GPU-Based Parallel Computations in Multicriterial Optimization

  • Victor GergelEmail author
  • Evgeny Kozinov
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 965)


In the present paper, an efficient approach for solving the time-consuming multicriterial optimization problems, in which the optimality criteria could be the multiextremal ones and computing the criteria values could require a large amount of computations is proposed. The proposed approach is based on the reduction of the multicriterial problems to the scalar optimization ones with the use of the minimax convolution of the partial criteria, on the dimensionality reduction with the use of the Peano space-filling curves, and on the application of the efficient information-statistical global optimization methods. An additional application of the block multistep scheme provides the opportunity of the large-scale parallel computations with the use of the graphics processing units (GPUs) with thousands of computational cores. The results of the numerical experiments have demonstrated such an approach to allow improving the computational efficiency of solving the multicriterial optimization problems considerably – hundreds and thousands.


Decision making Multicriterial optimization Global optimization High performance computations Dimensionality reduction Criteria convolution Global search algorithm Computational costs 



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


  1. 1.
    Marler, R.T., Arora, J.S.: Multi-Objective Optimization: Concepts and Methods for Engineering. VDM Verlag, Saarbrücken (2009)Google Scholar
  2. 2.
    Ehrgott, M.: Multicriteria Optimization. Springer, Heidelber (2005). (2nd ed., 2010)CrossRefzbMATHGoogle Scholar
  3. 3.
    Collette, Y., Siarry, P.: Multiobjective Optimization: Principles and Case Studies (Decision Engineering). Springer, Heidelberg (2011)zbMATHGoogle Scholar
  4. 4.
    Pardalos, P.M., Žilinskas, A., Žilinskas, J.: Non-Convex Multi-Objective Optimization. Springer, Cham (2017). Scholar
  5. 5.
    Hillermeier, C., Jahn, J.: Multiobjective optimization: survey of methods and industrial applications. Surv. Math. Ind. 11, 1–42 (2005)zbMATHGoogle Scholar
  6. 6.
    Cho, J.-H., Wang, Y., Chen, I.-R., Chan, K.S., Swami, A.: A survey on modeling and optimizing multi-objective systems. IEEE Commun. Surv. Tutor. 19(3), 1867–1901 (2017)CrossRefGoogle Scholar
  7. 7.
    Eichfelder, G.: Scalarizations for adaptively solving multi-objective optimization problems. Comput. Optim. Appl. 44, 249–273 (2009)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Strongin, R., Sergeyev, Y.: Global Optimization with Non-convex Constraints. Sequential and Parallel Algorithms. Kluwer Academic Publishers, Dordrecht (2000). (2nd ed. 2013, 3rd ed. 2014)CrossRefGoogle Scholar
  9. 9.
    Strongin, R., Gergel, V., Grishagin, V., Barkalov, K.: Parallel computations for global optimization problems, Moscow State University Press (2013). (in Russian)Google Scholar
  10. 10.
    Sergeyev, Y.D., Strongin, R.G., Lera, D.: Introduction to Global Optimization Exploiting Space-filling Curves. Springer, New York (2013). Scholar
  11. 11.
    Gergel, V.P., Kozinov, E.A.: Accelerating parallel multicriterial optimization methods based on intensive using of search information. Procedia Comput. Sci. 108, 1463–1472 (2017)CrossRefGoogle Scholar
  12. 12.
    Gergel, V., Kozinov, E.: Parallel computing for time-consuming multicriterial optimization problems. In: Malyshkin, V. (ed.) PaCT 2017. LNCS, vol. 10421, pp. 446–458. Springer, Cham (2017). Scholar
  13. 13.
    Gergel, V., Kozinov, E.: Efficient methods of multicriterial optimization based on the intensive use of search information. In: Kalyagin, V., Nikolaev, A., Pardalos, P., Prokopyev, O. (eds.) NET 2016. PROMS, vol. 197, pp. 27–45. Springer, Cham (2017). Scholar
  14. 14.
    Gergel, V., Kozinov, E.: An approach for parallel solving the multicriterial optimization problems with non-convex constraints. In: Voevodin, V., Sobolev, S. (eds.) RuSCDays 2017. CCIS, vol. 793, pp. 121–135. Springer, Cham (2017). Scholar
  15. 15.
    Cai, Y., See, S. (eds.): GPU Computing and Applications. Springer, Singapore (2015). Scholar
  16. 16.
    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)MathSciNetCrossRefGoogle Scholar
  17. 17.
    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)CrossRefGoogle Scholar
  18. 18.
    Garcia-Martinez, J.M., Garzon, E.M., Ortigosa, P.M.: A GPU implementation of a hybrid evolutionary algorithm: GPuEGO. J. Supercomput (2014).
  19. 19.
    Langdon, W.B.: Graphics processing units and genetic programming: an overview. Soft. Comput. 15(8), 1657–1669 (2011)CrossRefGoogle Scholar
  20. 20.
    Locatelli, M., Schoen, F.: Global Optimization: Theory, Algorithms, and Applications. SIAM (2013)Google Scholar
  21. 21.
    Floudas, C.A., Pardalos, M.P.: Recent Advances in Global Optimization. Princeton University Press, Princeton (2016)Google Scholar
  22. 22.
    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). Scholar
  23. 23.
    Gergel, V.P., Kuzmin, M.I., Solovyov, N.A., Grishagin, V.A.: Recognition of surface defects of cold-rolling sheets based on method of localities. Int. Rev. Autom. Control. 8(1), 51–55 (2015)Google Scholar
  24. 24.
    Modorskii, V.Y., Gaynutdinova, D.F., Gergel, V.P., Barkalov, K.A.: Optimization in design of scientific products for purposes of cavitation problems. In: AIP Conference Proceedings, vol. 1738, p. 400013 (2016).
  25. 25.
    Grishagin, V., Israfilov, R., Sergeyev, Y.: Convergence conditions and numerical comparison of global optimization methods based on dimensionality reduction schemes. Appl. Math. Comput. 318, 270–280 (2018). Scholar
  26. 26.
    Sergeyev, Y., Grishagin, V.: Parallel asynchronous global search and the nested optimization scheme. J. Comput. Anal. Appl. 3(2), 123–145 (2001)MathSciNetzbMATHGoogle Scholar
  27. 27.
    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
  28. 28.
    Gergel, V., Lebedev, I.: Heterogeneous parallel computations for solving global optimization problems. Procedia Comput. Sci. 66, 53–62 (2015)CrossRefGoogle Scholar
  29. 29.
    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). Scholar
  30. 30.
    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, MCSI, vol. 7423935, pp. 13–18 (2016)Google Scholar
  31. 31.
    Evtushenko, Y.G., Posypkin, M.A.: A deterministic algorithm for global multi-objective optimization. Optim. Methods Softw. 29(5), 1005–1019 (2014)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Žilinskas, A., Žilinskas, 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)MathSciNetCrossRefGoogle Scholar
  33. 33.
    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)MathSciNetCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Lobachevsky State University of Nizhni NovgorodNizhni NovgorodRussia

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