Solving GENOPT Problems with the Use of ExaMin Solver

  • Konstantin BarkalovEmail author
  • Alexander Sysoyev
  • Ilya Lebedev
  • Vladislav Sovrasov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10079)


This paper describes an algorithm for solving multidimensional multiextremal optimization problems. This algorithm uses Peano-type space-filling curves for dimension reduction. It has been used for solving problems at GENeralization-based contest in global OPTimization (GENOPT). Computational experiments are carried out on 1800 multidimensional problems.


Global optimization Multiextremal functions Space-filling curves Mixed global-local algorithm GENOPT 



This study was supported by the Russian Science Foundation, project No 15-11-30022 “Global optimization, supercomputing computations, and applications”.


  1. 1.
    Hill, J.D.: A search technique for multimodal surfaces. IEEE Trans. Syst. Sci. Cybern. 5(1), 2–8 (1969)CrossRefGoogle Scholar
  2. 2.
    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
  3. 3.
    Strongin, R.G., Sergeyev, Y.D.: Global Optimization with Non-convex Constraints. Sequential and Parallel Algorithms. Kluwer Academic Publishers, Dordrecht (2000)CrossRefzbMATHGoogle Scholar
  4. 4.
    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)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Grishagin, V.A.: Operation characteristics of some global optimization algorithms. Probl. Stoch. Search 7, 198–206 (1978). (in Russian)zbMATHGoogle Scholar
  6. 6.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Kvasov, D., Sergeyev, Y.D.: Multidimensional global optimization algorithm based on adaptive diagonal curves. Comput. Math. Math. Phys. 43(1), 40–56 (2003)MathSciNetGoogle Scholar
  8. 8.
    Sergeyev, Y.D., Strongin, R.G., Lera, D.: Introduction to Global Optimization Exploiting Space-filling Curves. Springer, New York (2013)CrossRefzbMATHGoogle Scholar
  9. 9.
    Lera, D., Sergeyev, Y.D.: Lipschitz and holder global optimization using space-filling curves. Appl. Numer. Math. 60(1–2), 115–129 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Sergeyev, Y.D., Grishagin, V.A.: A parallel method for finding the global minimum of univariate functions. J. Optim. Theory Appl. 80(3), 513–536 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Sergeyev, Y.D., Grishagin, V.A.: Sequential and parallel global optimization algorithms. Optim. Methods Softw. 3, 111–124 (1994)CrossRefzbMATHGoogle Scholar
  12. 12.
    Gergel, V.P.: A method of using derivatives in the minimization of multiextremum functions. Comput. Math. Math. Phys. 36(6), 729–742 (1996)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Gergel, V.P.: A global optimization algorithm for multivariate functions with lipschitzian first derivatives. J. Glob. Optim. 10(3), 257–281 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Gergel, V.P., Sergeyev, Y.D.: Sequential and parallel algorithms for global minimizing functions with Lipschitzian derivatives. Comput. Math. Appl. 37(4–5), 163–179 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Sergeyev, Y.D., Grishagin, V.A.: Parallel asynchronous global search and the nested optimization scheme. J. Comput. Anal. Appl. 3(2), 123–145 (2001)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Strongin, R.G., Sergeyev, Y.D.: Global optimization: fractal approach and non-redundant parallelism. J. Glob. Optim. 27(1), 25–50 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    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)CrossRefGoogle Scholar
  19. 19.
    Barkalov, K., Polovinkin, A., Meyerov, I., Sidorov, S., Zolotykh, N.: SVM regression parameters optimization using parallel global search algorithm. In: Malyshkin, V. (ed.) PaCT 2013. LNCS, vol. 7979, pp. 154–166. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-39958-9_14 CrossRefGoogle Scholar
  20. 20.
    Barkalov, K.A., Gergel, V.P.: Multilevel scheme of dimensionality reduction for parallel global search algorithms. In: Proceedings of the 1st International Conference on Engineering and Applied Sciences Optimization - OPT-i 2014, pp. 2111–2124 (2014)Google Scholar
  21. 21.
    Gergel, V., Grishagin, V., Israfilov, R.: Local tuning in nested scheme of global optimization. Procedia Comput. Sci. 51(1), 865–874 (2015)CrossRefGoogle Scholar
  22. 22.
    Gergel, V., Grishagin, V., Gergel, A.: Adaptive nested optimization scheme for multidimensional global search. J. Global Optim. 66, 35–51 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Barkalov, K., Gergel, V.: Parallel global optimization on GPU. J. Global Optim. 66, 3–20 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Paulavicius, R., Sergeyev, Y., Kvasov, D., Zilinskas, J.: Globally-biased DISIMPL algorithm for expensive global optimization. J. Global Optim. 59(2–3), 545–567 (2015)MathSciNetzbMATHGoogle Scholar
  26. 26.
    Hooke, R., Jeeves, T.A.: “Direct search” solution of numerical and statistical problems. J. ACM. 8(2), 212–229 (1961)CrossRefzbMATHGoogle Scholar
  27. 27.
    Wilde, D.J.: Optimum Seeking Methods. Prentice-Hall, Engelwood Cliffs (1964)zbMATHGoogle Scholar
  28. 28.
    Himmelblau, D.M.: Applied Nonlinear Programming. McGraw-Hill, New York (1972)zbMATHGoogle Scholar
  29. 29.

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Konstantin Barkalov
    • 1
    Email author
  • Alexander Sysoyev
    • 1
  • Ilya Lebedev
    • 1
  • Vladislav Sovrasov
    • 1
  1. 1.Lobachevsky State University of Nizhny NovgorodNizhny NovgorodRussia

Personalised recommendations