IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v79y2021i2d10.1007_s10898-020-00946-4.html
   My bibliography  Save this article

Cooperative multiobjective optimization with bounds on objective functions

Author

Listed:
  • I. Kaliszewski

    (Systems Research Institute, Polish Academy of Sciences
    Warsaw School of Information Technology)

  • J. Miroforidis

    (Systems Research Institute, Polish Academy of Sciences)

Abstract

When solving large-scale multiobjective optimization problems, solvers can get stuck because of memory and/or time limitations. In such cases, one is left with no information on the distance to the best feasible solution, found before the optimization process has stopped, to the true Pareto optimal solution. In this work, we show how to provide such information. To this aim we make use of the concept of lower shells and upper shells, developed in our earlier works. No specific assumptions about the problems to be solved are made. We illustrate the proposed approach on biobjective multidimensional knapsack problems derived from single-objective multidimensional knapsack problems in the Beasley OR Library. We address cases when a top-class commercial mixed-integer linear solver fails to provide Pareto optimal solutions attempted to be derived by scalarization.

Suggested Citation

  • I. Kaliszewski & J. Miroforidis, 2021. "Cooperative multiobjective optimization with bounds on objective functions," Journal of Global Optimization, Springer, vol. 79(2), pages 369-385, February.
    • Handle: RePEc:spr:jglopt:v:79:y:2021:i:2:d:10.1007_s10898-020-00946-4
    DOI: 10.1007/s10898-020-00946-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-020-00946-4
    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/s10898-020-00946-4?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. Ignacy Kaliszewski, 2006. "Soft Computing For Complex Multiple Criteria Decision Making," International Series in Operations Research and Management Science, Springer, number 978-0-387-30177-8, September.
    2. Kaliszewski, Ignacy & Miroforidis, Janusz & Podkopaev, Dmitry, 2012. "Interactive Multiple Criteria Decision Making based on preference driven Evolutionary Multiobjective Optimization with controllable accuracy," European Journal of Operational Research, Elsevier, vol. 216(1), pages 188-199.
    3. 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.
    4. I. Kaliszewski & J. Miroforidis, 2014. "Two-Sided Pareto Front Approximations," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 845-855, September.
    5. Ignacy Kaliszewski & Janusz Miroforidis & Dmitry Podkopaev, 2016. "Multiple Criteria Decision Making by Multiobjective Optimization," International Series in Operations Research and Management Science, Springer, number 978-3-319-32756-3, September.
    6. I. Kaliszewski & J. Miroforidis, 2018. "On upper approximations of Pareto fronts," Journal of Global Optimization, Springer, vol. 72(3), pages 475-490, November.
    7. 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.
    8. Mavrotas, George & Florios, Kostas & Figueira, José Rui, 2015. "An improved version of a core based algorithm for the multi-objective multi-dimensional knapsack problem: A computational study and comparison with meta-heuristics," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 25-43.
    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. I. Kaliszewski & J. Miroforidis, 2022. "Probing the Pareto front of a large-scale multiobjective problem with a MIP solver," Operational Research, Springer, vol. 22(5), pages 5617-5673, November.

    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. I. Kaliszewski & J. Miroforidis, 2022. "Probing the Pareto front of a large-scale multiobjective problem with a MIP solver," Operational Research, Springer, vol. 22(5), pages 5617-5673, November.
    2. Janusz Miroforidis, 2021. "Bounds on efficient outcomes for large-scale cardinality-constrained Markowitz problems," Journal of Global Optimization, Springer, vol. 80(3), pages 617-634, July.
    3. I. Kaliszewski & J. Miroforidis, 2018. "On upper approximations of Pareto fronts," Journal of Global Optimization, Springer, vol. 72(3), pages 475-490, November.
    4. Hartikainen, Markus & Miettinen, Kaisa & Klamroth, Kathrin, 2019. "Interactive Nonconvex Pareto Navigator for multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 275(1), pages 238-251.
    5. Kalyan Shankar Bhattacharjee & Hemant Kumar Singh & Tapabrata Ray, 2017. "An approach to generate comprehensive piecewise linear interpolation of pareto outcomes to aid decision making," Journal of Global Optimization, Springer, vol. 68(1), pages 71-93, May.
    6. Markus Hartikainen & Alberto Lovison, 2015. "PAINT–SiCon: constructing consistent parametric representations of Pareto sets in nonconvex multiobjective optimization," Journal of Global Optimization, Springer, vol. 62(2), pages 243-261, June.
    7. Benjamin Martin & Alexandre Goldsztejn & Laurent Granvilliers & Christophe Jermann, 2016. "On continuation methods for non-linear bi-objective optimization: towards a certified interval-based approach," Journal of Global Optimization, Springer, vol. 64(1), pages 3-16, January.
    8. Nguyen, Trung H. & Granger, Julien & Pandya, Deval & Paustian, Keith, 2019. "High-resolution multi-objective optimization of feedstock landscape design for hybrid first and second generation biorefineries," Applied Energy, Elsevier, vol. 238(C), pages 1484-1496.
    9. 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.
    10. Yadav, Deepanshu & Nagar, Deepak & Ramu, Palaniappan & Deb, Kalyanmoy, 2023. "Visualization-aided multi-criteria decision-making using interpretable self-organizing maps," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1183-1200.
    11. 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.
    12. 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).
    13. Saeed Vasebi & Yeganeh M. Hayeri, 2021. "Collective Driving to Mitigate Climate Change: Collective-Adaptive Cruise Control," Sustainability, MDPI, vol. 13(16), pages 1-30, August.
    14. Malavasi, Matteo & Ortobelli Lozza, Sergio & Trück, Stefan, 2021. "Second order of stochastic dominance efficiency vs mean variance efficiency," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1192-1206.
    15. Rastegar, Narges & Khorram, Esmaile, 2014. "A combined scalarizing method for multiobjective programming problems," European Journal of Operational Research, Elsevier, vol. 236(1), pages 229-237.
    16. 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.
    17. Krzysztof S. Targiel & Maciej Nowak & Tadeusz Trzaskalik, 2018. "Scheduling non-critical activities using multicriteria approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(3), pages 585-598, September.
    18. Elzbieta Rynska & Joanna Klimowicz & Slawomir Kowal & Krzysztof Lyzwa & Michal Pierzchalski & Wojciech Rekosz, 2020. "Smart Energy Solutions as an Indispensable Multi-Criteria Input for a Coherent Urban Planning and Building Design Process—Two Case Studies for Smart Office Buildings in Warsaw Downtown Area," Energies, MDPI, vol. 13(15), pages 1-24, July.
    19. 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.
    20. Gabriele Eichfelder & Corinna Krüger & Anita Schöbel, 2017. "Decision uncertainty in multiobjective optimization," Journal of Global Optimization, Springer, vol. 69(2), pages 485-510, October.

    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:79:y:2021:i:2:d:10.1007_s10898-020-00946-4. 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.