Skip to main content

Interval Methods for Computing the Pareto-front of a Multicriterial Problem

  • Conference paper
Parallel Processing and Applied Mathematics (PPAM 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4967))

Abstract

Interval methods are known to be a precise and robust tool of global optimization. Several interval algorithms have been developed to deal with various kinds of this problem. Far less has been written about the use of interval methods in multicriterial optimization. The paper surveys two methods presented by other researchers and proposes a modified approach, combining PICPA algorithm with the use of derivative information. Preliminary numerical results are presented.

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
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. Barichard, V., Hao, J.K.: Population and Interval Constraint Propagation Algorithm. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 88–101. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  2. Hansen, E.: Global Optimization Using Interval Analysis. Marcel Dekker, New York (1992)

    MATH  Google Scholar 

  3. Herbort, S., Ratz, D.: Improving the Efficiency of a Nonlinear–System–Solver Using the Componentwise Newton Method, available on the web at: http://www.ubka.uni-karlsruhe.de/vvv/1997/mathematik/5/5.pdf.gz

  4. Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysis. Springer, London (2001)

    MATH  Google Scholar 

  5. Jaulin, L., Walter, E.: Set Inversion Via Interval Analysis for nonlinear bounded-error estimation. Automatica 29, 1053–1064 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kearfott, R.B.: Rigorous Global Search: Continuous Problems. Kluwer, Dordrecht (1996)

    MATH  Google Scholar 

  7. Kearfott, R. B., Nakao, M. T., Neumaier, A., Rump, S. M., Shary, S. P., van Hentenryck, P.: Standardized notation in interval analysis, available on the web at: http://www.mat.univie.ac.at/~neum/software/int/notation.ps.gz

  8. Kim, I.Y., de Weck, O.L.: Adaptive weighted-sum method for bi-objective optimization: Pareto front generation. Structural and Multidisciplinary Optimization 29, 149–158 (2005)

    Article  Google Scholar 

  9. Kubica, B.J., Malinowski, K.: An Interval Global Optimization Algorithm Combining Symbolic Rewriting and Componentwise Newton Method Applied to Control a Class of Queueing Systems. Reliable Computing 11, 393–411 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Kubica, B.J., Niewiadomska-Szynkiewicz, E.: An Improved Interval Global Optimization Method and its Application to Price Management Problem. In: Kågström, B., Elmroth, E., Dongarra, J., Waśniewski, J. (eds.) PARA 2006. LNCS, vol. 4699, pp. 1055–1064. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  11. Ruetsch, G.R.: An interval algorithm for multi-objective optimization. Structural and Multidisciplinary Optimization 30, 27–37 (2005)

    Article  MathSciNet  Google Scholar 

  12. Shary, S.P.: A Surprising Approach in Interval Global Optimization. Reliable Computing 7, 497–505 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  13. Zitzler, E., Laumanns, M., Thiele, M.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm for Multiobjective Optimization. In: Giannakoglou, K., Tsahalis, D., Periaux, J., Papailiou, K., Fogarty, T. (eds.) Evolutionary Methods for Design Optimization and Control, CIMNE, Barcelona, Spain (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Roman Wyrzykowski Jack Dongarra Konrad Karczewski Jerzy Wasniewski

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kubica, B.J., Woźniak, A. (2008). Interval Methods for Computing the Pareto-front of a Multicriterial Problem. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2007. Lecture Notes in Computer Science, vol 4967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68111-3_146

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-68111-3_146

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68105-2

  • Online ISBN: 978-3-540-68111-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics