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Operational zones for comparing metaheuristic and deterministic one-dimensional global optimization algorithms

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  • Sergeyev, Yaroslav D.
  • Kvasov, Dmitri E.
  • Mukhametzhanov, Marat S.

Abstract

Univariate continuous global optimization problems are considered in this paper. Several widely used multidimensional metaheuristic global optimization methods–genetic algorithm, differential evolution, particle swarm optimization, artificial bee colony algorithm, and firefly algorithm–are adapted to the univariate case and compared with three Lipschitz global optimization algorithms. For this purpose, it has been introduced a methodology allowing one to compare stochastic methods with deterministic ones by using operational characteristics originally proposed for working with deterministic algorithms only. As a result, a visual comparison of methods having different nature on classes of randomly generated test functions becomes possible. A detailed description of the new methodology for comparing, called “operational zones”, is given and results of wide numerical experiments with five metaheuristics and three Lipschitz algorithms are reported.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:141:y:2017:i:c:p:96-109
    DOI: 10.1016/j.matcom.2016.05.006
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    References listed on IDEAS

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    1. 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.
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    Cited by:

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    7. 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.
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    9. 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.

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