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Performance of global random search algorithms for large dimensions

Author

Listed:
  • Andrey Pepelyshev

    (Cardiff University
    St.Petersburg State University)

  • Anatoly Zhigljavsky

    (Cardiff University
    Lobachevsky Nizhny Novgorod State University)

  • Antanas Žilinskas

    (Vilnius University)

Abstract

We investigate the rate of convergence of general global random search (GRS) algorithms. We show that if the dimension of the feasible domain is large then it is impossible to give any guarantee that the global minimizer is found by a general GRS algorithm with reasonable accuracy. We then study precision of statistical estimates of the global minimum in the case of large dimensions. We show that these estimates also suffer the curse of dimensionality. Finally, we demonstrate that the use of quasi-random points in place of the random ones does not give any visible advantage in large dimensions.

Suggested Citation

  • Andrey Pepelyshev & Anatoly Zhigljavsky & Antanas Žilinskas, 2018. "Performance of global random search algorithms for large dimensions," Journal of Global Optimization, Springer, vol. 71(1), pages 57-71, May.
    • Handle: RePEc:spr:jglopt:v:71:y:2018:i:1:d:10.1007_s10898-017-0535-8
    DOI: 10.1007/s10898-017-0535-8
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    References listed on IDEAS

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    1. Anatoly Zhigljavsky & Emily Hamilton, 2010. "Stopping rules in k-adaptive global random search algorithms," Journal of Global Optimization, Springer, vol. 48(1), pages 87-97, September.
    2. Anatoly Zhigljavsky & Antanas Žilinskas, 2008. "Stochastic Global Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-74740-8, September.
    3. Dette, Holger & Pepelyshev, Andrey & Zhigljavsky, Anatoly, 2016. "Optimal designs for regression models with autoregressive errors," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 107-115.
    4. L. De Haan & L. Peng, 1998. "Comparison of tail index estimators," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(1), pages 60-70, March.
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    Cited by:

    1. C. J. Price & M. Reale & B. L. Robertson, 2021. "Oscars-ii: an algorithm for bound constrained global optimization," Journal of Global Optimization, Springer, vol. 79(1), pages 39-57, January.
    2. Antanas Žilinskas & Jonathan Gillard & Megan Scammell & Anatoly Zhigljavsky, 2021. "Multistart with early termination of descents," Journal of Global Optimization, Springer, vol. 79(2), pages 447-462, February.
    3. Qiang Yang & Litao Hua & Xudong Gao & Dongdong Xu & Zhenyu Lu & Sang-Woon Jeon & Jun Zhang, 2022. "Stochastic Cognitive Dominance Leading Particle Swarm Optimization for Multimodal Problems," Mathematics, MDPI, vol. 10(5), pages 1-34, February.

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