Skip to main content

G–Indicator: An M–Ary Quality Indicator for the Evaluation of Non–dominated Sets

  • Conference paper
Book cover MICAI 2007: Advances in Artificial Intelligence (MICAI 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4827))

Included in the following conference series:

Abstract

Due to the big success of the Pareto’s Optimality Criteria for multi–objective problems, an increasing number of algorithms that use it have been proposed. The goal of these algorithms is to find a set of non–dominated solutions that are close to the True Pareto front. As a consequence, a new problem has arisen, how can the performance of different algorithms be evaluated? In this paper, we present a novel system to evaluate m non–dominated sets, based on a few assumptions about the preferences of the decision maker. In order to evaluate the performance of our approach, we build several test cases considering different topologies of the Pareto front. The results are compared with those of another popular metric, the S–metric, showing equal or better performance.

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. Leung, Y.-W., Wang, Y.-P.: U–Measure: a Quality Measure for Multiobjective Programming. IEEE Transactions on Systems, Man, and Cybernetics Part A 33(3), 337–343 (2003)

    Article  Google Scholar 

  2. Zitzler, E.: Evolutionary Algorithms Multiobjective Optimization: Methods and Applications. PhD thesis, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland (1999)

    Google Scholar 

  3. Veldhuizen, D.A.: Multiobjective Evolution Algorithms: Classifications, Analyses, and New Innovations. PhD thesis, Department Electrical Computer Engineering. Graduate School Engineering. Force Institute Technology, Wright Patterson AFB, Ohio (1999)

    Google Scholar 

  4. Knowles, J., Corne, D.: On Metrics for Comparing Non–Dominated Sets, Congress on Evolutionary Computation. In: CEC 2002 (2002)

    Google Scholar 

  5. Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A Fast Elitist Non–Dominated Sorting Genetic Algorithm for Multi–Objective Optimization: Nsga II. In: Proceedings of the Parallel Problem Solving from Nature VI Conference, Paris, France, 16–20 September, pp. 849–858 (2000)

    Google Scholar 

  6. Knowles, J., Corne, D.: The Pareto Archived Evolution Strategy: A New Baseline Algorithm for Multiobjective Optimisation. In: Proceedings of the 1999 Congress on Evolutionary Computation, pp. 98–105. IEEE Service Center, New Jersey (1999)

    Chapter  Google Scholar 

  7. Deb, K.: Multi–objective Optimization Using Evolutionary Algorithms. John Wiley and Sons, Chichester (2001)

    MATH  Google Scholar 

  8. Hansen, M.P., Jaszkiewicz, A.: Evaluating the Quality of Approximations to the Non–Dominated Set. Technical Report IMM–REP–1998–7, Technical University of Denmark (1998)

    Google Scholar 

  9. Deb, et al.: Scalable Test Problems for Evolutionary Multi–Objective Optimization. TIK–Technical Report No. 112 Institut für Technische Informatik und Kommunikationsnetze, ETH Zürich Gloriastrasse 35., ETH–Zentrum, CH–8092, Zürich, Switzerland (2001)

    Google Scholar 

  10. Mehr, A.F., Azarm, S.: Minimal Sets of Quality Metrics. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 405–417. Springer, Heidelberg (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Alexander Gelbukh Ángel Fernando Kuri Morales

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lizárraga, G., Hernández, A., Botello, S. (2007). G–Indicator: An M–Ary Quality Indicator for the Evaluation of Non–dominated Sets. In: Gelbukh, A., Kuri Morales, Á.F. (eds) MICAI 2007: Advances in Artificial Intelligence. MICAI 2007. Lecture Notes in Computer Science(), vol 4827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76631-5_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-76631-5_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-76630-8

  • Online ISBN: 978-3-540-76631-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics