Skip to main content
Log in

Generalized Parallel Computational Schemes for Time-Consuming Global Optimization

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

This paper addresses computationally intensive global optimization problems, for solving of which the supercomputing systems with exaflops performance can be required. To overcome such computational complexity, the paper proposes the generalized parallel computational schemes, which may involve numerous efficient parallel algorithms of global optimization. The proposed schemes include various ways of multilevel decomposition of parallel computations to guarantee the computational efficiency of supercomputing systems with shared and distributed memory multiprocessors with thousands of processors to meet global optimization challenges.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. C. A. Floudas and M. P. Pardalos, Recent Advances in Global Optimization (Princeton Univ. Press, Princeton, 2016).

    Google Scholar 

  2. M. Locatelli and F. Schoen, Global Optimization: Theory, Algorithms and Applications (SIAM, Philadelphia, 2013).

    Book  MATH  Google Scholar 

  3. R. G. Strongin and Y. D. Sergeyev, Global Optimization with Non-Convex Constraints. Sequential and Parallel Algorithms (Kluwer Academic, Dordrecht, 2000; 2nd ed. 2013; 3rd ed. 2014).

    MATH  Google Scholar 

  4. P. M. Pardalos, A. A. Zhigljavsky, and J. Žilinskas, Advances in Stochastic and Deterministic Global Optimization (Springer, New York, 2016).

    Book  MATH  Google Scholar 

  5. Y. D. Sergeyev and D. E. Kvasov, Deterministic Global Optimization. An Introduction to the Diagonal Approach, Springer Briefs in Optimization (Springer, New York, 2017).

    Book  MATH  Google Scholar 

  6. R. Paulavičius and J. Žilinskas, Simplicial Global Optimization, Springer Briefs in Optimization (Springer, New York, 2014).

    Book  MATH  Google Scholar 

  7. R. Čiegis, D. Henty, B. Kågström, and J. Žilinskas, Parallel Scientific Computing and Optimization: Advances and Applications (Springer, Berlin, Heidelberg, 2009).

    MATH  Google Scholar 

  8. G. Luque and E. Alba, Parallel Genetic Algorithms. Theory and Real World Applications (Springer, Berlin, 2011).

    Book  MATH  Google Scholar 

  9. R. G. Strongin, V. P. Gergel, V. A. Grishagin, and K. A. Barkalov, Parallel Computations for Global Optimization Problems (Mosk. Gos. Univ., Moscow, 2013) [in Russian].

    Google Scholar 

  10. Ya. D. Sergeyev, R. G. Strongin, and D. Lera, Introduction to Global Optimization Exploiting Space-Filling Curves, Springer Briefs in Optimization (Springer, New York, 2013).

    Book  MATH  Google Scholar 

  11. R. G. Strongin, Numerical Methods in Multiextremal Problems (Information-Statistical Algorithms) (Nauka, Moscow, 1978) [in Russian].

    MATH  Google Scholar 

  12. R. G. Strongin and Y. D. Sergeyev, “Global multidimensional optimization on parallel computer,” Parallel Comput. 18, 1259–1273 (1992).

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  14. V. P. Gergel and S. V. Sidorov, “A two-level parallel global search algorithm for solution of computationally intensive multiextremal optimization problems,” Lect. Notes Comput. Sci. 9251, 505–515 (2015).

    Article  Google Scholar 

  15. V. Gergel, “An unified approach to use of coprocessors of various types for solving global optimization problems,” in Proceedigns of the 2nd International Conference on Mathematics and Computers in Sciences and in Industry, 2015, pp. 13–18.

  16. K. Barkalov, V. Gergel, and I. Lebedev, “Solving global optimization problems on GPU cluster,” in Proceedings of the ICNAAM 2015, Ed. by T. E. Simos, AIPConf.Proc. 1738, 400006 (2016).

    Google Scholar 

  17. V. Gergel and E. Kozinov, “Efficientmethods of multicriterial optimization based on the intensive use of search information,” Springer Proc.Math. Stat. 197, 27–45 (2017).

    Article  MATH  Google Scholar 

  18. V. Gergel and E. Kozinov, “Parallel computing for time-consuming multicriterial optimization problems,” Lect. NotesComput. Sci. 10421, 446–458 (2017).

    Article  MATH  Google Scholar 

  19. V. Gergel, V. Grishagin, and A. Gergel, “Adaptive nested optimization scheme for multidimensional global search,” J. Global Optimiz. 66, 35–51 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  20. D. Lera and Y. D. Sergeyev, “Lipschitz and Holder global optimization using space-filling curves,” Appl. Numer.Math. 60, 115–129 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  21. V. A. Grishagin, “On convergence conditions for a class of global search algorithms,” in Proceedings of the 3rd All-Union Seminar on Numerical Methods of Nonlinear Programming, Kharkov, 1979, pp. 82–84.

  22. V. A. Grishagin, Y. D. Sergeyev, and R. G. Strongin, “Parallel characteristic algorithms for solving problems of global optimization,” J. Global Optimiz. 10, 185–206 (1997).

    Article  MATH  Google Scholar 

  23. R. G. Strongin, “Algorithms for multi-extremal mathematical programming problems employing the set of joint space-filling curves,” J. Global Optimiz. 2, 357–378 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  24. A. Sysoyev, K. Barkalov, V. Sovrasov, I. Lebedev, and V. Gergel, “Globalizer—a parallel software system for solving global optimization problems,” Lect. Notes Comput. Sci. 10421, 492–499 (2017).

    Article  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  26. M. Gaviano, D. Lera, D. E. Kvasov, and Ya. D. Sergeyev, “Software for generation of classes of test functions with known local and global minima for global optimization,” ACM Trans. Math. Software 29, 469–480 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  27. V. Y. Modorskii, D. F. Gaynutdinova, V. P. Gergel, and K. A. Barkalov, “Optimization in design of scientific products for purposes of cavitation problems,” AIP Conf. Proc. 1738, 400013 (2016).

    Article  Google Scholar 

  28. V. P. Gergel, M. I. Kuzmin, N. A. Solovyov, and V. A. Grishagin, “Recognition of surface defects of coldrolling sheets based on method of localities,” Int. Rev. Autom. Control 8, 51–55 (2015).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. G. Strongin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Strongin, R.G., Gergel, V.P., Barkalov, K.A. et al. Generalized Parallel Computational Schemes for Time-Consuming Global Optimization. Lobachevskii J Math 39, 576–586 (2018). https://doi.org/10.1134/S1995080218040133

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080218040133

Keywords and phrases

Navigation