Skip to main content
SpringerLink
Log in

An interval algorithm for multi-objective optimization

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

This paper presents an interval algorithm for solving multi-objective optimization problems. Similar to other interval optimization techniques, [see Hansen and Walster (2004)], the interval algorithm presented here is guaranteed to capture all solutions, namely all points on the Pareto front. This algorithm is a hybrid method consisting of local gradient-based and global direct comparison components. A series of example problems covering convex, nonconvex, and multimodal Pareto fronts is used to demonstrate the method.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. aleher83 Alefeld G, Herzberger J (1983) Introduction to interval computations. Academic, Amsterdam

  2. colsia03 Collette Y, Siarry P (2003) Multiobjective optimization: principles and case studies. Springer, Berlin Heidelberg New York

  3. dasden97 Das I, Dennis J (1997) A closer look at the drawbacks of minimizing weighted sums of objectives for pareto set generation in multicriteria optimization problems. Struct Optim 14(1):63–69

  4. deb98 Deb K (1998) Multiobjective genetic algorithms: problem difficulties and construction of test problems. Technical Report Technical Report CI-49/98, Dortmund Department of Computer Science

  5. hanwal04 Hansen ER, Walster GW (2004) Global optimization using interval analysis, 2nd edn. revised and expanded. Marcel Decker, New York

  6. jaukie01 Jaulin L, Kieffer M, Didrit O, Walter E (2001) Applied interval analysis. Springer, Berlin Heidelberg New York

  7. mesmel00 Messac A, Melachrinoudis E, Sukam CP (2000) Aggregate objective functions and pareto frontiers: required relationships and practical implications. Optim Eng J 1(2):171–188

  8. moo66 Moore RE (1966) Interval Analysis. Prentice-Hall, Englewood Cliffs, NJ

  9. moo79 Moore RE (1979) Methods and applications of interval analysis. SIAM

  10. neu90 Neumaier A (1990) Interval methods for systems of equations. Cambridge University Press

  11. neu01 Neumaier A (2001) Introduction to numerical analysis. Cambridge University Press

  12. ratrok88 Ratschek H, Rokne J (1988) New computer methods for global optimization. Ellis Horwood, Chichester

  13. sunf95 Sun Microsystems, Inc. (2002) Fortran 95 interval arithmetic programming reference

  14. vellam00 van Veldhuizen D, Lamont G (2000) Multiobjective evolutionary algorithms: analyzing the state-of-the-art. Evol Comput 8(2):125–147

  15. zitdeb00 Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: emperical results. Evol Comput 8(2):173–195

Download references

Author information

Authors and Affiliations

  1. Sun Microsystems, Inc., 3295 N.W. 211th Terrace, Hillsboro, OR, 97124, USA

    G.R. Ruetsch

Authors
  1. G.R. Ruetsch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G.R. Ruetsch.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ruetsch, G. An interval algorithm for multi-objective optimization. Struct Multidisc Optim 30, 27–37 (2005). https://doi.org/10.1007/s00158-004-0496-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-004-0496-7

Keywords

Search

Navigation