IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v206y2010i2p426-434.html
   My bibliography  Save this article

NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point

Author

Listed:
  • Miettinen, Kaisa
  • Eskelinen, Petri
  • Ruiz, Francisco
  • Luque, Mariano

Abstract

Most interactive methods developed for solving multiobjective optimization problems sequentially generate Pareto optimal or nondominated vectors and the decision maker must always allow impairment in at least one objective function to get a new solution. The NAUTILUS method proposed is based on the assumptions that past experiences affect decision makers' hopes and that people do not react symmetrically to gains and losses. Therefore, some decision makers may prefer to start from the worst possible objective values and to improve every objective step by step according to their preferences. In NAUTILUS, starting from the nadir point, a solution is obtained at each iteration which dominates the previous one. Although only the last solution will be Pareto optimal, the decision maker never looses sight of the Pareto optimal set, and the search is oriented so that (s)he progressively focusses on the preferred part of the Pareto optimal set. Each new solution is obtained by minimizing an achievement scalarizing function including preferences about desired improvements in objective function values. NAUTILUS is specially suitable for avoiding undesired anchoring effects, for example in negotiation support problems, or just as a means of finding an initial Pareto optimal solution for any interactive procedure. An illustrative example demonstrates how this new method iterates.

Suggested Citation

  • Miettinen, Kaisa & Eskelinen, Petri & Ruiz, Francisco & Luque, Mariano, 2010. "NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point," European Journal of Operational Research, Elsevier, vol. 206(2), pages 426-434, October.
  • Handle: RePEc:eee:ejores:v:206:y:2010:i:2:p:426-434
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00178-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Kalyanmoy Deb & Kaisa Miettinen, 2010. "Nadir Point Estimation Using Evolutionary Approaches: Better Accuracy and Computational Speed Through Focused Search," Lecture Notes in Economics and Mathematical Systems, in: Matthias Ehrgott & Boris Naujoks & Theodor J. Stewart & Jyrki Wallenius (ed.), Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems, pages 339-354, Springer.
    2. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    3. James S. Dyer & Peter C. Fishburn & Ralph E. Steuer & Jyrki Wallenius & Stanley Zionts, 1992. "Multiple Criteria Decision Making, Multiattribute Utility Theory: The Next Ten Years," Management Science, INFORMS, vol. 38(5), pages 645-654, May.
    4. Karasakal, Esra Koktener & Michalowski, Wojtek, 2003. "Incorporating wealth information into a multiple criteria decision making model," European Journal of Operational Research, Elsevier, vol. 150(1), pages 204-219, October.
    5. Aloysius, John A. & Davis, Fred D. & Wilson, Darryl D. & Ross Taylor, A. & Kottemann, Jeffrey E., 2006. "User acceptance of multi-criteria decision support systems: The impact of preference elicitation techniques," European Journal of Operational Research, Elsevier, vol. 169(1), pages 273-285, February.
    6. Luque, Mariano & Miettinen, Kaisa & Eskelinen, Petri & Ruiz, Francisco, 2009. "Incorporating preference information in interactive reference point methods for multiobjective optimization," Omega, Elsevier, vol. 37(2), pages 450-462, April.
    7. Ehrgott, Matthias & Tenfelde-Podehl, Dagmar, 2003. "Computation of ideal and Nadir values and implications for their use in MCDM methods," European Journal of Operational Research, Elsevier, vol. 151(1), pages 119-139, November.
    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. Ana B. Ruiz & Francisco Ruiz & Kaisa Miettinen & Laura Delgado-Antequera & Vesa Ojalehto, 2019. "NAUTILUS Navigator: free search interactive multiobjective optimization without trading-off," Journal of Global Optimization, Springer, vol. 74(2), pages 213-231, June.
    2. Kaisa Miettinen & Dmitry Podkopaev & Francisco Ruiz & Mariano Luque, 2015. "A new preference handling technique for interactive multiobjective optimization without trading-off," Journal of Global Optimization, Springer, vol. 63(4), pages 633-652, December.
    3. Bhupinder Singh Saini & Michael Emmerich & Atanu Mazumdar & Bekir Afsar & Babooshka Shavazipour & Kaisa Miettinen, 2022. "Optimistic NAUTILUS navigator for multiobjective optimization with costly function evaluations," Journal of Global Optimization, Springer, vol. 83(4), pages 865-889, August.
    4. Cui, Yunfei & Geng, Zhiqiang & Zhu, Qunxiong & Han, Yongming, 2017. "Review: Multi-objective optimization methods and application in energy saving," Energy, Elsevier, vol. 125(C), pages 681-704.
    5. Steuer, Ralph E. & Utz, Sebastian, 2023. "Non-contour efficient fronts for identifying most preferred portfolios in sustainability investing," European Journal of Operational Research, Elsevier, vol. 306(2), pages 742-753.
    6. Özgür Özpeynirci, 2017. "On nadir points of multiobjective integer programming problems," Journal of Global Optimization, Springer, vol. 69(3), pages 699-712, November.
    7. Kaisa Miettinen & Francisco Ruiz, 2016. "NAUTILUS framework: towards trade-off-free interaction in multiobjective optimization," Journal of Business Economics, Springer, vol. 86(1), pages 5-21, January.
    8. Maciej Nowak & Tadeusz Trzaskalik, 2022. "A trade-off multiobjective dynamic programming procedure and its application to project portfolio selection," Annals of Operations Research, Springer, vol. 311(2), pages 1155-1181, April.
    9. Piercy, Craig A. & Steuer, Ralph E., 2019. "Reducing wall-clock time for the computation of all efficient extreme points in multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 277(2), pages 653-666.
    10. Ruiz, Ana B. & Sindhya, Karthik & Miettinen, Kaisa & Ruiz, Francisco & Luque, Mariano, 2015. "E-NAUTILUS: A decision support system for complex multiobjective optimization problems based on the NAUTILUS method," European Journal of Operational Research, Elsevier, vol. 246(1), pages 218-231.
    11. Vesa Ojalehto & Kaisa Miettinen & Timo Laukkanen, 2014. "Implementation aspects of interactive multiobjective optimization for modeling environments: the case of GAMS-NIMBUS," Computational Optimization and Applications, Springer, vol. 58(3), pages 757-779, July.
    12. Gokhan Kirlik & Serpil Sayın, 2015. "Computing the nadir point for multiobjective discrete optimization problems," Journal of Global Optimization, Springer, vol. 62(1), pages 79-99, May.
    13. J. Cabello & M. Luque & F. Miguel & A. Ruiz & F. Ruiz, 2014. "A multiobjective interactive approach to determine the optimal electricity mix in Andalucía (Spain)," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 109-127, April.
    14. Jiménez, Mariano & Bilbao-Terol, Amelia & Arenas-Parra, Mar, 2021. "Incorporating preferential weights as a benchmark into a Sequential Reference Point Method," European Journal of Operational Research, Elsevier, vol. 291(2), pages 575-585.

