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AIMS Mathematics

2024, Volume 9, Issue 7: 18475-18505. doi: 10.3934/math.2024900
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Research article

A new filled function method based on global search for solving unconstrained optimization problems

  • 1.
    School of Mathematics and Information Sciences, North Minzu University, Yinchuan 750021, China
  • 2.
    Ningxia province cooperative innovation center of scientific computing and intelligent information processing, North Minzu University, Yinchuan 750021, China
  • Received: 09 April 2024 Revised: 22 May 2024 Accepted: 29 May 2024 Published: 03 June 2024

  • MSC : 90C26, 90C30

  • The filled function method is a deterministic algorithm for finding a global minimizer of global optimization problems, and its effectiveness is closely related to the form of the constructed filled function. Currently, the filled functions mainly have three drawbacks in form, namely, parameter adjustment and control (if any), inclusion of exponential or logarithmic functions, and properties that are discontinuous and non-differentiable. In order to overcome these limitations, this paper proposed a parameter-free filled function that does not include exponential or logarithmic functions and is continuous and differentiable. Based on the new filled function, a filled function method for solving unconstrained global optimization problems was designed. The algorithm selected points in the feasible domain that were far from the global minimum point as initial points, and improved the setting of the step size in the stage of minimizing the filled function to enhance the algorithm's global optimization capability. In addition, tests were conducted on 14 benchmark functions and compared with existing filled function algorithms. The numerical experimental results showed that the new algorithm proposed in this paper was feasible and effective.

    Citation: Jia Li, Yuelin Gao, Tiantian Chen, Xiaohua Ma. A new filled function method based on global search for solving unconstrained optimization problems[J]. AIMS Mathematics, 2024, 9(7): 18475-18505. doi: 10.3934/math.2024900

    Related Papers:

  • The filled function method is a deterministic algorithm for finding a global minimizer of global optimization problems, and its effectiveness is closely related to the form of the constructed filled function. Currently, the filled functions mainly have three drawbacks in form, namely, parameter adjustment and control (if any), inclusion of exponential or logarithmic functions, and properties that are discontinuous and non-differentiable. In order to overcome these limitations, this paper proposed a parameter-free filled function that does not include exponential or logarithmic functions and is continuous and differentiable. Based on the new filled function, a filled function method for solving unconstrained global optimization problems was designed. The algorithm selected points in the feasible domain that were far from the global minimum point as initial points, and improved the setting of the step size in the stage of minimizing the filled function to enhance the algorithm's global optimization capability. In addition, tests were conducted on 14 benchmark functions and compared with existing filled function algorithms. The numerical experimental results showed that the new algorithm proposed in this paper was feasible and effective.


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