Skip to main content

A Scalable Multi-objective Test Problem Toolkit

  • Conference paper
Evolutionary Multi-Criterion Optimization (EMO 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3410))

Included in the following conference series:

Abstract

This paper presents a new toolkit for creating scalable multi-objective test problems. The WFG Toolkit is flexible, allowing characteristics such as bias, multi-modality, and non-separability to be incorporated and combined as desired. A wide variety of Pareto optimal geometries are also supported, including convex, concave, mixed convex/concave, linear, degenerate, and disconnected geometries.

All problems created by the WFG Toolkit are well defined, are scalable with respect to both the number of objectives and the number of parameters, and have known Pareto optimal sets. Nine benchmark multi-objective problems are suggested, including one that is both multi-modal and non-separable, an important combination of characteristics that is lacking among existing (scalable) multi-objective problems.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Deb, K.: Multi-objective genetic algorithms: Problem difficulties and construction of test problems. Evolutionary Computation 7, 205–230 (1999)

    Article  Google Scholar 

  2. Van Veldhuizen, D.A.: Multiobjective Evolutionary Algorithms: Classifications, Analyses, and New Innovations. PhD thesis, Air Force Institute of Technology, Wright-Patterson AFB, Ohio (1999)

    Google Scholar 

  3. Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation 8, 173–195 (2000)

    Article  Google Scholar 

  4. Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. KanGAL Report 2001001, Kanpur Genetic Algorithms Laboratory, Indian Institute of Technology, Kanpur, India (2001)

    Google Scholar 

  5. Whitley, D., Mathias, K., Rana, S., Dzubera, J.: Building better test functions. In: 6th International Conference on Genetic Algorithms, pp. 239–246. Morgan Kaufmann, San Francisco (1995)

    Google Scholar 

  6. Bäck, T., Michalewicz, Z.: Test landscapes. In: Handbook of Evolutionary Computation, vol. B2.7, pp. 14–20. Institute of Physics Publishing (1997)

    Google Scholar 

  7. Fogel, D.B., Beyer, H.G.: A note on the empirical evaluation of intermediate recombination. Evolutionary Computation 3, 491–495 (1995)

    Article  Google Scholar 

  8. Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: CEC 2002, vol. 1, pp. 825–830. IEEE, Los Alamitos (2002)

    Google Scholar 

  9. Van Veldhuizen, D.A., Lamont, G.B.: Multiobjective evolutionary algorithm test suites. In: 1999 ACM Symposium on Applied Computing, pp. 351–357. ACM, New York (1999)

    Chapter  Google Scholar 

  10. Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: EUROGEN 2001, CIMNE, Barcelona, Spain, pp. 95–100 (2001)

    Google Scholar 

  11. Bentley, P.J., Wakefield, J.P.: Finding acceptable solutions in the pareto-optimal range using multiobjective genetic algorithms. In: Soft Computing in Engineering Design and Manufacturing, pp. 231–240. Springer, Heidelberg (1998)

    Google Scholar 

  12. Knowles, J.D., Corne, D.W.: Approximating the nondominated front using the Pareto archived evolution strategy. Evolutionary Computation 8, 149–172 (2000)

    Article  Google Scholar 

  13. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6, 182–197 (2002)

    Article  Google Scholar 

  14. Fonseca, C.M., Fleming, P.J.: On the performance assessment and comparison of stochastic multiobjective optimizers. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 584–593. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Huband, S., Barone, L., While, L., Hingston, P. (2005). A Scalable Multi-objective Test Problem Toolkit. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds) Evolutionary Multi-Criterion Optimization. EMO 2005. Lecture Notes in Computer Science, vol 3410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31880-4_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-31880-4_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24983-2

  • Online ISBN: 978-3-540-31880-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics