Search Advanced

AIMS Mathematics

2024, Volume 9, Issue 7: 18475-18505. doi: 10.3934/math.2024900
Previous Article Next Article
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.


    加载中


    [1] R. Soto, B. Crawford, R. Olivares, J. Barraza, I. Figueroa, F. Johnson, et al., Solving the non-unicost set covering problem by using cuckoo search and black hole optimization, Nat. Comput., 16 (2017), 213–229. http://doi.org/10.1007/s11047-016-9609-7 doi: 10.1007/s11047-016-9609-7
    [2] X. Liu, Y. Wang, M. Zhou, Dimensional learning strategy-based grey wolf optimizer for solving the global optimization problem, Comput. Intel. Neurosci., 2022 (2022). http://doi.org/10.1155/2022/3603607
    [3] J. S. Pan, A. Q. Tian, V. Snášel, L. Kong, S. C. Chu, Maximum power point tracking and parameter estimation for multiple-photovoltaic arrays based on enhanced pigeon-inspired optimization with taguchi method, Energy, 251 (2022), 123863. https://doi.org/10.1016/j.energy.2022.123863 doi: 10.1016/j.energy.2022.123863
    [4] A. Q. Tian, X. Y. Wang, H. Xu, J. S. Pan, V. Snášel, H. X. Lv, Multi-objective optimization model for railway heavy-haul traffic: addressing carbon emissions reduction and transport efficiency improvement, Energy, 294 (2024), 130927. https://doi.org/10.1016/j.energy.2024.130927 doi: 10.1016/j.energy.2024.130927
    [5] İ. ÇetınbaŞ, B. Tamyürek, M. Demırtaş, The hybrid harris hawks optimizer-arithmetic optimization algorithm: a new hybrid algorithm for sizing optimization and design of microgrids, IEEE Access, 10 (2022), 19254–19283. http://doi.org/10.1109/ACCESS.2022.3151119 doi: 10.1109/ACCESS.2022.3151119
    [6] A. Q. Tian, F. F. Liu, H. X. Lv, Snow geese algorithm: a novel migration-inspired meta-heuristic algorithm for constrained engineering optimization problems, Appl. Math. Model., 126 (2024), 327–347. https://doi.org/10.1016/j.apm.2023.10.045 doi: 10.1016/j.apm.2023.10.045
    [7] G. Renpu, A filled function method for finding a global minimizer of a function of several variables, Math. Program., 46 (1990), 191–204. http://doi.org/10.1007/bf01585737 doi: 10.1007/bf01585737
    [8] R. P. Ge, Y. F. Qin, A class of filled functions for finding global minimizers of a function of several variables, J. Optim. Theory Appl., 54 (1987), 241–252. http://doi.org/10.1007/bf00939433 doi: 10.1007/bf00939433
    [9] H. S. Ryoo, N. V. Sahinidis, A branch-and-reduce approach to global optimization, J. Global Optim., 8 (1996), 107–138. http://doi.org/10.1007/bf00138689 doi: 10.1007/bf00138689
    [10] A. V. Levy, A. Montalvo, The tunneling algorithm for the global minimization of functions, SIAM J. Sci. Stat. Comput., 6 (1985), 15–29. http://doi.org/10.1137/0906002 doi: 10.1137/0906002
    [11] L. S. Zhang, C. K. Ng, D. Li, W. W. Tian, A new filled function method for global optimization, J. Global Optim., 28 (2004), 17–43. http://doi.org/10.1023/b:jogo.0000006653.60256.f6 doi: 10.1023/b:jogo.0000006653.60256.f6
    [12] Y. Yang, Y. Shang, A new filled function method for unconstrained global optimization. Appl. Math. Comput., 173 (2006), 501–512. http://doi.org/10.1016/j.amc.2005.04.046
    [13] C. Wang, Y. Yang, J. Li, A new filled function method for unconstrained global optimization, J. Comput. Appl. Math., 225 (2009), 68–79. http://doi.org/10.1016/j.cam.2008.07.001 doi: 10.1016/j.cam.2008.07.001
    [14] F. Wei, Y. Wang, H. Lin, A new filled function method with two parameters for global optimization, J. Optim. Theory Appl., 163 (2014), 510–527. http://doi.org/10.1007/s10957-013-0515-1 doi: 10.1007/s10957-013-0515-1
    [15] Y. Gao, Y. Yang, M. You, A new filled function method for global optimization, Appl. Math. Comput., 268 (2015), 685–695. http://doi.org/10.1016/j.amc.2015.06.090 doi: 10.1016/j.amc.2015.06.090
    [16] T. M. El-Gindy, M. S. Salim, A. I. Ahmed, A new filled function method applied to unconstrained global optimization, Appl. Math. Comput., 273 (2016), 1246–1256. http://doi.org/10.1016/j.amc.2015.08.091 doi: 10.1016/j.amc.2015.08.091
    [17] X. Liu, Finding global minima with a computable filled function, J. Global Optim., 19 (2001), 151–161. http://doi.org/10.1023/a:1008330632677 doi: 10.1023/a:1008330632677
    [18] X. Liu, A class of generalized filled functions with improved computability, J. Comput. Appl. Math., 137 (2001), 61–69. http://doi.org/10.1016/S0377-0427(00)00697-X doi: 10.1016/S0377-0427(00)00697-X
    [19] H. Lin, Y. Gao, Y. Wang, A continuously differentiable filled function method for global optimization, Numer. Algor., 66 (2014), 511–523. http://doi.org/10.1007/s11075-013-9746-3 doi: 10.1007/s11075-013-9746-3
    [20] X. Wu, Y. Wang, N. Fan, A new filled function method based on adaptive search direction and valley widening for global optimization, Appl. Intell., 51 (2021), 6234–6254. http://doi.org/10.1007/s10489-020-02179-0 doi: 10.1007/s10489-020-02179-0
    [21] A. I. Ahmed, A new parameter free filled function for solving unconstrained global optimization problems, Int. J. Comput. Math., 98 (2021), 106–119. http://doi.org/10.1080/00207160.2020.1731484 doi: 10.1080/00207160.2020.1731484
    [22] S. Ma, Y. Yang, H. Liu, A parameter free filled function for unconstrained global optimization, Appl. Math. Comput., 215 (2010), 3610–3619. https://doi.org/10.1016/j.amc.2009.10.057 doi: 10.1016/j.amc.2009.10.057
    [23] H. Liu, Y. Wang, S. Guan, X. Liu, A new filled function method for unconstrained global optimization, Int. J. Comput. Math., 94 (2017), 2283–2296. http://doi.org/10.1080/00207160.2017.1283021 doi: 10.1080/00207160.2017.1283021
    [24] R. Pandiya, W. Widodo, Salmah, I. Endrayanto, Non parameter-filled function for global optimization, Appl. Math. Comput., 391 (2021), 125642. https://doi.org/10.1016/j.amc.2020.125642 doi: 10.1016/j.amc.2020.125642
    [25] R. Pandiya, S. Salmah, W. Widodo, I. Endrayanto, Finding global minima with an inflection point-based filled function algorithm, Numer. Algor., 92 (2023), 1403–1424. https://doi.org/10.1007/s11075-022-01346-3 doi: 10.1007/s11075-022-01346-3
    [26] A. Hedar, Test functions for unconstrained global optimization, 2013.
    [27] W. X. Zhu, Dynamic globally concavized filled function method for continuous global optimization, J. Optim. Theory Appl., 139 (2008), 635–648. https://doi.org/10.1007/s10957-008-9405-3 doi: 10.1007/s10957-008-9405-3
  • Reader Comments
  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(542) PDF downloads(29) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(10)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog