IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v73y2011i2p209-234.html
   My bibliography  Save this article

Constructing a Pareto front approximation for decision making

Author

Listed:
  • Markus Hartikainen
  • Kaisa Miettinen
  • Margaret Wiecek

Abstract

An approach to constructing a Pareto front approximation to computationally expensive multiobjective optimization problems is developed. The approximation is constructed as a sub-complex of a Delaunay triangulation of a finite set of Pareto optimal outcomes to the problem. The approach is based on the concept of inherent nondominance. Rules for checking the inherent nondominance of complexes are developed and applying the rules is demonstrated with examples. The quality of the approximation is quantified with error estimates. Due to its properties, the Pareto front approximation works as a surrogate to the original problem for decision making with interactive methods. Copyright Springer-Verlag 2011

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:73:y:2011:i:2:p:209-234
    DOI: 10.1007/s00186-010-0343-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-010-0343-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-010-0343-0?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. Markus Hartikainen & Kaisa Miettinen & Margaret M. Wiecek, 2011. "Decision Making on Pareto Front Approximations with Inherent Nondominance," Lecture Notes in Economics and Mathematical Systems, in: Yong Shi & Shouyang Wang & Gang Kou & Jyrki Wallenius (ed.), New State of MCDM in the 21st Century, chapter 0, pages 35-45, Springer.
    2. Miettinen, Kaisa & Makela, Marko M., 2006. "Synchronous approach in interactive multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 170(3), pages 909-922, May.
    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. Roman Efremov & Georgy Kamenev, 2009. "Properties of a method for polyhedral approximation of the feasible criterion set in convex multiobjective problems," Annals of Operations Research, Springer, vol. 166(1), pages 271-279, February.
    5. Keeney,Ralph L. & Raiffa,Howard, 1993. "Decisions with Multiple Objectives," Cambridge Books, Cambridge University Press, number 9780521438834.
    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. 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.
    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. Sarnataro, Michele & Barbati, Maria & Greco, Salvatore, 2021. "A portfolio approach for the selection and the timing of urban planning projects," Socio-Economic Planning Sciences, Elsevier, vol. 75(C).
    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. 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.
    6. 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.
    7. 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.

    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 & 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.
    2. 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.
    3. Kathrin Klamroth & Kaisa Miettinen, 2008. "Integrating Approximation and Interactive Decision Making in Multicriteria Optimization," Operations Research, INFORMS, vol. 56(1), pages 222-234, February.
    4. 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.
    5. 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.
    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. KARRI PASANEN & MIKKO KURTTILA & JOUNI PYKÄlÄINEN & JYRKI KANGAS & PEKKA LESKINEN, 2005. "Mesta — Non-Industrial Private Forest Owners' Decision-Support Environment For The Evaluation Of Alternative Forest Plans Over The Internet," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 4(04), pages 601-620.
    8. 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.
    9. Gerd Gigerenzer, 1997. "Bounded Rationality: Models of Fast and Frugal Inference," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 133(II), pages 201-218, June.
    10. Shuang Liu & Kirsten Maclean & Cathy Robinson, 2019. "A cost-effective framework to prioritise stakeholder participation options," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 221-241, November.
    11. Khaled, Oumaima & Minoux, Michel & Mousseau, Vincent & Michel, Stéphane & Ceugniet, Xavier, 2018. "A multi-criteria repair/recovery framework for the tail assignment problem in airlines," Journal of Air Transport Management, Elsevier, vol. 68(C), pages 137-151.
    12. Zhang, Tianyu & Dong, Peiwu & Zeng, Yongchao & Ju, Yanbing, 2022. "Analyzing the diffusion of competitive smart wearable devices: An agent-based multi-dimensional relative agreement model," Journal of Business Research, Elsevier, vol. 139(C), pages 90-105.
    13. 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.
    14. Smith, Chris M. & Shaw, Duncan, 2019. "The characteristics of problem structuring methods: A literature review," European Journal of Operational Research, Elsevier, vol. 274(2), pages 403-416.
    15. Anirban Basu & William Dale & Arthur Elstein & David Meltzer, 2009. "A linear index for predicting joint health‐states utilities from single health‐states utilities," Health Economics, John Wiley & Sons, Ltd., vol. 18(4), pages 403-419, April.
    16. Chorus, Caspar & van Cranenburgh, Sander & Daniel, Aemiro Melkamu & Sandorf, Erlend Dancke & Sobhani, Anae & Szép, Teodóra, 2021. "Obfuscation maximization-based decision-making: Theory, methodology and first empirical evidence," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 28-44.
    17. Wu, Desheng (Dash) & Lee, Chi-Guhn, 2010. "Stochastic DEA with ordinal data applied to a multi-attribute pricing problem," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1679-1688, December.
    18. Perrels, Adriaan & Molarius, Riitta & Porthin, Markus & Rosqvist, Tony, 2008. "Testing a Flood Protection Case by Means of a Group Decision Support System," Discussion Papers 449, VATT Institute for Economic Research.
    19. Fernandez del Pozo, J. A. & Bielza, C. & Gomez, M., 2005. "A list-based compact representation for large decision tables management," European Journal of Operational Research, Elsevier, vol. 160(3), pages 638-662, February.
    20. Mario Fedrizzi & Michele Fedrizzi & R. A. Marques Pereira, 2007. "Consensus Modelling In Group Decision Making: Dynamical Approach Based On Fuzzy Preferences," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 219-237.

    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:mathme:v:73:y:2011:i:2:p:209-234. 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.