Parallel Computing for Time-Consuming Multicriterial Optimization Problems

  • Victor GergelEmail author
  • Evgeny Kozinov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10421)


In the present paper, an efficient method for parallel solving the time-consuming multicriterial optimization problems, where the optimality criteria can be multiextremal, and the computation of the criteria values can require a large amount of computations, is proposed. The proposed scheme of parallel computations allows obtaining several efficient decisions of a multicriterial problem. During performing the computations, the maximum use of the search information is provided. The results of the numerical experiments have demonstrated such an approach to allow reducing the computational costs of solving the multicriterial optimization problems essentially – several tens and hundred times.


Decision making Multicriterial optimization Parallel computing Dimensionality reduction Criteria convolution Algorithm of global search Computation complexity 



This work has been supported by Russian Science Foundation, project No 16-11-10150 “Novel efficient methods and software tools for time-consuming decision making problems using superior-performance supercomputers.”


  1. 1.
    Mardani, A., Jusoh, A., Nor, K., Khalifah, Z., Zakwan, N., Valipour, A.: Multiple criteria decision-making techniques and their applications – a review of the literature from 2000 to 2014. Econ. Res.-Ekonomska Istraživanja 28(1), 516–571 (2015). doi: 10.1080/1331677X.2015.1075139 CrossRefGoogle Scholar
  2. 2.
    Miettinen K.: Nonlinear Multiobjective Optimization. Springer, New York (1999)Google Scholar
  3. 3.
    Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Heidelberg (2010)zbMATHGoogle Scholar
  4. 4.
    Collette, Y., Siarry, P.: Multiobjective Optimization: Principles and Case Studies (Decision Engineering). Springer, Heidelberg (2011)Google Scholar
  5. 5.
    Marler, R.T., Arora, J.S.: Survey of multi-objective optimization methods for engineering. Struct. Multidisciplin. Optim. 26, 369–395 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Figueira,J., Greco, S., Ehrgott, M. (eds.): Multiple Criteria Decision Analysis: State of the art Surveys. Springer, New York (2005)Google Scholar
  7. 7.
    Eichfelder, G.: Scalarizations for adaptively solving multi-objective optimization problems. Comput. Optim. Appl. 44, 249–273 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Siwale, I.: Practical multi-objective programming. Technical Report RD-14-2013. Apex Research Limited (2014)Google Scholar
  9. 9.
    Pintér, J.D.: Global optimization in action (continuous and Lipschitz optimization: algorithms, implementations and applications). Kluwer Academic Publishers, Dordrecht (1996)CrossRefzbMATHGoogle Scholar
  10. 10.
    Strongin, R.G.: Numerical Methods in Multiextremal Problems: Information-Statistical Algorithms. Nauka, Moscow (1978). (in Russian)zbMATHGoogle Scholar
  11. 11.
    Strongin, R., Sergeyev, Ya.: Global Optimization with Non-Convex Constraints. Sequential and Parallel Algorithms. Kluwer Academic Publishers, Dordrecht (2000). 2nd edn. (2013). 3rd edn. (2014)Google Scholar
  12. 12.
    Sergeyev Y.D., Strongin R.G., Lera D.: Introduction to Global Optimization Exploiting Space-Filling Curves. Springer, New York (2013)Google Scholar
  13. 13.
    Floudas, C.A., Pardalos, M.P.: Recent Advances in Global Optimization. Princeton University Press, Princeton (2016)Google Scholar
  14. 14.
    Locatelli, M., Schoen, F.: Global Optimization: Theory, Algorithms, and Applications. SIAM, Philadelphia (2013)Google Scholar
