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On stochastic global optimization of one-dimensional functions

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  • Hamacher, Kay

Abstract

We consider the applicability of stochastic global optimization algorithms on test-functions whose domain of definition is a simply-connected and finite interval of real numbers. We argue on the basis of theoretical reflections of statistical physics (namely random-walk) and computer simulations that there is a decisive difference between test-problems in one and multiple dimensions pointing to the necessity to only consider test-functions in higher dimensions. We argue that only test-problems in two or more dimensions provide for the possibility to discriminate the efficiency of stochastic global optimization algorithms with respect to the complexity of the underlying physical system at all.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:354:y:2005:i:c:p:547-557
    DOI: 10.1016/j.physa.2005.02.028
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    Cited by:

    1. 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.
    2. 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.
    3. Hamacher, Kay, 2007. "Energy landscape paving as a perfect optimization approach under detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 307-314.
    4. 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.

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