SpringerLink
Log in

A New Class of Filled Functions with Two Parameters for Solving Unconstrained Global Optimization Problems

  • Published:
Journal of the Operations Research Society of China Aims and scope Submit manuscript

Abstract

A new class of filled functions for esca** the current local minimizer of unconstrained global optimization is proposed. This kind of filled functions is continuously differentiable. And it has no exponential terms and logarithmic terms, which reduce the possibility of computation overflows. Theoretical properties of the proposed filled functions are studied, including discussing the specific conditions that the proposed functions must meet to qualify as a filled function. Then, a new solution algorithm is developed according to the theoretical analysis. Six benchmark problems are tested, and the performance of the new algorithm is compared with two filled function methods. The numerical results prove that the new algorithm is effective and reliable.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Algorithm 1

Similar content being viewed by others

References

  1. An, M.S., Zhang, L.S., Chen, M.L.: A parameter-free filled function for unconstrained global optimization. J. Shanghai Univ. 8, 117–123 (2004)

    Article  MathSciNet  Google Scholar 

  2. Ahmed, A.I.: A new parameter free filled function for solving unconstrained global optimization problems. Int. J. Comput. Math. 98(1), 106–119 (2020)

    Article  MathSciNet  Google Scholar 

  3. Banks, A., Vincent, J., Anyakoha, C.: A review of particle swarm optimization. Part I: background and development. Natural Comput. 6, 74–84 (2007)

    Article  Google Scholar 

  4. Bertolazzi, P., Liuzzi, G., Guerra, C.: A global optimization algorithm for protein surface alignment. In: IEEE International Conference on Bioinformatics and Biomedicine Workshop, pp. 93–100 (2009)

  5. Chew, S.H., Zhang, Q.: Integral Global Optimization. Lecture Notes in Economics and Mathematics Systems. Springer, Berlin (1988)

    Book  Google Scholar 

  6. Cetin, B.C., Barhen, J., Burdick, J.W.: Terminal repeller unconstrained subenergy tunneling (TRUST) for fast global optimization. J. Optim. Theory Appl. 77, 97–125 (1993)

    Article  MathSciNet  Google Scholar 

  7. Dorigo, M., Stutzle, T.: Ant Colony Optimization. MIT, Cambridge (2004)

    Book  Google Scholar 

  8. Felici, G., Tripathi, K.P., Evangelista, D., et al.: A mixed integer programming-based global optimization framework for analyzing gene expression data. J. Global Optim. 3, 727–744 (2017)

    Article  MathSciNet  Google Scholar 

  9. Ferrari, R., Froio, D., Rizzi, E., et al.: Model updating of a historic concrete bridge by sensitivity and global optimization based Latin Hypercube Sampling. Eng. Struct. 179, 139–160 (2019)

    Article  Google Scholar 

  10. Gomez, S., Levy, A.V.: The Tunnelling Method for Solving the Constrained Global Optimization Problem with Several Non-connected Feasible Regions. Numerical Analysis. Springer, Berlin (1982)

    Google Scholar 

  11. Ge, R.P.: The theory of filled function methods for finding global minimizers of nonlinearly constrained minimization problems. J. Comput. Math. 5, 1–9 (1987)

    MathSciNet  Google Scholar 

  12. Ge, R.P., Qin, Y.F.: A class of filled functions for finding global minimizers of a function of several variables. J. Optim. Theory Appl. 54, 241–252 (1987)

    Article  MathSciNet  Google Scholar 

  13. Ge, R.P.: A filled function method for finding a global minimizer of a function of several variables. Math. Program. 46, 191–204 (1990)

    Article  MathSciNet  Google Scholar 

  14. Ge, R.P.: Finding more and more solutions of a system of nonlinear equations. Appl. Math. Comput. 36, 15–30 (1990)

    MathSciNet  Google Scholar 

  15. Ge, R.P., Qin, Y.F.: The globally convexized filled functions for global optimization. Appl. Math. Comput. 35, 31–158 (1990)

