Skip to main content
SpringerLink
Log in

Global Optimization Method Based on the Survival of the Fittest Algorithm

  • Conference paper
  • First Online:
Mathematical Modeling and Supercomputer Technologies (MMST 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1750))

Abstract

One of the most important theoretical questions for evolutionary methods of global optimization is their convergence. The majority of evolutionary methods do not guarantee that the generated sequence of test points converges to a global extremum in any sense. The purpose of this paper is to construct and prove convergence of a new evolutionary global optimization algorithm. This algorithm is created on the base of the Survival of the Fittest algorithm using ideas of Differential Evolution. It is proved that the sequence of test points of this algorithm converges to the solution with probability one. The new method is compared with other evolutionary algorithms. It is shown that the method has higher efficiency for some classes of relevant multidimensional functions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Strongin, R., Barkalov, K., Bevzuk, S.: Global optimization method with dual Lipschitz constant estimates for problems with non-convex constraints. Soft. Comput. 24(16), 11853–11865 (2020)

    Article  MATH  Google Scholar 

  2. Zhigljavsky, A., Žilinskas, A.: Stochastic Global Optimization. Springer, Boston (2008). https://doi.org/10.1007/978-0-387-74740-8

    Book  MATH  Google Scholar 

  3. Zhigljavsky, A., Sergeyev, Y.D., Strongin, R.G., Lera, D.: Introduction to global optimization exploiting space-lling curves. J. Glob. Optim. 60(3), 595–596 (2014)

    Article  Google Scholar 

  4. Gergel, V., Grishagin, V., Israfilov, R.: Local tuning in nested scheme of global optimization. Proc. Comput. Sci. 51, 865–874 (2015)

    Article  Google Scholar 

  5. Deb, K.: Multiobjective Optimization Using Evolutionary Algorithms. Wiley, New York (2001)

    MATH  Google Scholar 

  6. Rai, D., Tyagi, K.: Bio-inspired optimization techniques: a critical comparative study. SIGSOFT Softw. Eng. Notes 38(4), 1–7 (2013)

    Article  Google Scholar 

  7. Galletly, J.: Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms. Kybernetes 27(8), 979–980 (1998)

    Article  Google Scholar 

  8. Storn, R., Price, K.: Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  9. Patti, F.D., Fanelli, D., Piazza, F.: Optimal search strategies on complex multilinked networks. Sci. Rep. 5(1), 1–6 (2015)

    Article  Google Scholar 

  10. Lynn, N., Ali, M.Z., Suganthan, P.N.: Population topologies for particle swarm optimization and differential evolution. Swarm Evol. Comput. 39, 24–35 (2018)

    Article  Google Scholar 

  11. Hui, S., Suganthan, P.N.: Ensemble and arithmetic recombination-based speciation differential evolution for multimodal optimization. IEEE Trans. Cybern. 46(1), 64–74 (2016)

    Article  Google Scholar 

  12. Brest, J., Greiner, S., Boskovic, B., Mernik, M., Zumer, V.: Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans. Evol. Comput. 10(6), 646–657 (2006)

    Article  Google Scholar 

  13. Qin, A.K., Huang, V.L., Suganthan, P.N.: Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans. Evol. Comput. 13(2), 398–417 (2009)

    Article  Google Scholar 

  14. Zhang, J., Sanderson, A.C.: JADE: adaptive differential evolution with optional external archive. IEEE Trans. Evol. Comput. 13(5), 945–958 (2009)

    Article  Google Scholar 

  15. Guo, S.-M., Tsai, J.S.-H., Yang, C.-C., Hsu, P.-H.: A self-optimization approach for l-shade incorporated with eigenvector-based crossover and successful-parent selecting framework on CEC 2015 benchmark set. In: 2015 IEEE Congress on Evolutionary Computation (CEC), pp. 1003–1010 (2015)

    Google Scholar 

  16. Das, S., Mullick, S.S., Suganthan, P.N.: Recent advances in differential evolution - an updated survey. Swarm Evol. Comput. 27, 1–30 (2016)

    Article  Google Scholar 

  17. Brest, J., Maučec, M.S., Bošković, B.: The 100-digit challenge: algorithm JDE100. In: 2019 IEEE Congress on Evolutionary Computation (CEC), pp. 19–26 (2019)

    Google Scholar 

  18. Viktorin, A., Senkerik, R., Pluhacek, M., Kadavy, T., Zamuda, A.: Dish algorithm solving the CEC 2019 100-digit challenge. In: 2019 IEEE Congress on Evolutionary Computation (CEC), pp. 1–6 (2019)

    Google Scholar 

  19. Kumar, A., Misra, R.K., Singh, D., Das, S.: Testing a multi-operator based differential evolution algorithm on the 100-digit challenge for single objective numerical optimization. In: 2019 IEEE Congress on Evolutionary Computation (CEC), pp. 34–40 (2019)

    Google Scholar 

  20. Mavrovouniotis, M., Li, C., Yang, S.: A survey of swarm intelligence for dynamic optimization: Algorithms and applications. Swarm Evol. Comput. 33, 1–17 (2017)

    Article  Google Scholar 

  21. Morozov, A.Y., Kuzenkov, O.A., Sandhu, S.K.: Global optimisation in hilbert spaces using the survival of the ttest algorithm. Commun. Nonlinear Sci. Numer. Simul. 103, 106007 (2021)

    Google Scholar 

  22. Gorban, A.N.: Selection theorem for systems with inheritance. Math. Model. Nat. Phenom. 2(4), 1–45 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  23. Kuzenkov, O.A., Ryabova, E.A.: Limit possibilities of solution of a hereditary control system. Differ. Eqn. 51(4), 523–532 (2015). https://doi.org/10.1134/S0012266115040096

    Article  MathSciNet  MATH  Google Scholar 

  24. Kuzenkov, O.A., Novozhenin, A.V.: Optimal control of measure dynamics. Commun. Nonlinear Sci. Numer. Simul. 21(1), 159–171 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  25. Kuzenkov, O., Morozov, A.: Towards the construction of a mathematically rigorous framework for the modelling of evolutionary fitness. Bull. Math. Biol. 81(11), 4675–4700 (2019). https://doi.org/10.1007/s11538-019-00602-3

    Article  MathSciNet  MATH  Google Scholar 

  26. Da Silva Santos, C.H., Gonçalves, M.S., Hernández-Figueroa, H.E.: Designing novel photonic devices by bio-inspired computing. IEEE Photonics Technol. Lett. 22(15), 1177–1179 (2010)

    Article  Google Scholar 

  27. Da Silva Santos, C.H.: Parallel and bio-inspired computing applied to analyze microwave and photonic metamaterial strucutures (2010)

    Google Scholar 

  28. Kaelo, P., Ali, M.M.: Some variants of the controlled random search algorithm for global optimization. J. Optim. Theory Appl. 130(2), 253–264 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  29. Price, W.L.: Global optimization by controlled random search. J. Optim. Theory Appl. 40(3), 333–348 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  30. Price, W.L.: A controlled random search procedure for global optimisation. Comput. J. 20(4), 367–370 (1977)

    Article  MATH  Google Scholar 

  31. Rinnooy Kan, A.H.G., Timmer, G.T.: Stochastic global optimization methods part 1: clustering methods. Math. Programm. 39(1), 27–56 (1987)

    Google Scholar 

  32. Rinnooy Kan, A.H.G., Timmer, G.T.: Stochastic global optimization methods part 2: multi level methods. Math. Program. 39(1), 57–78 (1987)

    Google Scholar 

  33. Kuzenkov, O.A., Grishagin, V.A.: Global optimization in hilbert space. AIP Conf. Proc. 1738(1), 400007 (2016)

    Google Scholar 

  34. Irkhina, A.L., Kuzenkov, O.: Identification of the distribution of deformations in a rod as a problem of optimal control. J. Comput. Syst. Sci. Int. 44(5), 689–94 (2005)

    MATH  Google Scholar 

  35. Sergeyev, Y.D., Kvasov, D.E., Mukhametzhanov, M.S.: On the efficiency of natureinspired metaheuristics in expensive global optimization with limited budget. Sci. Rep. 8(1), 453 (2018)

    Article  Google Scholar 

  36. Rönkkönen, J., Li, X., Kyrki, V., Lampinen, J.: A framework for generating tunable test functions for multimodal optimization. Soft Computing 15, 1689–1706 (2011)

    Article  Google Scholar 

  37. 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 (2011)

    Google Scholar 

  38. Sergeyev, Y.D., Kvasov, D.E., Mukhametzhanov, M.S.: A generator of multiextremal test classes with known solutions for black-box constrained global optimization. IEEE Trans. Evol. Comput. (2021)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lobachevsky State University, Gagarin Av. 23, Nizhny Novgorod, 603950, Russia

    Oleg Kuzenkov & Dmitriy Perov

Authors
  1. Oleg Kuzenkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dmitriy Perov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dmitriy Perov .

Editor information

Editors and Affiliations

  1. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    Dmitry Balandin

  2. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    Konstantin Barkalov

  3. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    Iosif Meyerov

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kuzenkov, O., Perov, D. (2022). Global Optimization Method Based on the Survival of the Fittest Algorithm. In: Balandin, D., Barkalov, K., Meyerov, I. (eds) Mathematical Modeling and Supercomputer Technologies. MMST 2022. Communications in Computer and Information Science, vol 1750. Springer, Cham. https://doi.org/10.1007/978-3-031-24145-1_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-24145-1_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-24144-4

  • Online ISBN: 978-3-031-24145-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation