Lobachevskii Journal of Mathematics

, Volume 39, Issue 4, pp 576–586 | Cite as

Generalized Parallel Computational Schemes for Time-Consuming Global Optimization

  • R. G. Strongin
  • V. P. Gergel
  • K. A. Barkalov
  • A. V. Sysoyev


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.

Keywords and phrases

Global optimization information-statistical theory parallel computations high-performance computing supercomputing technologies 


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  1. 1.
    C. A. Floudas and M. P. Pardalos, Recent Advances in Global Optimization (Princeton Univ. Press, Princeton, 2016).Google Scholar
  2. 2.
    M. Locatelli and F. Schoen, Global Optimization: Theory, Algorithms and Applications (SIAM, Philadelphia, 2013).CrossRefzbMATHGoogle Scholar
  3. 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).zbMATHGoogle Scholar
  4. 4.
    P. M. Pardalos, A. A. Zhigljavsky, and J. Žilinskas, Advances in Stochastic and Deterministic Global Optimization (Springer, New York, 2016).CrossRefzbMATHGoogle Scholar
  5. 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).CrossRefzbMATHGoogle Scholar
  6. 6.
    R. Paulavičius and J. Žilinskas, Simplicial Global Optimization, Springer Briefs in Optimization (Springer, New York, 2014).CrossRefzbMATHGoogle Scholar
  7. 7.
    R. Čiegis, D. Henty, B. Kågström, and J. Žilinskas, Parallel Scientific Computing and Optimization: Advances and Applications (Springer, Berlin, Heidelberg, 2009).zbMATHGoogle Scholar
  8. 8.
    G. Luque and E. Alba, Parallel Genetic Algorithms. Theory and Real World Applications (Springer, Berlin, 2011).CrossRefzbMATHGoogle Scholar
  9. 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. 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).CrossRefzbMATHGoogle Scholar
  11. 11.
    R. G. Strongin, Numerical Methods in Multiextremal Problems (Information-Statistical Algorithms) (Nauka, Moscow, 1978) [in Russian].zbMATHGoogle Scholar
  12. 12.
    R. G. Strongin and Y. D. Sergeyev, “Global multidimensional optimization on parallel computer,” Parallel Comput. 18, 1259–1273 (1992).MathSciNetCrossRefzbMATHGoogle Scholar
  13. 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).MathSciNetzbMATHGoogle Scholar
  14. 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).CrossRefGoogle Scholar
  15. 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.Google Scholar
  16. 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. 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).CrossRefzbMATHGoogle Scholar
  18. 18.
    V. Gergel and E. Kozinov, “Parallel computing for time-consuming multicriterial optimization problems,” Lect. NotesComput. Sci. 10421, 446–458 (2017).CrossRefzbMATHGoogle Scholar
  19. 19.
    V. Gergel, V. Grishagin, and A. Gergel, “Adaptive nested optimization scheme for multidimensional global search,” J. Global Optimiz. 66, 35–51 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    D. Lera and Y. D. Sergeyev, “Lipschitz and Holder global optimization using space-filling curves,” Appl. Numer.Math. 60, 115–129 (2010).MathSciNetCrossRefzbMATHGoogle Scholar
  21. 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.Google Scholar
  22. 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).CrossRefzbMATHGoogle Scholar
  23. 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).MathSciNetCrossRefzbMATHGoogle Scholar
  24. 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).CrossRefGoogle Scholar
  25. 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).MathSciNetzbMATHGoogle Scholar
  26. 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).MathSciNetCrossRefzbMATHGoogle Scholar
  27. 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).CrossRefGoogle Scholar
  28. 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

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • R. G. Strongin
    • 1
  • V. P. Gergel
    • 1
  • K. A. Barkalov
    • 1
  • A. V. Sysoyev
    • 1
  1. 1.Lobachevsky State University of Nizhni NovgorodNiznij NovgorodRussia

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