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A deterministic method for continuous global optimization using a dense curve

Author

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  • Ziadi, Raouf
  • Bencherif-Madani, Abdelatif
  • Ellaia, Rachid

Abstract

In this paper, we develop a new approach for solving a large class of global optimization problems for objective functions which are only continuous on a rectangle of Rn. This method is based on the reducing transformation technique by running in the feasible domain a single parametrized Lissajous curve, which becomes increasingly denser and progressively fills the feasible domain. By means of the one-dimensional Evtushenko algorithm, we realize a mixed method which explores the feasible domain. To speed up the mixed exploration algorithm, we have incorporated a DIRECT local search type algorithm to explore promising regions. This method converges in a finite number of iterations to the global minimum within a prescribed accuracy ε>0. Simulations on some typical test problems with diverse properties and different dimensions indicate that the algorithm is promising and competitive.

Suggested Citation

  • Ziadi, Raouf & Bencherif-Madani, Abdelatif & Ellaia, Rachid, 2020. "A deterministic method for continuous global optimization using a dense curve," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 62-91.
    • Handle: RePEc:eee:matcom:v:178:y:2020:i:c:p:62-91
    DOI: 10.1016/j.matcom.2020.05.029
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    References listed on IDEAS

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    1. Ziadi, Raouf & Bencherif-Madani, Abdelatif & Ellaia, Rachid, 2016. "Continuous global optimization through the generation of parametric curves," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 65-83.
    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. 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.
    4. Ferreiro, Ana M. & García-Rodríguez, José Antonio & Vázquez, Carlos & e Silva, E. Costa & Correia, A., 2019. "Parallel two-phase methods for global optimization on GPU," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 67-90.
    5. 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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