Skip to main content
SpringerLink
Log in

A Comparison of Metaheurisitics for the Problem of Solving Parametric Interval Linear Systems

  • Conference paper
Numerical Methods and Applications (NMA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6046))

Included in the following conference series:

Abstract

The problem of computing a hull solution of parametric interval linear systems with general dependencies is considered. It can be reduced to the problem of solving a family of constrained optimizatiom problems. In this study, different metaheuristics are used to solve those problems. Comparison of evolutionary algorithm, simulated annealing and tabu search algorithm together with analysis of variance tests are provided on the basis of three different practical problems.

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. Corliss, G., Foley, C., Kearfott, R.B.: Formulation for Reliable Analysis of Structural Frames. In: Proceedings of NSF Workshop on Reliable Engineering Computing, Savannah, Georgia, USA (2004)

    Google Scholar 

  2. Dréo, J., Pétrowski, A., Siarry, P., Taillard, E.: Metaheuristics for Hard Optimization. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  3. Alefeld, G., Kreinovich, V., Mayer, G.: The Shape of the Solution Set for Systems of Interval Linear Equations with Dependent Coefficients. Mathematische Nachrichten 192(1), 23–36 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Luke, S.: Essentials of Metaheuristics. eBook 226 pages (2009), http://cs.gmu.edu/~sean/book/metaheuristics/

  5. Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer, Berlin (1996)

    Book  MATH  Google Scholar 

  6. Michalewicz, Z., Fogel, D.: How to Solve It: Modern Heuristics. Springer, Heidelberg (2004)

    Book  MATH  Google Scholar 

  7. Neumaier, A.: Interval Methods for Systems of Equations. Cambridge University Press, Cambridge (1990)

    MATH  Google Scholar 

  8. Popova, E.: Solving Linear Systems whose Input Data are Rational Functions of Interval Parameters. In: Boyanov, T., Dimova, S., Georgiev, K., Nikolov, G. (eds.) NMA 2006. LNCS, vol. 4310, pp. 345–352. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  9. Rohn, J., Kreinovich, V.: Computing exact componentwise bounds on solutions of linear systems with interval data is NP-hard. SIAM Journal on Matrix Analysis and Applications (SIMAX) 16, 415–420 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  10. Shary, S.P.: On optimal solution of interval equations. SIAM Journal on Numerical Analysis 32(2), 610–630 (1995)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. AGH University of Science and Technology, Krakow, Poland

    Iwona Skalna & Jerzy Duda

Authors
  1. Iwona Skalna
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jerzy Duda
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Computer and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev 25 A, 1113, Sofia, Bulgaria

    Ivan Dimov

  2. Faculty of Mathematics and Informatics, Department Numerical Methods and Algorithms, University of Sofia "St. Kliment Ohridski",, blvd. James Bourchier 5, 1164, Sofia, Bulgaria

    Stefka Dimova

  3. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. Bonchev St.,Bl.8, 1113, Sofia, Bulgaria

    Natalia Kolkovska

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Skalna, I., Duda, J. (2011). A Comparison of Metaheurisitics for the Problem of Solving Parametric Interval Linear Systems. In: Dimov, I., Dimova, S., Kolkovska, N. (eds) Numerical Methods and Applications. NMA 2010. Lecture Notes in Computer Science, vol 6046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18466-6_36

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-18466-6_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18465-9

  • Online ISBN: 978-3-642-18466-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation