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Continuous global optimization through the generation of parametric curves

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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. The objective function is only continuous, non-smooth and non-Lipschitzian, defined on a rectangle of Rn. This approach is based on the generation, in the feasible set, of a family of parametrized curves satisfying certain properties combined with the one-dimensional Evtushenko algorithm. To accelerate the corresponding mixed algorithm, we have incorporated in a variant a Pattern Search-type deterministic local optimization method and in another variant a new stochastic local optimization method. Both variants have been applied to several typical test problems. A comparison with some well known methods is highlighted through numerical experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:282:y:2016:i:c:p:65-83
    DOI: 10.1016/j.amc.2016.01.067
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    References listed on IDEAS

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    1. Mishra, Sudhanshu, 2006. "Some new test functions for global optimization and performance of repulsive particle swarm method," MPRA Paper 2718, University Library of Munich, Germany.
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    Cited by:

    1. Naffeti, Bechir & Ammar, Hamadi, 2021. "A new trisection method for solving Lipschitz bi-objective optimization problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1186-1205.
    2. 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.

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