  15. 15.
    Sergeyev, Y.D.: An information global optimization algorithm with local tuning. SIAM J. Optim. 5(4), 858–870 (1995)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.
    Törn, A., Žilinskas, A. (eds.): Global Optimization. LNCS, vol. 350. Springer, Heidelberg (1989). doi: 10.1007/3-540-50871-6 zbMATHGoogle Scholar
  18. 18.
    Zhigljavsky, A.A.: Theory of Global Random Search. Kluwer Academic Publishers, Dordrecht (1991)CrossRefGoogle Scholar
  19. 19.
    Marler, R.T., Arora, J.S.: Multi-Objective Optimization: Concepts and Methods for Engineering. VDM Verlag, Saarbrucken (2009)Google Scholar
  20. 20.
    Hillermeier, C., Jahn, J.: Multiobjective optimization: survey of methods and industrial applications. Surv. Math. Ind. 11, 1–42 (2005)zbMATHGoogle Scholar
  21. 21.
    Forrester, A.I.J., Keane, A.J.: Recent advances in surrogate-based optimization. Prog. Aerosp. Sci. 45(1), 50–79 (2009)CrossRefGoogle Scholar
  22. 22.
    Krasnoshekov, P.S., Morozov, V.V., Fedorov, V.V.: Decompozition in design problems. Eng. Cybern. 2, 7–17 (1979). (in Russian)Google Scholar
  23. 23.
    Wierzbicki, A.: The use of reference objectives in multiobjective optimization. In: Fandel, G., Gal, T. (eds.) Multiple Objective Decision Making, Theory and Application, vol. 177, pp. 468–486. Springer, New York (1980)Google Scholar
  24. 24.
    Gergel, V., Sidorov, S.: A two-level parallel global search algorithm for solution of computationally intensive multiextremal optimization problems. In: Malyshkin, V. (ed.) PaCT 2015. LNCS, vol. 9251, pp. 505–515. Springer, Cham (2015). doi: 10.1007/978-3-319-21909-7_49 CrossRefGoogle Scholar
  25. 25.
    Barkalov, K., Gergel, V., Lebedev, I.: Use of Xeon Phi coprocessor for solving global optimization problems. In: Malyshkin, V. (ed.) PaCT 2015. LNCS, vol. 9251, pp. 307–318. Springer, Cham (2015). doi: 10.1007/978-3-319-21909-7_31 CrossRefGoogle Scholar
  26. 26.
    Gergel, V.: An unified approach to use of coprocessors of various types for solving global optimization problems. In: 2nd International Conference on Mathematics and Computers in Sciences and in Industry, pp. 13–18 (2015) doi: 10.1109/MCSI.2015.18
  27. 27.
    Gergel, V.P., Grishagin, V.A., Gergel, A.V.: Adaptive nested optimization scheme for multidimensional global search. J. Global Optim. 66(1), 1–17 (2015)MathSciNetzbMATHGoogle Scholar
  28. 28.
    Gergel, V., Kozinov, E.: Accelerating parallel multicriterial optimization methods based on intensive using of search information. Procedia Comput. Sci. 108, 1463–1472 (2017)CrossRefGoogle Scholar
  29. 29.
    Evtushenko, Y.G., Posypkin, M.A.: A deterministic algorithm for global multi-objective optimization. Optim. Methods Softw. 29(5), 1005–1019 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Gergel, V., Lebedev, I.: Heterogeneous parallel computations for solving global optimization problems. Procedia Comput. Sci. 66, 53–62 (2015). doi: 10.1007/s10898-016-0411-y CrossRefGoogle Scholar
  31. 31.
    Strongin, R., Gergel, V., Grishagin, V., Barkalov, K.: Parallel Computations for Global Optimization Problems. Moscow State University, Moscow (2013). (in Russian)Google Scholar
  32. 32.
    Zilinskas, A., Zilinskas, J.: Adaptation of a one-step worst-case optimal univariate algorithm of bi-objective Lipschitz optimization to multidimensional problems. Commun. Nonlinear Sci. Numer. Simul. 21, 89–98 (2015)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Lobachevsky State University of Nizhny NovgorodNizhny NovgorodRussia

Personalised recommendations