Skip to main content
SpringerLink
Log in

Indicator-Based Selection

  • Chapter
Springer Handbook of Computational Intelligence

Part of the book series: Springer Handbooks ((SHB))

Abstract

The goal of multiobjective evolutionary optimization is to determine a set of solutions that satisfies certain optimality properties. Recently, there is a growing number of very competitive search algorithms that are based on an explicit formulation of the optimization goal as a set property, i. e., they build on the concept of set indicators. These indicators are used to guide the selection process which is usually denoted as indicator-based selection. This major breakthrough leads to several advantages in terms of analysis and algorithm design: Algorithms are conceptually simpler and more robust as they are largely based on a single indicator; certain convergence properties can be proven; the optimization criterion is made explicit; by changing the set indicator, it is possible to explicitly consider preferences of a user. The chapter introduces step-by-step the concept of set indicators and their use in indicator-based selection.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 269.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 349.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Abbreviations

IBEA:

indicator-based evolutionary algorithm

NSGA:

nondominated sorting genetic algorithm

SPAM:

set preference algorithm for multiobjective optimization

SPEA:

strength Pareto evolutionary algorithm

References

  1. K. Deb, S. Agrawal, A. Pratap, T. Meyarivan: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II, Lect. Notes Comput. Sci. 1917, 849–858 (2000)

    Article  Google Scholar 

  2. E. Zitzler, M. Laumanns, L. Thiele: SPEA2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization, Evol. Methods Des. Optim. Control Appl. Ind. Probl. (2002) pp. 95–100

    Google Scholar 

  3. M. Laumanns, L. Thiele, K. Deb, E. Zitzler: Combining convergence and diversity in evolutionary multiobjective optimization, Evol. Comput. 10(3), 263–282 (2002)

    Article  Google Scholar 

  4. T. Wagner, N. Beume, B. Naujoks: Pareto-, aggregation-, and indicator-based methods in many-objective optimization, Lect. Notes Comput. Sci. 4403, 742–756 (2007)

    Article  Google Scholar 

  5. E. Zitzler, L. Thiele, J. Bader: On set-based multiobjective optimization, IEEE Trans. Evol. Comput. 14(1), 58–79 (2010)

    Article  Google Scholar 

  6. V. da Grunert Fonseca, C.M. Fonseca, A.O. Hall: Inferential performance assessment of stochastic optimisers and the attainment function, Conf. Evol. Multi-Criterion Optim. (EMO 2001), ed. by E. Zitzler, K. Deb, L. Thiele, C.A. Coello Coelle, D. Corne (Springer, Berlin, Zurich 2001) pp. 213–225

    Chapter  Google Scholar 

  7. J. Knowles, D. Corne: On metrics for comparing non-dominated sets, Conf. Evol. Comput. (2002) pp. 711–716

    Google Scholar 

  8. D.A. Van Veldhuizen, G.B. Lamont: On measuring multiobjective evolutionary algorithm performance, Congr. Evol. Comput. (2000) pp. 204–211

    Google Scholar 

  9. E. Zitzler, L. Thiele: Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach, IEEE Trans. Evol. Comput. 3(4), 257–271 (1999)

    Article  Google Scholar 

  10. M. Fleischer: The measure of Pareto optima. Applications to multi-objective metaheuristics, Conf. Evol. Multi-Criterion Optim. (2003) pp. 519–533

    Chapter  Google Scholar 

  11. E. Zitzler, S. Künzli: Indicator-based selection in multiobjective search, Lect. Notes Comput. Sci. 3242, 832–842 (2004)

    Article  Google Scholar 

  12. M. Emmerich, N. Beume, B. Naujoks: An EMO algorithm using the hypervolume measure as selection criterion, Evol. Multi-Criterion Optim. 3rd Int. Conf. (2005) pp. 62–76

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  14. J.D. Knowles, D. Corne: Properties of an adaptive archiving algorithm for storing nondominated vectors, IEEE Trans. Evol. Comput. 7(2), 100–116 (2003)

    Article  Google Scholar 

  15. E. Zitzler, L. Thiele, M. Laumanns, C.M. Fonseca, V. da Grunert Fonseca: Performance assessment of multiobjective optimizers: An analysis and review, IEEE Trans. Evol. Comput. 7(2), 117–132 (2003)

    Article  Google Scholar 

  16. M.P. Hansen, A. Jaszkiewicz: Evaluating the Quality of Approximations to the Non-dominated Set, Tech. Rep. IMM-REP-1998-7 (Technical Univ. of Denmark, Lyngby 2010) pp. 1–31

    Google Scholar 

  17. C.H. Papadimitriou, M. Yannakakis: On the approximability of trade-offs and optimal access of web sources, 41st Annu. Symp. Found. Comput. Sci. (2000) pp. 86–92

    Chapter  Google Scholar 

  18. K. Bringmann, T. Friedrich: The maximum hypervolume set yields near-optimal approximation, Genet. Evol. Comput. Conf. (2010) pp. 511–518

    Google Scholar 

  19. E. Zitzler, L. Thiele: Multiobjective optimization using evolutionary algorithms – A comparative case study, Lect. Notes Comput. Sci. 1498, 292–304 (1998)

    Article  Google Scholar 

  20. K. Bringmann, T. Friedrich: Approximating the volume of unions and intersections of high-dimensional geometric objects, Lect. Notes Comput. Sci. 5369, 436–447 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  21. C.M. Fonseca, L. Paquete, M. López-Ibáñez: An improved dimension-sweep algorithm for the hypervolume indicator, Congr. Evol. Comput. (2006) pp. 1157–1163

    Google Scholar 

  22. N. Beume: S-Metric calculation by considering dominated hypervolume as Klee's measure problem, Evol. Comput. 17(4), 477–492 (2009)

    Article  Google Scholar 

  23. K. Bringmann, T. Friedrich: S-Metric calculation by considering dominated hypervolume as Klee's measure problem, Comput. Geom. 43(6/7), 601–610 (2010)

    Article  MathSciNet  Google Scholar 

  24. L. Thiele, K. Miettinen, P.J. Korhonen, J. Molina: A preference-based evolutionary algorithm for multi-objective optimization, Evol. Comput. 17(3), 411–436 (2009)

    Article  Google Scholar 

  25. K. Bringmann, T. Friedrich, F. Neumann, M. Wagner: Approximation-guided evolutionary multi-objective optimization, Proc. 22nd Int. Jt. Conf. Artif. Intell. (2011) pp. 1198–1203

    Google Scholar 

  26. E. Zitzler, L. Thiele, J. Bader: SPAM: Set preference algorithm for multiobjective optimization, Lect. Notes Comput. Sci. 5199, 847–858 (2008)

    Article  Google Scholar 

  27. G. Rudolph, A. Agapie: Convergence properties of some multi-objective evolutionary algorithms, Congr. Evol. Comput. (2000) pp. 1010–1016

    Google Scholar 

  28. K. Bringmann, T. Friedrich: Convergence of hypervolume-based archiving algorithms I: Effectiveness, 13th Annu. Genet. Evol. Comput. Conf. (2011) pp. 745–752

    Google Scholar 

  29. K. Bringmann, T. Friedrich: An efficient algorithm for computing hypervolume contributions, Evol. Comput. 18(3), 383–402 (2010)

    Article  Google Scholar 

  30. K. Bringmann, T. Friedrich: Approximating the least hypervolume contributor: NP-hard in general, but fast in practice, evolutionary multi-criterion optimization, Lect. Notes Comput. Sci. 5467, 6–20 (2009)

    Article  Google Scholar 

  31. J. Bader, E. Zitzler: HypE: An algorithm for fast hypervolume-based many-objective optimization, Evol. Comput. 19(1), 45–76 (2011)

    Article  Google Scholar 

  32. N. Srinivas, K. Deb: Multiobjective optimization using nondominated sorting in genetic algorithms, Evol. Comput. 2(3), 221–248 (1994)

    Article  Google Scholar 

  33. D.E. Goldberg: Multiobjective optimization. In: Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading 1989) pp. 197–201

    Google Scholar 

  34. C.M. Fonseca, P.J. Fleming: Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization, Proc. 5th Conf. Genet. Algorithms (1993) pp. 416–423

    Google Scholar 

  35. J. Bader: Hypervolume-Based Search for Multiobjective Optimization: Theory and Methods, Ph.D. Thesis (CreateSpace, ETH Zurich 2010)

    Google Scholar 

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

    Article  Google Scholar 

  37. C.A. Coello Coello: Handling preferences in evolutionary multiobjective optimization: A survey, Congr. Evol. Comput. (2000) pp. 30–37

    Google Scholar 

  38. K. Deb, J. Sundar: Reference point based multi-objective optimization using evolutionary algorithms, Genet. Evol. Comput. Conf. (2006) pp. 635–642

    Google Scholar 

  39. A. Auger, J. Bader, D. Brockhoff, E. Zitzler: Articulating user preferences in many-objective problems by sampling the weighted hypervolume, Genet. Evol. Comput. Conf. (2009) pp. 555–562

    Google Scholar 

  40. A. Wierzbicki: The use of reference objectives in multiobjective optimization, Lect. Notes Econ. Math. Syst. 177, 468–486 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  41. E. Zitzler, D. Brockhoff, L. Thiele: The hypervolume indicator revisited: On the design of Pareto-compliant indicators via weighted integration, Lect. Notes Comput. Sci. 4403, 862–876 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Engineering and Networks Lab., Swiss Federal Institute of Technology Zurich, Gloriastrasse 35, 8092, Zurich, Switzerland

    Lothar Thiele

Authors
  1. Lothar Thiele
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lothar Thiele .

Editor information

Editors and Affiliations

  1. Systems Research Inst., Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

  2. Dep. Electrical and Computer Engineering, University of Alberta, 116 Street 9107, T6J 2V4, Edmonton, Alberta, Canada

    Witold Pedrycz

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Thiele, L. (2015). Indicator-Based Selection. In: Kacprzyk, J., Pedrycz, W. (eds) Springer Handbook of Computational Intelligence. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43505-2_48

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-43505-2_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43504-5

  • Online ISBN: 978-3-662-43505-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation