tobias Friedrich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Trent Kroeger
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Frank Neumann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Trent Kroeger.

Additional information

A conference version appeared in the Proceedings of the Australasian Conference on Artificial Intelligence 2011 [9].

Rights and permissions

Reprints and permissions

About this article

Cite this article

Friedrich, T., Kroeger, T. & Neumann, F. Weighted preferences in evolutionary multi-objective optimization. Int. J. Mach. Learn. & Cyber. 4, 139–148 (2013). https://doi.org/10.1007/s13042-012-0083-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-012-0083-y

Keywords

Search

Navigation