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Metaheuristic vs. deterministic global optimization algorithms: The univariate case

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  • Kvasov, Dmitri E.
  • Mukhametzhanov, Marat S.

Abstract

Many practical problems involve the search for the global extremum in the space of the system parameters. The functions to be optimized are often highly multiextremal, black-box with unknown analytical representations, and hard to evaluate even in the case of one parameter to be adjusted in the presence of non-linear constraints. The interest of both the stochastic (in particular, metaheuristic) and mathematical programming (in particular, deterministic) communities to the comparison of metaheuristic and deterministic classes of methods is well recognized. Although both the communities have a huge number of journal and proceedings papers, a few of them are really dedicated to a systematic comparison of the methods belonging to these two classes. This paper meets the requirement of such a comparison between nature-inspired metaheuristic and deterministic algorithms (more than 125,000 launches of the methods have been performed) and presents an attempt (beneficial to practical fields including engineering design) to bring together two rather disjoint communities of metaheuristic and mathematical programming researchers and applied users.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:318:y:2018:i:c:p:245-259
    DOI: 10.1016/j.amc.2017.05.014
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    References listed on IDEAS

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    1. Konstantin Barkalov & Victor Gergel, 2016. "Parallel global optimization on GPU," Journal of Global Optimization, Springer, vol. 66(1), pages 3-20, September.
    2. Giampaolo Liuzzi & Stefano Lucidi & Veronica Piccialli, 2010. "A partition-based global optimization algorithm," Journal of Global Optimization, Springer, vol. 48(1), pages 113-128, September.
    3. 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.
    4. Luis Rios & Nikolaos Sahinidis, 2013. "Derivative-free optimization: a review of algorithms and comparison of software implementations," Journal of Global Optimization, Springer, vol. 56(3), pages 1247-1293, July.
    5. 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.
    6. 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.
    7. Garg, Harish, 2016. "A hybrid PSO-GA algorithm for constrained optimization problems," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 292-305.
    8. 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.
    9. Anatoly Zhigljavsky & Antanas Žilinskas, 2008. "Stochastic Global Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-74740-8, September.
    10. Yaroslav D. Sergeyev & Dmitri E. Kvasov & Marat S. Mukhametzhanov, 2016. "On the Least-Squares Fitting of Data by Sinusoids," Springer Optimization and Its Applications, in: Panos M. Pardalos & Anatoly Zhigljavsky & Julius Žilinskas (ed.), Advances in Stochastic and Deterministic Global Optimization, pages 209-226, Springer.
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    10. Linas Stripinis & Remigijus Paulavičius, 2023. "Novel Algorithm for Linearly Constrained Derivative Free Global Optimization of Lipschitz Functions," Mathematics, MDPI, vol. 11(13), pages 1-19, June.
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