    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. Kaisa Miettinen & Francisco Ruiz, 2016. "NAUTILUS framework: towards trade-off-free interaction in multiobjective optimization," Journal of Business Economics, Springer, vol. 86(1), pages 5-21, January.
    2. Kaisa Miettinen & Dmitry Podkopaev & Francisco Ruiz & Mariano Luque, 2015. "A new preference handling technique for interactive multiobjective optimization without trading-off," Journal of Global Optimization, Springer, vol. 63(4), pages 633-652, December.
    3. Mariano Luque & Ana Ruiz & Rubén Saborido & Óscar Marcenaro-Gutiérrez, 2015. "On the use of the $$L_{p}$$ L p distance in reference point-based approaches for multiobjective optimization," Annals of Operations Research, Springer, vol. 235(1), pages 559-579, December.
    4. Ana B. Ruiz & Francisco Ruiz & Kaisa Miettinen & Laura Delgado-Antequera & Vesa Ojalehto, 2019. "NAUTILUS Navigator: free search interactive multiobjective optimization without trading-off," Journal of Global Optimization, Springer, vol. 74(2), pages 213-231, June.
    5. O. D. Marcenaro-Gutierrez & M. Luque & L. A. Lopez-Agudo, 2016. "Balancing Teachers’ Math Satisfaction and Other Indicators of the Education System’s Performance," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 129(3), pages 1319-1348, December.
    6. Ana Ruiz & Rubén Saborido & Mariano Luque, 2015. "A preference-based evolutionary algorithm for multiobjective optimization: the weighting achievement scalarizing function genetic algorithm," Journal of Global Optimization, Springer, vol. 62(1), pages 101-129, May.
    7. Ruiz, Ana B. & Sindhya, Karthik & Miettinen, Kaisa & Ruiz, Francisco & Luque, Mariano, 2015. "E-NAUTILUS: A decision support system for complex multiobjective optimization problems based on the NAUTILUS method," European Journal of Operational Research, Elsevier, vol. 246(1), pages 218-231.
    8. Andrea C. Hupman & Jay Simon, 2023. "The Legacy of Peter Fishburn: Foundational Work and Lasting Impact," Decision Analysis, INFORMS, vol. 20(1), pages 1-15, March.
    9. Stefanescu, Razvan & Dumitriu, Ramona, 2015. "Alegerea soluţiilor pentru expunerile faţă de risc [Choosing solutions to risk exposures]," MPRA Paper 65074, University Library of Munich, Germany.
    10. Jiménez, Mariano & Bilbao-Terol, Amelia & Arenas-Parra, Mar, 2021. "Incorporating preferential weights as a benchmark into a Sequential Reference Point Method," European Journal of Operational Research, Elsevier, vol. 291(2), pages 575-585.
    11. Pérez-Moreno, Salvador & Rodríguez, Beatriz & Luque, Mariano, 2016. "Assessing global competitiveness under multi-criteria perspective," Economic Modelling, Elsevier, vol. 53(C), pages 398-408.
    12. Dimitris Bertsimas & Allison O'Hair, 2013. "Learning Preferences Under Noise and Loss Aversion: An Optimization Approach," Operations Research, INFORMS, vol. 61(5), pages 1190-1199, October.
    13. Schuwirth, N. & Reichert, P. & Lienert, J., 2012. "Methodological aspects of multi-criteria decision analysis for policy support: A case study on pharmaceutical removal from hospital wastewater," European Journal of Operational Research, Elsevier, vol. 220(2), pages 472-483.
    14. Alessandro Golkar & Edward F. Crawley, 2014. "A Framework for Space Systems Architecture under Stakeholder Objectives Ambiguity," Systems Engineering, John Wiley & Sons, vol. 17(4), pages 479-502, December.
    15. Özgür Özpeynirci, 2017. "On nadir points of multiobjective integer programming problems," Journal of Global Optimization, Springer, vol. 69(3), pages 699-712, November.
    16. Ziho Kang & Thomas Morin, 2016. "Multi-Attribute Decision Making in a Bidding Game with Imperfect Information and Uncertainty," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 63-81, January.
    17. Seow Eng Ong & Davin Wang & Calvin Chua, 2023. "Disruptive Innovation and Real Estate Agency: The Disruptee Strikes Back," The Journal of Real Estate Finance and Economics, Springer, vol. 67(2), pages 287-317, August.
    18. Christiane Goodfellow & Dirk Schiereck & Steffen Wippler, 2013. "Are behavioural finance equity funds a superior investment? A note on fund performance and market efficiency," Journal of Asset Management, Palgrave Macmillan, vol. 14(2), pages 111-119, April.
    19. Philippe Fevrier & Sebastien Gay, 2005. "Informed Consent Versus Presumed Consent The Role of the Family in Organ Donations," HEW 0509007, University Library of Munich, Germany.
    20. Shuang Yao & Donghua Yu & Yan Song & Hao Yao & Yuzhen Hu & Benhai Guo, 2018. "Dry Bulk Carrier Investment Selection through a Dual Group Decision Fusing Mechanism in the Green Supply Chain," Sustainability, MDPI, vol. 10(12), pages 1-19, November.

    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:206:y:2010:i:2:p:426-434. 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.