IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v171y2016i1d10.1007_s10957-016-0947-5.html
   My bibliography  Save this article

Derivative-Free Local Tuning and Local Improvement Techniques Embedded in the Univariate Global Optimization

Author

Listed:
  • Yaroslav D. Sergeyev

    (Università della Calabria
    Lobachevsky State University of Nizhni Novgorod)

  • Marat S. Mukhametzhanov

    (Università della Calabria
    Lobachevsky State University of Nizhni Novgorod)

  • Dmitri E. Kvasov

    (Università della Calabria
    Lobachevsky State University of Nizhni Novgorod)

  • Daniela Lera

    (Università di Cagliari)

Abstract

Geometric and information frameworks for constructing global optimization algorithms are considered, and several new ideas to speed up the search are proposed. The accelerated global optimization methods automatically realize a local behavior in the promising subregions without the necessity to stop the global optimization procedure. Moreover, all the trials executed during the local phases are used also in the course of the global ones. The resulting geometric and information global optimization methods have a similar structure, and a smart mixture of new and traditional computational steps leads to 22 different global optimization algorithms. All of them are studied and numerically compared on three test sets including 120 benchmark functions and 4 applied problems.

Suggested Citation

  • Yaroslav D. Sergeyev & Marat S. Mukhametzhanov & Dmitri E. Kvasov & Daniela Lera, 2016. "Derivative-Free Local Tuning and Local Improvement Techniques Embedded in the Univariate Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 186-208, October.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:1:d:10.1007_s10957-016-0947-5
    DOI: 10.1007/s10957-016-0947-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-016-0947-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-016-0947-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hamacher, Kay, 2005. "On stochastic global optimization of one-dimensional functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 547-557.
    2. Jonathan Gillard & Anatoly Zhigljavsky, 2013. "Optimization challenges in the structured low rank approximation problem," Journal of Global Optimization, Springer, vol. 57(3), pages 733-751, November.
    3. Anatoly Zhigljavsky & Antanas Žilinskas, 2008. "Stochastic Global Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-74740-8, December.
    4. Antanas Žilinskas, 2010. "On similarities between two models of global optimization: statistical models and radial basis functions," Journal of Global Optimization, Springer, vol. 48(1), pages 173-182, September.
    5. Daniela Lera & Yaroslav Sergeyev, 2010. "An information global minimization algorithm using the local improvement technique," Journal of Global Optimization, Springer, vol. 48(1), pages 99-112, September.
    6. Remigijus Paulavičius & Yaroslav Sergeyev & Dmitri Kvasov & Julius Žilinskas, 2014. "Globally-biased Disimpl algorithm for expensive global optimization," Journal of Global Optimization, Springer, vol. 59(2), pages 545-567, July.
    7. James M. Calvin & Yvonne Chen & Antanas Žilinskas, 2012. "An Adaptive Univariate Global Optimization Algorithm and Its Convergence Rate for Twice Continuously Differentiable Functions," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 628-636, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. R. Cavoretto & A. Rossi & M. S. Mukhametzhanov & Ya. D. Sergeyev, 2021. "On the search of the shape parameter in radial basis functions using univariate global optimization methods," Journal of Global Optimization, Springer, vol. 79(2), pages 305-327, February.
    2. Grishagin, Vladimir & Israfilov, Ruslan & Sergeyev, Yaroslav, 2018. "Convergence conditions and numerical comparison of global optimization methods based on dimensionality reduction schemes," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 270-280.
    3. Albertas Gimbutas & Antanas Žilinskas, 2018. "An algorithm of simplicial Lipschitz optimization with the bi-criteria selection of simplices for the bi-section," Journal of Global Optimization, Springer, vol. 71(1), pages 115-127, May.
    4. Anis Fradi & Chafik Samir & Ines Adouani, 2024. "A New Bayesian Approach to Global Optimization on Parametrized Surfaces in $$\mathbb {R}^{3}$$ R 3," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1077-1100, September.
    5. Sergeyev, Yaroslav D. & Kvasov, Dmitri E. & Mukhametzhanov, Marat S., 2017. "Operational zones for comparing metaheuristic and deterministic one-dimensional global optimization algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 96-109.
    6. Falcone, Alberto & Garro, Alfredo & Mukhametzhanov, Marat S. & Sergeyev, Yaroslav D., 2021. "A Simulink-based software solution using the Infinity Computer methodology for higher order differentiation," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    7. Renato Bruni & Fabio Celani, 2019. "Combining Global and Local Strategies to Optimize Parameters in Magnetic Spacecraft Control via Attitude Feedback," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 997-1014, June.
