Skip to main content

Parallel global optimization on GPU


This work considers a parallel algorithm for solving multidimensional multiextremal optimization problems. This algorithm uses Peano-type space filling curves for dimension reduction. Conditions of non-redundant parallelization of the algorithm are considered. Efficiency of the algorithm on modern computing systems with the use of graphics processing units (GPUs) is investigated. Speedup of the algorithm using GPU as compared with the same algorithm implemented on CPU only is demonstrated experimentally. Computational experiments are carried out on a series of several hundred multidimensional multiextremal problems.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4


  1. Pinter, J.D. (ed.): Global Optimization: Scientific and Engineering Case Studies. Springer, New York (2006)

    MATH  Google Scholar 

  2. Hwu, W.: GPU Computing Gems Emerald Edition (Applications of GPU Computing Series). Morgan Kaufmann, San Francisco (2011)

  3. D’Apuzzo, M., Marino, M., Migdalas, A., Pardalos, P.M., Toraldo, G.: Parallel computing in global optimization. In: Handbook of Parallel Computing and Statistics. Chapman & Hall, London, pp. 225–258 (2006)

  4. Ferreiro, A.M., Garcia, J.A., Lopez-Salas, J.G., Vazquez, C.: An efficient implementation of parallel simulated annealing algorithm in GPUs. J. Glob. Optim. 57(3), 863–890 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Zhu, W.: Massively parallel differential evolution-pattern search optimization with graphics hardware acceleration: an investigation on bound constrained optimization problems. J. Glob. Optim. 50(3), 417–437 (2011)

    Article  Google Scholar 

  6. Garcia-Martinez, J.M., Garzon, E.M., Ortigosa, P.M.: A GPU implementation of a hybrid evolutionary algorithm: GPuEGO. J. Supercomput. (2014). doi:10.1007/s11227-014-1136-7

  7. Mussi, L., et al.: GPU implementation of a road sign detector based on particle swarm optimization. Evol. Intel. 3(3), 155–169 (2010)

    Article  Google Scholar 

  8. Langdon, W.B.: Graphics processing units and genetic programming: an overview. Soft. Comput. 15(8), 1657–1669 (2011)

    Article  Google Scholar 

  9. Gergel, V.P., Strongin, R.G.: Parallel computing for globally optimal decision making on cluster systems. Future Gener. Comput. Syst. 21(5), 673–678 (2005)

    Article  Google Scholar 

  10. Evtushenko, YuG, Malkova, V.U., Stanevichyus, A.A.: Parallel global optimization of functions of several variables. Comput. Math. Math. Phys. 49(2), 246–260 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. He, J., Verstak, A., Watson, L.T., Sosonkina, M.: Design and implementation of a massively parallel version of DIRECT. Comput. Optim. Appl. 40(2), 217–245 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Paulavicius, R., Zilinskas, J., Grothey, A.: Parallel branch and bound for global optimization with combination of Lipschitz bounds. Optim. Methods Softw. 26(3), 487–498 (2011)

    Article  MathSciNet  Google Scholar 

  13. Boukedjar A., Lalami M. E., El Baz D.: Parallel branch and bound on a CPU–GPU system. In: 20th International Conference on Parallel, Distributed and Network-Based Processing, pp. 392–398 (2012)

  14. Carneiro, T. et al.: A new parallel schema for branch-and-bound algorithms using GPGPU. In: 23rd International Symposium on Computer Architecture and High Performance Computing, pp. 41–47 (2011)

  15. Kindratenko, V. (ed.): Numerical Computations with GPUs. Springer, New York (2014)

    MATH  Google Scholar 

  16. 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 

  17. Lebedev, I.G., Barkalov, K.A.: A GPU implementation of a parallel global search algorithm. PNRPU Aerosp. Eng. Bull. 36, 64–82 (2014). (in Russian)

    Google Scholar 

  18. Sergeyev, YaD, 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  MathSciNet  MATH  Google Scholar 

  19. Zilinskas, J.: Branch and bound with simplicial partitions for global optimization. Math. Model. Anal. 13(1), 145–159 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  20. Sergeyev, Y.D., Strongin, R.G., Lera, D.: Introduction to Global Optimization Exploiting Space-Filling Curves. Springer, New York (2013)

    Book  MATH  Google Scholar 

  21. Molinaro, A., Pizzuti, C., Sergeyev, YaD: Acceleration tools for diagonal information global optimization algorithms: Comput. Optim. Appl. 18, 5–26 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  22. 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)

    MathSciNet  MATH  Google Scholar 

  23. Gergel, V.P.: A method of using derivatives in the minimization of multiextremum functions. Comput. Math. Math. Phys. 36(6), 729–742 (1996)

    MathSciNet  MATH  Google Scholar 

  24. Gergel, V.P.: A global optimization algorithm for multivariate functions with lipschitzian first derivatives. J. Glob. Optim. 10(3), 257–281 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  25. Sergeyev, YaD, Grishagin, V.A.: A parallel method for finding the global minimum of univariate functions. J. Optim. Theory Appl. 80(3), 513–536 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  26. Sergeyev, YaD, Grishagin, V.A.: Sequential and parallel global optimization algorithms. Optim. Methods Softw. 3, 111–124 (1994)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  29. Gergel, V.P., Sergeyev, YaD: Sequential and parallel algorithms for global minimizing functions with Lipschitzian derivatives. Comput. Math. Appl. 37(4–5), 163–179 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  30. Strongin, R.G., Sergeyev, YaD: Global optimization: fractal approach and non-redundant parallelism. J. Glob. Optim. 27(1), 25–50 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  31. Barkalov, K., Polovinkin, A., Meyerov, I., Sidorov, S., Zolotykh, N.: SVM regression parameters optimization using parallel global search algorithm. In: Lecture Notes in Computer Science, vol. 7979, pp. 154–166 (2013)

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

    Article  MathSciNet  MATH  Google Scholar 

  33. Jones, D.R., Perttunen, C.D., Stuckman, B.E.: Lipschitzian optimization without the lipschitz constant. J. Optim. Theory Appl. 79(1), 157–181 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  34. Gablonsky, J.M., Kelley, C.T.: A locally-biased form of the DIRECT algorithm. J. Glob. Optim. 21(1), 27–37 (2001)

    Article  MathSciNet  MATH  Google Scholar 

Download references


The authors of the paper express their gratitude to Ilya Lebedev for assistance in carrying out the computational experiments.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Konstantin Barkalov.

Additional information

The revised version of the paper was supported by the Russian Science Foundation, Project No 15-11-30022 “Global optimization, supercomputing computations, and applications”.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Barkalov, K., Gergel, V. Parallel global optimization on GPU. J Glob Optim 66, 3–20 (2016).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: