Skip to main content
SpringerLink
Log in

Test Problems for Parallel Algorithms of Constrained Global Optimization

  • Conference paper
  • First Online:
Learning and Intelligent Optimization (LION 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10556))

Included in the following conference series:

Abstract

This work considers the problem of building a class of test problems for global optimization algorithms. The authors present an approach to building multidimensional multiextremal problems, which can clearly demonstrate the nature of the best current approximation, regardless of the problems dimensionality. As part of this approach, the objective function and constraints arise in the process of solving an auxiliary approximation problem. The proposed generator allows the problem to be simplified or complicated, which results in changes to its dimensionality and changes in the feasible domain. The generator was tested by building and solving 100 problems using a parallel global optimization index algorithm. The algorithm’s results are presented using different numbers of computing cores, which clearly demonstrate its acceleration and non-redundancy.

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 EPUB and 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

References

  1. Hill, J.D.: A search technique for multimodal surfaces. IEEE Trans. Syst. Sci. Cybern. 5(1), 2–8 (1969)

    Article  Google Scholar 

  2. Toropov, V.V.: Simulation approach to structural optimization. Struct. Optim. 1, 37–46 (1989)

    Article  Google Scholar 

  3. Shekel, J.: Test functions for multimodal search technique. In: Proceedings of the 5th Princeton Conference on Information Science Systems, pp. 354–359. Princeton University Press, Princeton (1971)

    Google Scholar 

  4. Strongin, R.G., Gergel, V.P., Tropichev, A.V.: Globalizer. Investigation of minimizing sequences generated by global search algorithms for univariate functions. User’s guide. Nizhny Novgorod University Press, Nizhny Novgorod (1995)

    Google Scholar 

  5. Strongin, R.G., Sergeyev, Y.D.: Global Optimization with Non-convex Constraints: Sequential and Parallel Algorithms. Kluwer Academic Publishers, Dordrecht (2000)

    Book  MATH  Google Scholar 

  6. Barkalov, K.A., Strongin, R.G.: A global optimization technique with an adaptive order of checking for constraints. Comput. Math. Math. Phys. 42(9), 1289–1300 (2002)

    MATH  MathSciNet  Google Scholar 

  7. Grishagin, V.A., Sergeyev, Y.D., Strongin, R.G.: Parallel characteristical algorithms for solving problems of global optimization. J. Glob. Optim. 10(2), 185–206 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  8. Sergeyev, Y.D., Grishagin, V.A.: Sequential and parallel algorithms for global optimization. Optim. Methods Softw. 3, 111–124 (1994)

    Article  MATH  Google Scholar 

  9. Sergeyev, Y.D., Grishagin, V.A.: Parallel asynchronous global search and the nested optimization scheme. J. Comput. Anal. Appl. 3(2), 123–145 (2001)

    MATH  MathSciNet  Google Scholar 

  10. Gergel, V., Grishagin, V., Gergel, A.: Adaptive nested optimization scheme for multidimensional global search. J. Glob. Optim. 66(1), 35–51 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  11. Gaviano, M., Kvasov, D.E., Lera, D., Sergeyev, Y.D.: Software for generation of classes of test functions with known local and global minima for global optimization. ACM Trans. Math. Softw. 29(4), 469–480 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  12. Sergeyev, Y.D., Kvasov, D.E.: Global search based on efficient diagonal partitions and a set of Lipschitz constants. SIAM J. Optim. 16(3), 910–937 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Lera, D., Sergeyev, Y.D.: Lipschitz and Holder global optimization using space-filling curves. Appl. Numer. Math. 60(1–2), 115–129 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  14. Paulavicius, R., Sergeyev, Y., Kvasov, D., Zilinskas, J.: Globally-biased DISIMPL algorithm for expensive global optimization. J. Glob. Optim. 59(2–3), 545–567 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  15. Sergeyev, Y.D., Kvasov, D.E.: A deterministic global optimization using smooth diagonal auxiliary functions. Commun. Nonlinear Sci. Numer. Simul. 21(1–3), 99–111 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  16. Floudas, C.A., Pardalos, P.M.: A Collection of Test Problems for Constrained Global Optimization Algorithms. LNCS, vol. 455. Springer, Heidelberg (1990). doi:10.1007/3-540-53032-0

    MATH  Google Scholar 

  17. Floudas, C.A., et al.: Handbook of Test Problems in Local and Global Optimization. Springer, New York (1999). doi:10.1007/978-1-4757-3040-1

    Book  MATH  Google Scholar 

  18. Pardalos, P.M., Phillips, A.T., Rosen, J.B.: Topics in Parallel Computing in Mathematical Programming. Science Press, New York (1992)

    MATH  Google Scholar 

  19. Sergeyev, Y.D., Strongin, R.G., Lera, D.: Introduction to Global Optimization Exploiting Space-Filling Curves. Springer, New York (2013). doi:10.1007/978-1-4614-8042-6

    Book  MATH  Google Scholar 

  20. Gergel, V.P., Kuzmin, M.I., Solovyov, N.A., Grishagin, V.A.: Recognition of surface defects of cold-rolling sheets based on method of localities. Int. Rev. Autom. Control 8(1), 51–55 (2015)

    Google Scholar 

  21. Modorskii, V.Y., Gaynutdinova, D.F., Gergel, V.P., Barkalov, K.A.: Optimization in design of scientific products for purposes of cavitation problems. In: Simos, T.E. (ed.) ICNAAM 2015. AIP Conference Proceedings, vol. 1738 (2016). Article No. 400013

    Google Scholar 

  22. Grishagin, V.A.: Operating characteristics of some global search algorithms. Probl. Stoch. Search 7, 198–206 (1978). (in Russian)

    MATH  Google Scholar 

Download references

Acknowledgments

This study was supported by the Russian Science Foundation, project No. 16-11-10150.

Author information

Authors and Affiliations

  1. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    Konstantin Barkalov & Roman Strongin

Authors
  1. Konstantin Barkalov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roman Strongin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Konstantin Barkalov .

Editor information

Editors and Affiliations

  1. University of Trento, Trento, Italy

    Roberto Battiti

  2. University of Calabria, Rende, Italy

    Dmitri E. Kvasov

  3. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Barkalov, K., Strongin, R. (2017). Test Problems for Parallel Algorithms of Constrained Global Optimization. In: Battiti, R., Kvasov, D., Sergeyev, Y. (eds) Learning and Intelligent Optimization. LION 2017. Lecture Notes in Computer Science(), vol 10556. Springer, Cham. https://doi.org/10.1007/978-3-319-69404-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-69404-7_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-69403-0

  • Online ISBN: 978-3-319-69404-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation