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Optimistic NAUTILUS navigator for multiobjective optimization with costly function evaluations

Author

Listed:
  • Bhupinder Singh Saini

    (University of Jyvaskyla)

  • Michael Emmerich

    (University of Jyvaskyla
    Leiden Institute of Advanced Computer Science)

  • Atanu Mazumdar

    (University of Jyvaskyla)

  • Bekir Afsar

    (University of Jyvaskyla)

  • Babooshka Shavazipour

    (University of Jyvaskyla)

  • Kaisa Miettinen

    (University of Jyvaskyla)

Abstract

We introduce novel concepts to solve multiobjective optimization problems involving (computationally) expensive function evaluations and propose a new interactive method called O-NAUTILUS. It combines ideas of trade-off free search and navigation (where a decision maker sees changes in objective function values in real time) and extends the NAUTILUS Navigator method to surrogate-assisted optimization. Importantly, it utilizes uncertainty quantification from surrogate models like Kriging or properties like Lipschitz continuity to approximate a so-called optimistic Pareto optimal set. This enables the decision maker to search in unexplored parts of the Pareto optimal set and requires a small amount of expensive function evaluations. We share the implementation of O-NAUTILUS as open source code. Thanks to its graphical user interface, a decision maker can see in real time how the preferences provided affect the direction of the search. We demonstrate the potential and benefits of O-NAUTILUS with a problem related to the design of vehicles.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:83:y:2022:i:4:d:10.1007_s10898-021-01119-7
    DOI: 10.1007/s10898-021-01119-7
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    References listed on IDEAS

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    1. W C M van Beers & J P C Kleijnen, 2003. "Kriging for interpolation in random simulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(3), pages 255-262, March.
    2. Kaisa Miettinen & Jussi Hakanen & Dmitry Podkopaev, 2016. "Interactive Nonlinear Multiobjective Optimization Methods," 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 927-976, Springer.
    3. 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..
    4. Michael Emmerich & Kaifeng Yang & André Deutz & Hao Wang & Carlos M. Fonseca, 2016. "A Multicriteria Generalization of Bayesian Global Optimization," Springer Optimization and Its Applications, in: Panos M. Pardalos & Anatoly Zhigljavsky & Julius Žilinskas (ed.), Advances in Stochastic and Deterministic Global Optimization, pages 229-242, Springer.
    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. 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.
    7. 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.
    8. 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.
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