IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v25y2017i2d10.1007_s11750-016-0430-3.html
   My bibliography  Save this article

A Benson type algorithm for nonconvex multiobjective programming problems

Author

Listed:
  • Soghra Nobakhtian

    (University of Isfahan
    Institute for Research in Fundamental Sciences (IPM))

  • Narjes Shafiei

    (University of Isfahan)

Abstract

In this paper, an approximation algorithm for solving nonconvex multiobjective programming problems (NCMOPs) is presented. We modify Benson’s method using cones instead of hyperplanes. This algorithm uses an inner approximation and an outer approximation to generate (weakly) efficient solutions and (weakly $$\varepsilon $$ ε -) nondominated points of NCMOPs. Some numerical examples are presented to clarify the proposed algorithm.

Suggested Citation

  • Soghra Nobakhtian & Narjes Shafiei, 2017. "A Benson type algorithm for nonconvex multiobjective programming problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 271-287, July.
    • Handle: RePEc:spr:topjnl:v:25:y:2017:i:2:d:10.1007_s11750-016-0430-3
    DOI: 10.1007/s11750-016-0430-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11750-016-0430-3
    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/s11750-016-0430-3?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. Andreas Löhne & Birgit Rudloff & Firdevs Ulus, 2014. "Primal and dual approximation algorithms for convex vector optimization problems," Journal of Global Optimization, Springer, vol. 60(4), pages 713-736, December.
    2. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, March.
    3. Andreas Hamel & Andreas Löhne & Birgit Rudloff, 2014. "Benson type algorithms for linear vector optimization and applications," Journal of Global Optimization, Springer, vol. 59(4), pages 811-836, August.
    4. P. Khanh & L. Tung, 2015. "Erratum to: First- and second-order optimality conditions for multiobjective fractional programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 618-618, July.
    5. P. Khanh & L. Tung, 2015. "First- and second-order optimality conditions for multiobjective fractional programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 419-440, July.
    6. S. Ruzika & M. M. Wiecek, 2005. "Approximation Methods in Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 473-501, September.
    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. Birgit Rudloff & Firdevs Ulus, 2019. "Certainty Equivalent and Utility Indifference Pricing for Incomplete Preferences via Convex Vector Optimization," Papers 1904.09456, arXiv.org, revised Oct 2020.
    2. Eichfelder, Gabriele & Warnow, Leo, 2023. "Advancements in the computation of enclosures for multi-objective optimization problems," European Journal of Operational Research, Elsevier, vol. 310(1), pages 315-327.
    3. Wissam AlAli & c{C}au{g}{i}n Ararat, 2024. "Systemic values-at-risk and their sample-average approximations," Papers 2408.08511, arXiv.org.
    4. Gabriele Eichfelder & Oliver Stein & Leo Warnow, 2024. "A Solver for Multiobjective Mixed-Integer Convex and Nonconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1736-1766, November.
    5. 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.

    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. Rennen, G. & van Dam, E.R. & den Hertog, D., 2009. "Enhancement of Sandwich Algorithms for Approximating Higher Dimensional Convex Pareto Sets," Other publications TiSEM e2255959-6691-4ef1-88a4-5, Tilburg University, School of Economics and Management.
    2. Gabriele Eichfelder & Leo Warnow, 2022. "An approximation algorithm for multi-objective optimization problems using a box-coverage," Journal of Global Optimization, Springer, vol. 83(2), pages 329-357, June.
    3. Notte, Gastón & Cancela, Héctor & Pedemonte, Martín & Chilibroste, Pablo & Rossing, Walter & Groot, Jeroen C.J., 2020. "A multi-objective optimization model for dairy feeding management," Agricultural Systems, Elsevier, vol. 183(C).
    4. Andreas Löhne & Birgit Rudloff & Firdevs Ulus, 2014. "Primal and dual approximation algorithms for convex vector optimization problems," Journal of Global Optimization, Springer, vol. 60(4), pages 713-736, December.
    5. Daniel Dörfler, 2022. "On the Approximation of Unbounded Convex Sets by Polyhedra," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 265-287, July.
    6. Zachary Feinstein & Birgit Rudloff, 2017. "A recursive algorithm for multivariate risk measures and a set-valued Bellman’s principle," Journal of Global Optimization, Springer, vol. 68(1), pages 47-69, May.
    7. Tran Su & Dinh Dieu Hang, 2022. "Optimality and duality in nonsmooth multiobjective fractional programming problem with constraints," 4OR, Springer, vol. 20(1), pages 105-137, March.
    8. Birgit Rudloff & Firdevs Ulus, 2019. "Certainty Equivalent and Utility Indifference Pricing for Incomplete Preferences via Convex Vector Optimization," Papers 1904.09456, arXiv.org, revised Oct 2020.
    9. Ina Lammel & Karl-Heinz Küfer & Philipp Süss, 2024. "An approximation algorithm for multiobjective mixed-integer convex optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 321-350, August.
    10. Gabriela Kov'av{c}ov'a & Birgit Rudloff, 2018. "Time consistency of the mean-risk problem," Papers 1806.10981, arXiv.org, revised Jan 2020.
    11. Robert Bassett & Khoa Le, 2016. "Multistage Portfolio Optimization: A Duality Result in Conic Market Models," Papers 1601.00712, arXiv.org, revised Jan 2016.
    12. Daniel Vanderpooten & Lakmali Weerasena & Margaret M. Wiecek, 2017. "Covers and approximations in multiobjective optimization," Journal of Global Optimization, Springer, vol. 67(3), pages 601-619, March.
    13. c{C}au{g}{i}n Ararat & Nurtai Meimanjan, 2019. "Computation of systemic risk measures: a mixed-integer programming approach," Papers 1903.08367, arXiv.org, revised Aug 2023.
    14. Firdevs Ulus, 2018. "Tractability of convex vector optimization problems in the sense of polyhedral approximations," Journal of Global Optimization, Springer, vol. 72(4), pages 731-742, December.
    15. Zachary Feinstein & Birgit Rudloff, 2022. "Deep Learning the Efficient Frontier of Convex Vector Optimization Problems," Papers 2205.07077, arXiv.org, revised May 2024.
    16. Alexander Engau & Margaret M. Wiecek, 2008. "Interactive Coordination of Objective Decompositions in Multiobjective Programming," Management Science, INFORMS, vol. 54(7), pages 1350-1363, July.
    17. Samira Fallah & Ted K. Ralphs & Natashia L. Boland, 2024. "On the relationship between the value function and the efficient frontier of a mixed integer linear optimization problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 175-220, August.
    18. 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.
    19. Zachary Feinstein & Birgit Rudloff, 2015. "A recursive algorithm for multivariate risk measures and a set-valued Bellman's principle," Papers 1508.02367, arXiv.org, revised Jul 2016.
    20. Fancello, Giovanna & Tsoukiàs, Alexis, 2021. "Learning urban capabilities from behaviours. A focus on visitors values for urban planning," Socio-Economic Planning Sciences, Elsevier, vol. 76(C).

    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:topjnl:v:25:y:2017:i:2:d:10.1007_s11750-016-0430-3. 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.