Skip to main content
SpringerLink
Log in

On Two Approaches to Constructing Optimal Algorithms for Multi-objective Optimization

  • Conference paper
Information and Software Technologies (ICIST 2013)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 403))

Included in the following conference series:

  • 1725 Accesses

Abstract

Multi-objective optimization problems with expensive, black box objectives are difficult to tackle. For such type of problems in the single objective case the algorithms, which are in some sense optimal, have proved well suitable. Two concepts of optimality substantiate the construction of algorithms: worst case optimality and average case optimality. In the present paper the extension of these concepts to the multi-objective optimization is discussed. Two algorithms representing both concepts are implemented and experimentally compared.

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

Access this chapter

Log in via an institution
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. Arora, S., Barak, B.: Computational Complexity a Modern Approach. Cambridge University Press (2009)

    Google Scholar 

  2. Calvin, J., Žilinskas, A.: A one-dimensional P-algorithm with convergence rate O(n − 3 + δ). J. Optimization Theory and Applications 106, 297–307 (2000)

    Article  MATH  Google Scholar 

  3. Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. J. Wiley, Chichester (2009)

    MATH  Google Scholar 

  4. Fishburn P. (1970). Utility Theory for Decision Making. J.Wiley, Chichester.

    MATH  Google Scholar 

  5. Fonseca, C., Fleming, P.: On the performance assessment and comparison of 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 

  6. Horst, R., Pardalos, P., Thoai, N.: Introduction to Global Optimization. KAP, Boston (2000)

    Google Scholar 

  7. Jančauskas, V., Mackutė-Varoneckienė, A., Varoneckas, A., Žilinskas, A.: Multi-objective optimization aided visualization of graphs related to business process management. Comm. in Comp. and Inform. Sci. 319, 87–100 (2012)

    Article  Google Scholar 

  8. Kushner, H.: A versatile stochastic model of a function of unknown and time-varying form. J. Math. Anal. and Appl. 5, 150–167 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  9. Miettinen, K.: l Nonlinear multiobjective optimization. KAP, Boston (1999)

    Google Scholar 

  10. Mockus, J.: Bayesian approach to global optimization. KAP, Boston (1988)

    Google Scholar 

  11. Nakayama, H., Yun, Y., Yoon, M.: Sequential Approximate Multiobjective Optimization Using Computational Intelligence. Springer, Berlin (2009)

    MATH  Google Scholar 

  12. Pijavskii, S.: An algorithm for finding the absolute extremum of a function. USSR Computational Mathematics and Mathematical Physics 12, 57–67 (1972)

    Article  MathSciNet  Google Scholar 

  13. Shubert, B.: A sequential method seeking the global maximum of a function. SIAM J. Numer. Anal. 9, 379–388 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  14. Strongin, R., Sergeyev, Y.: Global Optimization with Non-convex Constraints: Sequential and Parallel Algorithms. KAP, Boston (2000)

    Book  Google Scholar 

  15. Törn, A., Žilinskas, A.: Global Optimization. LNCS, vol. 350, pp. 1–225. Springer, Heidelberg (1989)

    MATH  Google Scholar 

  16. Sukharev, A.: On optimal strategies of search for an extremum. USSR Comput. Math. and Math. Physics 11, 910–924 (1971) (in Russian)

    Google Scholar 

  17. Sukharev, A.: Best strategies of sequential search for an extremum. USSR Comput. Math. and Math. Physics 12, 35–50 (1972) (in Russian)

    Google Scholar 

  18. Žilinskas, A.: Optimization of one-dimensional multimodal functions, Algorithm AS-133. Journal of Royal Statistical Society, ser. C 23, 367–385 (1978)

    Google Scholar 

  19. Žilinskas, A.: Axiomatic approach to statistical models and their use in multimodal optimizatio theory. Mathematical Programming 22, 104–116 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  20. Žilinskas, A.: Axiomatic characterization of a global optimization algorithm and investigation of its search strategy. Operat. Res. Letters 4, 35–39 (1985)

    Article  MATH  Google Scholar 

  21. Žilinskas, A.: A statistical model-based algorithm for black-box multi-objective optimization. International Journal of Systems Science (2012) (Published on Internet July 4, 2012), doi:10.1080/00207721.2012.702244

    Google Scholar 

  22. Žilinskas, A.: On the worst-case optimal multi-objective global optimization. Optimization Letters (2012) (Published on Internet September 14, 2012), doi:10.1007/s11590-012-0547-8

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania

    Antanas Žilinskas

Authors
  1. Antanas Žilinskas
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Kaunas University of Technology, Studentu g. 50-313a, 51368, Kaunas, Lithuania

    Tomas Skersys

  2. Centre of Information Systems Design Technologies, Kaunas University of Technology, Studentu st. 50-313a, 51368, Kaunas, Lithuania

    Rimantas Butleris

  3. Kaunas University of Technology, Studentu g. 50-309a, 51368, Kaunas, Lithuania

    Rita Butkiene

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Žilinskas, A. (2013). On Two Approaches to Constructing Optimal Algorithms for Multi-objective Optimization. In: Skersys, T., Butleris, R., Butkiene, R. (eds) Information and Software Technologies. ICIST 2013. Communications in Computer and Information Science, vol 403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41947-8_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-41947-8_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41946-1

  • Online ISBN: 978-3-642-41947-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation