IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v68y2017i1d10.1007_s10898-016-0454-0.html
   My bibliography  Save this article

An approach to generate comprehensive piecewise linear interpolation of pareto outcomes to aid decision making

Author

Listed:
  • Kalyan Shankar Bhattacharjee

    (The University of New South Wales)

  • Hemant Kumar Singh

    (The University of New South Wales)

  • Tapabrata Ray

    (The University of New South Wales)

Abstract

Multiple criteria decision making is a well established field encompassing aspects of search for solutions and selection of solutions in presence of more than one conflicting objectives. In this paper, we discuss an approach aimed towards the latter. The decision maker is presented with a limited number of Pareto optimal outcomes and is required to identify regions of interest for further investigation. The inherent sparsity of the given Pareto optimal outcomes in high dimensional space makes it an arduous task for the decision maker. To address this problem, an existing line of thought in literature is to generate a set of approximated Pareto optimal outcomes using piecewise linear interpolation. We present an approach within this paradigm, but one that delivers a comprehensive linearly interpolated set as opposed to its subset delivered by existing methods. We illustrate the advantage in doing so in comparison to stricter non-dominance conditions imposed in existing PAreto INTerpolation method. The interpolated set of outcomes delivered by the proposed approach are non-dominated with respect to the given Pareto optimal outcomes, and additionally the interpolated outcomes along uniformly distributed reference directions are presented to the decision maker. The errors in the given interpolations are also estimated in order to further aid decision making by establishing confidence in achieving true Pareto outcomes in their vicinity. The proposed approach for interpolation is computationally less demanding (for higher number of objectives) and also further amenable to parallelization. We illustrate the performance of the approach using six well established tri-objective test problems and two real-life examples. The problems span different types of fronts, such as convex, concave, mixed, degenerate, highlighting the wide applicability of the approach.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:68:y:2017:i:1:d:10.1007_s10898-016-0454-0
    DOI: 10.1007/s10898-016-0454-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-016-0454-0
    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/s10898-016-0454-0?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. Alberto Lovison, 2013. "Global search perspectives for multiobjective optimization," Journal of Global Optimization, Springer, vol. 57(2), pages 385-398, October.
    2. 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.
    3. 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.
    4. C. Hillermeier, 2001. "Generalized Homotopy Approach to Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 557-583, September.
    5. Markus Hartikainen & Kaisa Miettinen & Margaret Wiecek, 2011. "Constructing a Pareto front approximation for decision making," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(2), pages 209-234, April.
    6. Margaret M. Wiecek & Matthias Ehrgott & Alexander Engau, 2016. "Continuous Multiobjective Programming," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 739-815, Springer.
    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. 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.
    2. 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.
    3. 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.
    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. 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.
    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. 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.
    8. 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.
    9. Alberto Lovison & Kaisa Miettinen, 2021. "On the Extension of the DIRECT Algorithm to Multiple Objectives," Journal of Global Optimization, Springer, vol. 79(2), pages 387-412, February.
    10. 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.
    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. Tobias Kuhn & Stefan Ruzika, 2017. "A coverage-based Box-Algorithm to compute a representation for optimization problems with three objective functions," Journal of Global Optimization, Springer, vol. 67(3), pages 581-600, March.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Gabriele Eichfelder & Peter Kirst & Laura Meng & Oliver Stein, 2021. "A general branch-and-bound framework for continuous global multiobjective optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 195-227, May.

    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:68:y:2017:i:1:d:10.1007_s10898-016-0454-0. 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.