IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v89y2024i3d10.1007_s10898-023-01358-w.html
   My bibliography  Save this article

A criterion-space branch-reduction-bound algorithm for solving generalized multiplicative problems

Author

Listed:
  • Hongwei Jiao

    (Henan Institute of Science and Technology)

  • Binbin Li

    (Henan Institute of Science and Technology)

  • Wenqiang Yang

    (Henan Institute of Science and Technology)

Abstract

In this paper, we investigate a generalized multiplicative problem (GMP) that is known to be NP-hard even with one linear product term. We first introduce some criterion-space variables to obtain an equivalent problem of the GMP. A criterion-space branch-reduction-bound algorithm is then designed, which integrates some basic operations such as the two-level linear relaxation technique, rectangle branching rule and criterion-space region reduction technologies. The global convergence of the presented algorithm is proved by means of the subsequent solutions of a series of linear relaxation problems, and its maximum number of iterations is estimated on the basis of exhaustiveness of branching rule. Finally, numerical results demonstrate the presented algorithm can efficiently find the global optimum solutions for some test instances with the robustness.

Suggested Citation

  • Hongwei Jiao & Binbin Li & Wenqiang Yang, 2024. "A criterion-space branch-reduction-bound algorithm for solving generalized multiplicative problems," Journal of Global Optimization, Springer, vol. 89(3), pages 597-632, July.
  • Handle: RePEc:spr:jglopt:v:89:y:2024:i:3:d:10.1007_s10898-023-01358-w
    DOI: 10.1007/s10898-023-01358-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-023-01358-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10898-023-01358-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jiao, Hong-Wei & Liu, San-Yang, 2015. "A practicable branch and bound algorithm for sum of linear ratios problem," European Journal of Operational Research, Elsevier, vol. 243(3), pages 723-730.
    2. Abouei Ardakan, Mostafa & Zeinal Hamadani, Ali, 2014. "Reliability optimization of series–parallel systems with mixed redundancy strategy in subsystems," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 132-139.
    3. Lizhen Shao & Matthias Ehrgott, 2014. "An objective space cut and bound algorithm for convex multiplicative programmes," Journal of Global Optimization, Springer, vol. 58(4), pages 711-728, April.
    4. Takahito Kuno & Toshiyuki Masaki, 2013. "A practical but rigorous approach to sum-of-ratios optimization in geometric applications," Computational Optimization and Applications, Springer, vol. 54(1), pages 93-109, January.
    5. Benson, Harold P., 2007. "A simplicial branch and bound duality-bounds algorithm for the linear sum-of-ratios problem," European Journal of Operational Research, Elsevier, vol. 182(2), pages 597-611, October.
    6. H. P. Benson, 2005. "Decomposition Branch-and-Bound Based Algorithm for Linear Programs with Additional Multiplicative Constraints," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 41-61, July.
    7. H. P. Benson & G. M. Boger, 2000. "Outcome-Space Cutting-Plane Algorithm for Linear Multiplicative Programming," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 301-322, February.
    8. Jiao, Hongwei & Ma, Junqiao, 2022. "An efficient algorithm and complexity result for solving the sum of general affine ratios problem," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jiao, Hongwei & Ma, Junqiao, 2022. "An efficient algorithm and complexity result for solving the sum of general affine ratios problem," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Huang, Bingdi & Shen, Peiping, 2024. "An efficient branch and bound reduction algorithm for globally solving linear fractional programming problems," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. Hezhi Luo & Youmin Xu & Huixian Wu & Guoqiang Wang, 2025. "A New branch-and-cut algorithm for linear sum-of-ratios problem based on SLO method and LO relaxation," Computational Optimization and Applications, Springer, vol. 90(1), pages 257-301, January.
    4. Hongwei Jiao & Binbin Li & Youlin Shang, 2024. "An Outer Space Approach to Tackle Generalized Affine Fractional Program Problems," Journal of Optimization Theory and Applications, Springer, vol. 201(1), pages 1-35, April.
    5. Shen, Peiping & Zhu, Zeyi & Chen, Xiao, 2019. "A practicable contraction approach for the sum of the generalized polynomial ratios problem," European Journal of Operational Research, Elsevier, vol. 278(1), pages 36-48.
    6. Gao, YueLin & Zhang, Bo, 2023. "Output-space branch-and-bound reduction algorithm for generalized linear fractional-multiplicative programming problem," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    7. Bo Zhang & Hongyu Wang & Yuelin Gao, 2024. "Output-Space Outer Approximation Branch-and-Bound Algorithm for a Class of Linear Multiplicative Programs," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 997-1026, September.
    8. Bingdi Huang & Peiping Shen, 2025. "An efficient global optimization algorithm for the sum of linear ratios problems based on a novel adjustable branching rule," Computational Optimization and Applications, Springer, vol. 91(3), pages 1339-1371, July.
    9. Bo Zhang & Yuelin Gao & Xia Liu & Xiaoli Huang, 2020. "Output-Space Branch-and-Bound Reduction Algorithm for a Class of Linear Multiplicative Programs," Mathematics, MDPI, vol. 8(3), pages 1-34, March.
    10. João Paulo Costa & Maria João Alves, 2025. "A branch and cut algorithm to optimize a weighted sum-of-ratios in multiobjective mixed-integer fractional programming," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 47(2), pages 667-695, June.
    11. Han, Zhong & Tian, Liting & Cheng, Lin, 2021. "A deducing-based reliability optimization for electrical equipment with constant failure rate components duration their mission profile," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    12. Jiao, Hong-Wei & Liu, San-Yang, 2015. "A practicable branch and bound algorithm for sum of linear ratios problem," European Journal of Operational Research, Elsevier, vol. 243(3), pages 723-730.
    13. Ardakan, Mostafa Abouei & Talkhabi, Sajjad & Juybari, Mohammad N., 2022. "Optimal activation order vs. redundancy strategies in reliability optimization problems," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    14. Abdossaber Peiravi & Mahdi Karbasian & Mostafa Abouei Ardakan, 2018. "K-mixed strategy: A new redundancy strategy for reliability problems," Journal of Risk and Reliability, , vol. 232(1), pages 38-51, February.
    15. Boddiford, Ashley N. & Kaufman, Daniel E. & Skipper, Daphne E. & Uhan, Nelson A., 2023. "Approximating a linear multiplicative objective in watershed management optimization," European Journal of Operational Research, Elsevier, vol. 305(2), pages 547-561.
    16. Chatwattanasiri, Nida & Coit, David W. & Wattanapongsakorn, Naruemon, 2016. "System redundancy optimization with uncertain stress-based component reliability: Minimization of regret," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 73-83.
    17. Lizhen Shao & Matthias Ehrgott, 2014. "An objective space cut and bound algorithm for convex multiplicative programmes," Journal of Global Optimization, Springer, vol. 58(4), pages 711-728, April.
    18. Peiravi, Abdossaber & Nourelfath, Mustapha & Zanjani, Masoumeh Kazemi, 2022. "Universal redundancy strategy for system reliability optimization," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    19. Gholinezhad, Hadi & Zeinal Hamadani, Ali, 2017. "A new model for the redundancy allocation problem with component mixing and mixed redundancy strategy," Reliability Engineering and System Safety, Elsevier, vol. 164(C), pages 66-73.
    20. Kuo, Ching-Chang & Ke, Jau-Chuan, 2016. "Comparative analysis of standby systems with unreliable server and switching failure," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 74-82.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:89:y:2024:i:3:d:10.1007_s10898-023-01358-w. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.