Advertisement

Globalizer – A Parallel Software System for Solving Global Optimization Problems

  • Alexander SysoyevEmail author
  • Konstantin Barkalov
  • Vladislav Sovrasov
  • Ilya Lebedev
  • Victor Gergel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10421)

Abstract

In this paper, we describe the Globalizer software system for solving global optimization problems. The system implements an approach to solving the global optimization problems using the block multistage scheme of the dimension reduction, which combines the use of Peano curve type evolvents and the multistage reduction scheme. The scheme allows an efficient parallelization of the computations and increasing the number of processors employed in the parallel solving of the global optimization problems many times.

Keywords

Multidimensional multiextremal optimization Global search algorithms Parallel computations Dimension reduction Block multistage dimension reduction scheme 

References

  1. 1.
    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, pp. 2111–2124 (2014)Google Scholar
  2. 2.
    Bussieck, M.R., Meeraus, A.: General algebraic modeling system (GAMS). In: Kallrath, J. (ed.) Modeling Languages in Mathematical Optimization, pp. 137–157. Springer, Boston (2004). doi: 10.1007/978-1-4613-0215-5_8 CrossRefGoogle Scholar
  3. 3.
    Egorov, I.N., Kretinin, G.V., Leshchenko, I.A., Kuptzov, S.V.: IOSO optimization toolkit - novel software to create better design. In: 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, Georgia (2002). http://www.iosotech.com/text/2002_4329.pdf
  4. 4.
    Gaviano, M., Lera, D., Kvasov, D.E., Sergeyev, Y.D.: 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
  5. 5.
    Gergel, V.P.: A software system for multiextremal optimization. Eur. J. Oper. Res. 65(3), 305–313 (1993)CrossRefzbMATHGoogle Scholar
  6. 6.
    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
  7. 7.
    Gergel, V.P.: A global optimization algorithm for multivariate function with Lipschitzian first derivatives. J. Glob. Optim. 10(3), 257–281 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Gergel, V., Lebedev, I.: Heterogeneous parallel computations for solving global optimization problems. Procedia Comput. Sci. 66, 53–62 (2015)CrossRefGoogle Scholar
  9. 9.
    Gergel, V.P., Strongin, R.G.: Parallel computing for globally optimal decision making. In: Malyshkin, V.E. (ed.) PaCT 2003. LNCS, vol. 2763, pp. 76–88. Springer, Heidelberg (2003). doi: 10.1007/978-3-540-45145-7_7 CrossRefGoogle Scholar
  10. 10.
    Holmström, K., Edvall, M.M.: The TOMLAB optimization environment. In: Kallrath, J. (ed.) Modeling Languages in Mathematical Optimization. Applied Optimization, vol. 88, pp. 369–376. Springer, Boston (2004). doi: 10.1007/978-1-4613-0215-5_19 CrossRefGoogle Scholar
  11. 11.
    Kearfott, R.B.: GlobSol user guide. Optim. Methods Softw. 24, 687–708 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Lin, Y., Schrage, L.: The global solver in the LINDO API. Optim. Methods Softw. 24, 657–668 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Mullen, K.M.: Continuous global optimization in R. J. Stat. Softw. 60(6) (2014)Google Scholar
  14. 14.
    Pintér, J.D.: Global Optimization in Action: Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications. Springer, New York (1996). doi: 10.1007/978-1-4757-2502-5 zbMATHGoogle Scholar
  15. 15.
    Sahinidis, N.V.: BARON: a general purpose global optimization software package. J. Glob. Optim. 8(2), 201–205 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Sergeyev, Y.D.: An information global optimization algorithm with local tuning. SIAM J. Optim. 5(4), 858–870 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Sergeyev, Y.D.: Multidimensional global optimization using the first derivatives. Comput. Math. Math. Phys. 39(5), 743–752 (1999)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Sergeyev, Y.D., Grishagin, V.A.: A parallel method for finding the global minimum of univariate functions. J. Optim. Theor. Appl. 80(3), 513–536 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    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
  20. 20.
    Sergeyev, Y., 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 CrossRefzbMATHGoogle Scholar
  21. 21.
    Strongin, R.G., Gergel, V.P., Grishagin, V.A., Barkalov, K.A.: Parallel Compucations for Global Optimization Problems. Moscow State University, Moscow (2013). (In Russian)Google Scholar
  22. 22.
    Strongin, R.G., Sergeyev, Y.D.: Global Optimization with Non-convex Constraints: Sequential and Parallel Algorithms. Springer, New York (2000). doi: 10.1007/978-1-4615-4677-1 CrossRefzbMATHGoogle Scholar
  23. 23.
    Venkataraman, P.: Applied Optimization with MATLAB Programming. Wiley, Chichester (2009)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

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

Personalised recommendations