IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v273y2019i1p44-57.html
   My bibliography  Save this article

Extension of Zoutendijk method for solving constrained multiobjective optimization problems

Author

Listed:
  • Morovati, Vahid
  • Pourkarimi, Latif

Abstract

This paper extends the use of Zoutendijk method for constrained multiobjective optimization problems. This extension is a nonparametric direction-based algorithm. More precisely, considering all objective functions and binding constraints, this algorithm proposes a convex quadratic subproblem for generating a convenient improving feasible direction. Then, by using some elementary computation, the step length corresponding to the current direction is obtained. Some useful theoretical results corresponding to the proposed method are demonstrated. Using some of these theoretical results and under some mild conditions, the convergence of the proposed method is proved. The Zoutendijk multiobjective optimization (ZMO) method is not a population-based method. However, in order to find an approximation of the nondominated frontier, we need to have an appropriate population of initial feasible solutions. To achieve this aim, in this paper a cutting plane-like procedure which can generate an appropriate population of feasible solutions over the feasible set is proposed.

Suggested Citation

  • Morovati, Vahid & Pourkarimi, Latif, 2019. "Extension of Zoutendijk method for solving constrained multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 44-57.
  • Handle: RePEc:eee:ejores:v:273:y:2019:i:1:p:44-57
    DOI: 10.1016/j.ejor.2018.08.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221718307136
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2018.08.018?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. Qu, Shaojian & Ji, Ying & Jiang, Jianlin & Zhang, Qingpu, 2017. "Nonmonotone gradient methods for vector optimization with a portfolio optimization application," European Journal of Operational Research, Elsevier, vol. 263(2), pages 356-366.
    2. Pourkarimi, L. & Zarepisheh, M., 2007. "A dual-based algorithm for solving lexicographic multiple objective programs," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1348-1356, February.
    3. Kely D. V. Villacorta & Paulo R. Oliveira & Antoine Soubeyran, 2014. "A Trust-Region Method for Unconstrained Multiobjective Problems with Applications in Satisficing Processes," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 865-889, March.
    4. Markus Hartikainen & Kaisa Miettinen & Margaret Wiecek, 2012. "PAINT: Pareto front interpolation for nonlinear multiobjective optimization," Computational Optimization and Applications, Springer, vol. 52(3), pages 845-867, July.
    5. Brito, A.S. & Cruz Neto, J.X. & Santos, P.S.M. & Souza, S.S., 2017. "A relaxed projection method for solving multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 256(1), pages 17-23.
    6. Jörg Fliege & Benar Fux Svaiter, 2000. "Steepest descent methods for multicriteria optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(3), pages 479-494, August.
    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. Mingcheng Zuo & Yuan Xue, 2024. "Population Feasibility State Guided Autonomous Constrained Multi-Objective Evolutionary Optimization," Mathematics, MDPI, vol. 12(6), pages 1-24, March.
    2. Chen, Jian & Tang, Liping & Yang, Xinmin, 2023. "A Barzilai-Borwein descent method for multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 311(1), pages 196-209.
    3. Kabgani, Alireza & Soleimani-damaneh, Majid, 2022. "Semi-quasidifferentiability in nonsmooth nonconvex multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 299(1), pages 35-45.