    8. Kvasov, Dmitri E. & Mukhametzhanov, Marat S., 2018. "Metaheuristic vs. deterministic global optimization algorithms: The univariate case," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 245-259.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sergeyev, Yaroslav D. & Kvasov, Dmitri E. & Mukhametzhanov, Marat S., 2017. "Operational zones for comparing metaheuristic and deterministic one-dimensional global optimization algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 96-109.
    2. Daniela Lera & Yaroslav D. Sergeyev, 2018. "GOSH: derivative-free global optimization using multi-dimensional space-filling curves," Journal of Global Optimization, Springer, vol. 71(1), pages 193-211, May.
    3. Kvasov, Dmitri E. & Mukhametzhanov, Marat S., 2018. "Metaheuristic vs. deterministic global optimization algorithms: The univariate case," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 245-259.
    4. Lera, Daniela & Posypkin, Mikhail & Sergeyev, Yaroslav D., 2021. "Space-filling curves for numerical approximation and visualization of solutions to systems of nonlinear inequalities with applications in robotics," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    5. Albertas Gimbutas & Antanas Žilinskas, 2018. "An algorithm of simplicial Lipschitz optimization with the bi-criteria selection of simplices for the bi-section," Journal of Global Optimization, Springer, vol. 71(1), pages 115-127, May.
    6. Grishagin, Vladimir & Israfilov, Ruslan & Sergeyev, Yaroslav, 2018. "Convergence conditions and numerical comparison of global optimization methods based on dimensionality reduction schemes," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 270-280.
    7. Nazih-Eddine Belkacem & Lakhdar Chiter & Mohammed Louaked, 2024. "A Novel Approach to Enhance DIRECT -Type Algorithms for Hyper-Rectangle Identification," Mathematics, MDPI, vol. 12(2), pages 1-24, January.
    8. Remigijus Paulavičius & Lakhdar Chiter & Julius Žilinskas, 2018. "Global optimization based on bisection of rectangles, function values at diagonals, and a set of Lipschitz constants," Journal of Global Optimization, Springer, vol. 71(1), pages 5-20, May.
    9. James Calvin & Gražina Gimbutienė & William O. Phillips & Antanas Žilinskas, 2018. "On convergence rate of a rectangular partition based global optimization algorithm," Journal of Global Optimization, Springer, vol. 71(1), pages 165-191, May.
    10. R. Cavoretto & A. Rossi & M. S. Mukhametzhanov & Ya. D. Sergeyev, 2021. "On the search of the shape parameter in radial basis functions using univariate global optimization methods," Journal of Global Optimization, Springer, vol. 79(2), pages 305-327, February.
    11. James M. Calvin & Antanas Žilinskas, 2014. "On a Global Optimization Algorithm for Bivariate Smooth Functions," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 528-547, November.
    12. Vasiliy V. Grigoriev & Petr N. Vabishchevich, 2021. "Bayesian Estimation of Adsorption and Desorption Parameters for Pore Scale Transport," Mathematics, MDPI, vol. 9(16), pages 1-16, August.
    13. Hai-Bang Ly & Tien-Thinh Le & Huong-Lan Thi Vu & Van Quan Tran & Lu Minh Le & Binh Thai Pham, 2020. "Computational Hybrid Machine Learning Based Prediction of Shear Capacity for Steel Fiber Reinforced Concrete Beams," Sustainability, MDPI, vol. 12(7), pages 1-34, March.
    14. Rudolf Scitovski, 2017. "A new global optimization method for a symmetric Lipschitz continuous function and the application to searching for a globally optimal partition of a one-dimensional set," Journal of Global Optimization, Springer, vol. 68(4), pages 713-727, August.
    15. Rudolf Scitovski & Kristian Sabo, 2019. "Application of the DIRECT algorithm to searching for an optimal k-partition of the set $$\mathcal {A}\subset \mathbb {R}^n$$ A ⊂ R n and its application to the multiple circle detection problem," Journal of Global Optimization, Springer, vol. 74(1), pages 63-77, May.
    16. M. Rivier & P. M. Congedo, 2019. "Surrogate-assisted Bounding-Box approach for optimization problems with tunable objectives fidelity," Journal of Global Optimization, Springer, vol. 75(4), pages 1079-1109, December.
    17. G. Liuzzi & S. Lucidi & V. Piccialli, 2016. "Exploiting derivative-free local searches in DIRECT-type algorithms for global optimization," Computational Optimization and Applications, Springer, vol. 65(2), pages 449-475, November.
    18. Konstantin Barkalov & Roman Strongin, 2018. "Solving a set of global optimization problems by the parallel technique with uniform convergence," Journal of Global Optimization, Springer, vol. 71(1), pages 21-36, May.
    19. E. F. Campana & M. Diez & G. Liuzzi & S. Lucidi & R. Pellegrini & V. Piccialli & F. Rinaldi & A. Serani, 2018. "A multi-objective DIRECT algorithm for ship hull optimization," Computational Optimization and Applications, Springer, vol. 71(1), pages 53-72, September.
    20. Jonas Mockus & Remigijus Paulavičius & Dainius Rusakevičius & Dmitrij Šešok & Julius Žilinskas, 2017. "Application of Reduced-set Pareto-Lipschitzian Optimization to truss optimization," Journal of Global Optimization, Springer, vol. 67(1), pages 425-450, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:171:y:2016:i:1:d:10.1007_s10957-016-0947-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.