    MathSciNet  Google Scholar 

  16. Horst, R., Pardalos, P.M., Thoai, N.V.: Introduction to Global Optimization. Kluwer Academic Publishers, Seconded (2000)

    Book  Google Scholar 

  17. Jiang, Y., Huang, C.C., Wu, X.: An improved particle swarm optimization algorithm. Appl. Math. Comput. 19, 3231–239 (2007)

    Google Scholar 

  18. Kong, M.: On the filled function method for nonsmooth program. J. Syst. Sci. Math. 20, 149–154 (2004)

    Google Scholar 

  19. Kanazaki, M., Matsuno, T., Maeda, K., et al.: Efficient global optimization applied to wind tunnel evaluation-based optimization for improvement of flow control by plasma actuators. Eng. Optim. 47, 1226–1242 (2015)

    Article  Google Scholar 

  20. Levy, A.V., Montalvo, A.: The tunneling algorithm for the global minimization of functions. SIAM J. Sci. Stat. Comput. 6, 15–29 (1985)

    Article  MathSciNet  Google Scholar 

  21. Lundy, M., Mess, A.: Convergence of an annealing algorithm. Math. Program. 34, 11–24 (1986)

    Article  MathSciNet  Google Scholar 

  22. Liu, X.: Finding global minima with a computable filled function. J. Global Optim. 19, 151–161 (2001)

    Article  MathSciNet  Google Scholar 

  23. Liu, X.: A class of generalized filled functions with improved computability. J. Comput. Appl. Math. 137, 61–69 (2001)

    Article  MathSciNet  Google Scholar 

  24. Liu, X.: A computable filled function used for global minimization. Appl. Math. Comput. 126, 271–278 (2002)

    MathSciNet  Google Scholar 

  25. Liu, X., Xu, W.: A new filled function applied to global optimization. Comput. Oper. Res. 31, 61–80 (2004)

    Article  MathSciNet  Google Scholar 

  26. Lin, H.W., Wang, Y.P., Fan, L.: A filled function method with one parameter for unconstrained global optimization. Appl. Math. Comput. 218, 3776–3785 (2011)

    MathSciNet  Google Scholar 

  27. Liu, H.Y., Wang, Y.P., Guan, S.W., Liu, X.Y.: A new filled function method for unconstrained global optimization. Int. J. Comput. Math. 94, 2283–2296 (2017)

    Article  MathSciNet  Google Scholar 

  28. Ma, S., Shang, C., Wang, C.M., et al.: Thermodynamic rules for zeolite formation from machine learning based global optimization. Chem. Sci. 11, 10113–10118 (2020)

    Article  Google Scholar 

  29. Pandiya, R., et al.: A novel parameter-free filled function applied to global optimization. Eng. Lett. 29, 191–200 (2021)

    Google Scholar 

  30. Pandiya, R., et al.: Non parameter-filled function for global optimzation. Appl. Math. Comput. 391, 1–13 (2021)

    MathSciNet  Google Scholar 

  31. Qing, W., Liu, S.Y., Zhang, L.Y., Liu, C.C.: A modified filled function method for a global minimizer of a nonsmooth programming problem. Math. Appl. 17, 36–40 (2004)

    Google Scholar 

  32. Ribeiro, I.M., Simões, M.L.O.: The fully actuated traffic control problem solved by global optimization and complementarity. Eng. Optim. 48, 199–212 (2016)

    Article  MathSciNet  Google Scholar 

  33. Shang, Y.L., Pu, D.G., Jiang, A.P.: Finding global minimizer with one parameter filled function on unconstrained global optimization. Appl. Math. Comput. 191, 176–182 (2007)

    MathSciNet  Google Scholar 

  34. Salim, S.M., EI-Gindy, M.T., Ahmed, I.A.: A new filled function method applied to unconstrained global optimization. Appl. Math. Comput. 73, 1246–1256 (2016)

    MathSciNet  Google Scholar 

  35. Whitley, D.: A genetic algorithm tutorial. Stat. Comput. 4, 65–85 (1994)

    Article  Google Scholar 

  36. Wang, W.X., Shang, Y.L., Zhang, L.S.: A filled function method with one parameter for box constrained global optimization. Appl. Math. Comput. 194, 54–66 (2007)

    MathSciNet  Google Scholar 

  37. Wang, C.J., Yang, Y.J., Li, J.: A new filled function method for unconstrained global optimization. J. Comput. Appl. Math. 225, 68–79 (2009)

    Article  MathSciNet  Google Scholar 

  38. Wang, S., **ng, J., Jiang, Z., et al.: A decentralized, model-free, global optimization method for energy saving in heating, ventilation and air conditioning systems. Build. Serv. Eng. Res. Technol. 41, 414–428 (2020)

    Article  Google Scholar 

  39. Xu, Z., Huang, H., Pardalos, P., Xu, C.: Filled functions for unconstrained global optimization. J. Global Optim. 20, 49–65 (2001)

    Article  MathSciNet  Google Scholar 

  40. Yao, Y.: Dynamic tunneling algorithm for global optimization. IEEE Trans. Syst. Man Cybern. 5, 1222–1230 (1989)

    Article  MathSciNet  Google Scholar 

  41. Yuan, Y.: On a subproblem of trust region algorithms for constrained optimization. Math. Program. 47, 53–63 (1990)

    Article  MathSciNet  Google Scholar 

  42. Yang, Y.J., Shang, Y.L.: A new filled function method for unconstrained global optimization. Appl. Math. Comput. 173, 501–512 (2006)

    MathSciNet  Google Scholar 

  43. Yan, Q., Chen, W., Yang, X.M.: A novel one-parameter filled function method with an application to pathological analysis. Optim. Lett. 18(3), 803–824 (2023)

    Article  MathSciNet  Google Scholar 

  44. Zhu, W.X.: A class of filled functions irrelevant to the number of local minimizers for global optimization. J. Syst. Sci. Math. 22, 406–413 (2002)

    MathSciNet  Google Scholar 

  45. Zhang, Y., Xu, Y.T.: A one parameter filled function method applied to nonsmooth constrained global optimization. Comput. Math. Appl. 58, 1230–1238 (2009)

    Article  MathSciNet  Google Scholar 

  46. Zhang, Y., Zhang, L.S., Xu, Y.T.: New filled functions for nonsmooth global optimization. Appl. Math. Model. 33, 3114–3129 (2009)

    Article  MathSciNet  Google Scholar 

  47. Zhang, Y.: Photocatalytic activity of \(\text{ MoS}_2\) with water monolayers: global optimization. J. Chem. Phys. 18, 184703–184709 (2022)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Sciences, Shanghai University, Shanghai, 200444, China

    Qiao Chen

  2. Editing and Publishing Center, Chongqing Normal University, Chongqing, 401331, China

    Qiao Chen

  3. National Center for Applied Mathematics of Chongqing, Chongqing Normal University, Chongqing, 401331, China

    **n-Min Yang

  4. College of Science, Chongqing University of Technology, Chongqing, 400054, China

    Qian Yan

Authors
  1. Qiao Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. **n-Min Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qian Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Q. Chen has contributed to analysis and writing and revision. X-M. Yang has contributed to proposing the idea and method and revision of the manuscript. Q. Yan has contributed to analysis and revision.

Corresponding author

Correspondence to **n-Min Yang.

Ethics declarations

Conflict of interest

X.-M. Yang is an editorial board member for Journal of the Operations Research Society of China and he was not involved in the editorial review or the decision to publish this article. All authors declare that there are no competing interests.

Additional information

This work was supported by the Major Program of the National Natural Science Foundation of China (Nos. 11991020, 11991024) and by the National Natural Science Foundation of China (No. 12271071).

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, Q., Yang, XM. & Yan, Q. A New Class of Filled Functions with Two Parameters for Solving Unconstrained Global Optimization Problems. J. Oper. Res. Soc. China (2024). https://doi.org/10.1007/s40305-024-00548-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40305-024-00548-x

Keywords

Mathematics Subject Classification

Search

Navigation