    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. Xiaopeng Zhao & Jen-Chih Yao, 2022. "Linear convergence of a nonmonotone projected gradient method for multiobjective optimization," Journal of Global Optimization, Springer, vol. 82(3), pages 577-594, March.
    2. Suyun Liu & Luis Nunes Vicente, 2023. "Convergence Rates of the Stochastic Alternating Algorithm for Bi-Objective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 165-186, July.
    3. Chen, Jian & Tang, Liping & Yang, Xinmin, 2023. "A Barzilai-Borwein descent method for multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 311(1), pages 196-209.
    4. M. L. N. Gonçalves & F. S. Lima & L. F. Prudente, 2022. "Globally convergent Newton-type methods for multiobjective optimization," Computational Optimization and Applications, Springer, vol. 83(2), pages 403-434, November.
    5. Qu, Shaojian & Ji, Ying & Jiang, Jianlin & Zhang, Qingpu, 2017. "Nonmonotone gradient methods for vector optimization with a portfolio optimization application," European Journal of Operational Research, Elsevier, vol. 263(2), pages 356-366.
    6. Mustapha El Moudden & Ahmed El Ghali, 2018. "A new reduced gradient method for solving linearly constrained multiobjective optimization problems," Computational Optimization and Applications, Springer, vol. 71(3), pages 719-741, December.
    7. Kanako Mita & Ellen H. Fukuda & Nobuo Yamashita, 2019. "Nonmonotone line searches for unconstrained multiobjective optimization problems," Journal of Global Optimization, Springer, vol. 75(1), pages 63-90, September.
    8. Mustapha El Moudden & Abdelkrim El Mouatasim, 2021. "Accelerated Diagonal Steepest Descent Method for Unconstrained Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 220-242, January.
    9. Ana Luísa Custódio & Youssef Diouane & Rohollah Garmanjani & Elisa Riccietti, 2021. "Worst-Case Complexity Bounds of Directional Direct-Search Methods for Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 73-93, January.
    10. Vahid Morovati & Hadi Basirzadeh & Latif Pourkarimi, 2018. "Quasi-Newton methods for multiobjective optimization problems," 4OR, Springer, vol. 16(3), pages 261-294, September.
    11. El Mehdi, Er Raqabi & Ilyas, Himmich & Nizar, El Hachemi & Issmaïl, El Hallaoui & François, Soumis, 2023. "Incremental LNS framework for integrated production, inventory, and vessel scheduling: Application to a global supply chain," Omega, Elsevier, vol. 116(C).
    12. Oliver Stein & Maximilian Volk, 2023. "Generalized Polarity and Weakest Constraint Qualifications in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1156-1190, September.
    13. Alberto Pajares & Xavier Blasco & Juan Manuel Herrero & Miguel A. Martínez, 2021. "A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization," Mathematics, MDPI, vol. 9(9), pages 1-28, April.
    14. Miglierina, E. & Molho, E. & Recchioni, M.C., 2008. "Box-constrained multi-objective optimization: A gradient-like method without "a priori" scalarization," European Journal of Operational Research, Elsevier, vol. 188(3), pages 662-682, August.
    15. Erik Alex Papa Quiroz & Nancy Baygorrea Cusihuallpa & Nelson Maculan, 2020. "Inexact Proximal Point Methods for Multiobjective Quasiconvex Minimization on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 879-898, September.
    16. Kely D. V. Villacorta & Paulo R. Oliveira & Antoine Soubeyran, 2014. "A Trust-Region Method for Unconstrained Multiobjective Problems with Applications in Satisficing Processes," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 865-889, March.
    17. Francisco Salas-Molina & Juan A. Rodriguez-Aguilar & Pablo Díaz-García, 2018. "Selecting cash management models from a multiobjective perspective," Annals of Operations Research, Springer, vol. 261(1), pages 275-288, February.
    18. Miglierina Enrico & Molho Elena & Recchioni Maria Cristina, 2006. "Box-constrained vector optimization: a steepest descent method without “a priori” scalarization," Economics and Quantitative Methods qf0603, Department of Economics, University of Insubria.
    19. Mitrović, Sandra & Baesens, Bart & Lemahieu, Wilfried & De Weerdt, Jochen, 2018. "On the operational efficiency of different feature types for telco Churn prediction," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1141-1155.
    20. A. Garcia-Bernabeu & J. V. Salcedo & A. Hilario & D. Pla-Santamaria & Juan M. Herrero, 2019. "Computing the Mean-Variance-Sustainability Nondominated Surface by ev-MOGA," Complexity, Hindawi, vol. 2019, pages 1-12, December.

    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:eee:ejores:v:273:y:2019:i:1:p:44-57. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.