Skip to main content

An Alternative Preference Relation to Deal with Many-Objective Optimization Problems

  • Conference paper
Evolutionary Multi-Criterion Optimization (EMO 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7811))

Included in the following conference series:

Abstract

In this paper, we use an alternative preference relation that couples an achievement function and the ε-indicator in order to improve the scalability of a Multi-Objective Evolutionary Algorithm (moea) in many-objective optimization problems. The resulting algorithm was assessed using the Deb-Thiele-Laumanns-Zitzler (dtlz) and the Walking- Fish-Group (wfg) test suites. Our experimental results indicate that our proposed approach has a good performance even when using a high number of objectives. Regarding the dtlz test problems, their main difficulty was found to lie on the presence of dominance resistant solutions. In contrast, the hardness of wfg problems was not found to be significantly increased by adding more objectives.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Coello Coello, C.A., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd edn. Springer, New York (2007) ISBN 978-0-387-33254-3

    MATH  Google Scholar 

  2. Hughes, E.J.: Evolutionary Many-Objective Optimisation: Many Once or One Many? In: CEC 2005, Edinburgh, Scotland, vol. 1, pp. 222–227 (September 2005)

    Google Scholar 

  3. Wagner, T., Beume, N., Naujoks, B.: Pareto-, Aggregation-, and Indicator-Based Methods in Many-Objective Optimization. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 742–756. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Purshouse, R.C., Fleming, P.J.: Evolutionary Multi-Objective Optimisation: An Exploratory Analysis. In: CEC 2003, Canberra, Australia, vol. 3, pp. 2066–2073 (December 2003)

    Google Scholar 

  5. Knowles, J., Corne, D.: Quantifying the Effects of Objective Space Dimension in Evolutionary Multiobjective Optimization. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 757–771. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  6. Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Evolutionary many-objective optimization: A short review. In: CEC 2008, Hong Kong, pp. 2424–2431 (June 2008)

    Google Scholar 

  7. Schütze, O., Lara, A., Coello Coello, C.A.: On the Influence of the Number of Objectives on the Hardness of a Multiobjective Optimization Problem. IEEE Transactions on Evolutionary Computation 15(4), 444–455 (2011)

    Article  Google Scholar 

  8. Sato, H., Aguirre, H.E., Tanaka, K.: Genetic Diversity and Effective Crossover in Evolutionary Many-Objective Optimization. In: Coello, C.A.C. (ed.) LION 5. LNCS, vol. 6683, pp. 91–105. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  9. Ikeda, K., Kita, H., Kobayashi, S.: Failure of Pareto-based MOEAs: Does Non-dominated Really Mean Near to Optimal? In: CEC 2001, Piscataway, New Jersey, vol. 2, pp. 957–962 (May 2001)

    Google Scholar 

  10. Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Multi-Objective Optimization Test Problems. In: CEC 2002, Piscataway, New Jersey, vol. 1, pp. 825–830 (May 2002)

    Google Scholar 

  11. Huband, S., Barone, L., While, L., Hingston, P.: A Scalable Multi-objective Test Problem Toolkit. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 280–295. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  12. López Jaimes, A., Arias-Montaño, A., Coello Coello, C.A.: Preference Incorporation to Solve Many-Objective Airfoil Design Problems. In: CEC 2011, New Orleans, USA (June 2011)

    Google Scholar 

  13. Wierzbicki, A.: The use of reference objectives in multiobjective optimisation. In: Fandel, G., Gal, T. (eds.) Multiple Criteria Decision Making Theory and Application. Lecture Notes in Economics and Mathematical Systems, Vol. 177, pp. 468–486. Springer (1980)

    Google Scholar 

  14. Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Berlin (2005)

    MATH  Google Scholar 

  15. Bentley, P.J., Wakefield, J.P.: Finding Acceptable Solutions in the Pareto-Optimal Range using Multiobjective Genetic Algorithms. In: Chawdhry, P.K., Roy, R., Pant, R.K. (eds.) Soft Computing in Engineering Design and Manufacturing, pp. 231–240. Springer, London (1997)

    Google Scholar 

  16. Kukkonen, S., Lampinen, J.: Ranking-Dominance and Many-Objective Optimization. In: CEC 2007, Singapore, pp. 3983–3990 (September 2007)

    Google Scholar 

  17. Drechsler, N., Drechsler, R., Becker, B.: Multi-Objected Optimization in Evolutionary Algorithms Using Satisfyability Classes. In: Reusch, B. (ed.) International Conference on Computational Intelligence, Theory and Applications, 6th Fuzzy Days, Dortmund, Germany, pp. 108–117 (1999)

    Google Scholar 

  18. di Pierro, F., Khu, S.T., Savić, D.A.: An Investigation on Preference Order Ranking Scheme for Multiobjective Evolutionary Optimization. IEEE Transactions on Evolutionary Computation 11(1), 17–45 (2007)

    Article  Google Scholar 

  19. Sato, H., Aguirre, H.E., Tanaka, K.: Controlling Dominance Area of Solutions and Its Impact on the Performance of MOEAs. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 5–20. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  20. Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance Assessment of Multiobjective Optimizers: An Analysis and Review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)

    Article  Google Scholar 

  21. Zitzler, E., Künzli, S.: Indicator-Based Selection in Multiobjective Search. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN VIII. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  22. Balling, R.: The Maximin Fitness Function; Multi-objective City and Regional Planning. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 1–15. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

L’opez, A., Coello, C.A.C., Oyama, A., Fujii, K. (2013). An Alternative Preference Relation to Deal with Many-Objective Optimization Problems. In: Purshouse, R.C., Fleming, P.J., Fonseca, C.M., Greco, S., Shaw, J. (eds) Evolutionary Multi-Criterion Optimization. EMO 2013. Lecture Notes in Computer Science, vol 7811. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37140-0_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-37140-0_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37139-4

  • Online ISBN: 978-3-642-37140-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics