IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v58y2014i4p711-728.html

An objective space cut and bound algorithm for convex multiplicative programmes

Author

Listed:
  • Lizhen Shao

  • Matthias Ehrgott

Abstract

Multiplicative programming problems are global optimisation problems known to be NP-hard. In this paper we propose an objective space cut and bound algorithm for approximately solving convex multiplicative programming problems. This method is based on an objective space approximation algorithm for convex multi-objective programming problems. We show that this multi-objective optimisation algorithm can be changed into a cut and bound algorithm to solve convex multiplicative programming problems. We use an illustrative example to demonstrate the working of the algorithm. Computational experiments illustrate the superior performance of our algorithm compared to other methods from the literature. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:58:y:2014:i:4:p:711-728
    DOI: 10.1007/s10898-013-0102-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-013-0102-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-013-0102-x?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Arthur M. Geoffrion, 1967. "Solving Bicriterion Mathematical Programs," Operations Research, INFORMS, vol. 15(1), pages 39-54, February.
    2. 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.
    3. Miettinen, Kaisa & Makela, Marko M. & Kaario, Katja, 2006. "Experiments with classification-based scalarizing functions in interactive multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 175(2), pages 931-947, December.
    4. H. P. Benson & G. M. Boger, 1997. "Multiplicative Programming Problems: Analysis and Efficient Point Search Heuristic," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 487-510, August.
    5. Matthias Ehrgott & Lizhen Shao & Anita Schöbel, 2011. "An approximation algorithm for convex multi-objective programming problems," Journal of Global Optimization, Springer, vol. 50(3), pages 397-416, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Vahid Mahmoodian & Iman Dayarian & Payman Ghasemi Saghand & Yu Zhang & Hadi Charkhgard, 2022. "A Criterion Space Branch-and-Cut Algorithm for Mixed Integer Bilinear Maximum Multiplicative Programs," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1453-1470, May.
    3. Hongwei Jiao & Haibing Ma, 2026. "Spatial Algorithm for Mixed Integer Generalized Affine Multiplicative Problems," Journal of Optimization Theory and Applications, Springer, vol. 209(1), pages 1-36, April.
    4. Yaping Deng & Peiping Shen, 2025. "A new branch-and-bound algorithm for generalized affine multiplicative programming," Journal of Global Optimization, Springer, vol. 93(1), pages 87-112, September.

    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. Yaping Deng & Peiping Shen, 2025. "A new branch-and-bound algorithm for generalized affine multiplicative programming," Journal of Global Optimization, Springer, vol. 93(1), pages 87-112, September.
    2. 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.
    3. 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).
    4. 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.
    5. T. Kuno, 1999. "Solving a Class of Multiplicative Programs with 0–1 Knapsack Constraints," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 121-135, October.
    6. 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.
    7. Çağın Ararat & Firdevs Ulus & Muhammad Umer, 2022. "A Norm Minimization-Based Convex Vector Optimization Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 681-712, August.
    8. Ismail I. Almaraj & Theodore B. Trafalis, 2022. "A robust optimization approach in a multi-objective closed-loop supply chain model under imperfect quality production," Annals of Operations Research, Springer, vol. 319(2), pages 1479-1505, December.
    9. 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.
    10. Gabriela Kováčová & Birgit Rudloff, 2022. "Convex projection and convex multi-objective optimization," Journal of Global Optimization, Springer, vol. 83(2), pages 301-327, June.
    11. Ke, Jintao & Li, Xinwei & Yang, Hai & Yin, Yafeng, 2021. "Pareto-efficient solutions and regulations of congested ride-sourcing markets with heterogeneous demand and supply," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 154(C).
    12. Robert L. Carraway & Robert L. Schmidt & Lawrence R. Weatherford, 1993. "An algorithm for maximizing target achievement in the stochastic knapsack problem with normal returns," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(2), pages 161-173, March.
    13. Ruiz, Francisco & Luque, Mariano & Miguel, Francisca & del Mar Munoz, Maria, 2008. "An additive achievement scalarizing function for multiobjective programming problems," European Journal of Operational Research, Elsevier, vol. 188(3), pages 683-694, August.
    14. Koenen, Melissa & Balvert, Marleen & Fleuren, H.A., 2023. "A Renewed Take on Weighted Sum in Sandwich Algorithms : Modification of the Criterion Space," Discussion Paper 2023-012, Tilburg University, Center for Economic Research.
    15. 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.
    16. J. Fülöp & L. D. Muu, 2000. "Branch-and-Bound Variant of an Outcome-Based Algorithm for Optimizing over the Efficient Set of a Bicriteria Linear Programming Problem," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 37-54, April.
    17. Ina Lammel & Karl-Heinz Küfer & Philipp Süss, 2025. "Efficient Approximation Quality Computation for Sandwiching Algorithms for Convex Multicriteria Optimization," Journal of Optimization Theory and Applications, Springer, vol. 204(3), pages 1-21, March.
    18. Cai, Zeen & Mo, Dong & Geng, Maosi & Tang, Wei & Chen, Xiqun Michael, 2023. "Integrating ride-sourcing with electric vehicle charging under mixed fleets and differentiated services," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 169(C).
    19. Michael Holzhauser & Sven O. Krumke & Clemens Thielen, 2016. "Budget-constrained minimum cost flows," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1720-1745, May.
    20. Hamacher, Horst W. & Pedersen, Christian Roed & Ruzika, Stefan, 2007. "Multiple objective minimum cost flow problems: A review," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1404-1422, February.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:58:y:2014:i:4:p:711-728. 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.