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Interactive Nonlinear Multiobjective Optimization Methods

In: Multiple Criteria Decision Analysis

Author

Listed:
  • Kaisa Miettinen

    (University of Jyvaskyla)

  • Jussi Hakanen

    (University of Jyvaskyla)

  • Dmitry Podkopaev

    (University of Jyvaskyla)

Abstract

An overview of interactive methods for solving nonlinear multiobjective optimization problems is given. In interactive methods, the decision maker progressively provides preference information so that the her or his most satisfactory Pareto optimal solution can be found. The basic features of several methods are introduced and some theoretical results are provided. In addition, references to modifications and applications as well as to other methods are indicated. As the role of the decision maker is very important in interactive methods, methods presented are classified according to the type of preference information that the decision maker is assumed to provide.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:isochp:978-1-4939-3094-4_22
    DOI: 10.1007/978-1-4939-3094-4_22
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    Citations

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    Cited by:

    1. Outi Montonen & Ville-Pekka Eronen & Timo Ranta & Jani A. S. Huttunen & Marko M. Mäkelä, 2020. "Multiobjective Mixed Integer Nonlinear Model to Plan the Schedule for the Final Disposal of the Spent Nuclear Fuel in Finland," Mathematics, MDPI, vol. 8(4), pages 1-29, April.
    2. 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.
    3. Finke, Jonas & Bertsch, Valentin, 2022. "Implementing a highly adaptable method for the multi-objective optimisation of energy systems," MPRA Paper 115504, University Library of Munich, Germany.
    4. Carlos Alberto Barrera-Diaz & Amir Nourmohammadi & Henrik Smedberg & Tehseen Aslam & Amos H. C. Ng, 2023. "An Enhanced Simulation-Based Multi-Objective Optimization Approach with Knowledge Discovery for Reconfigurable Manufacturing Systems," Mathematics, MDPI, vol. 11(6), pages 1-23, March.
    5. Argyris, Nikolaos & Karsu, Özlem & Yavuz, Mirel, 2022. "Fair resource allocation: Using welfare-based dominance constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 560-578.
    6. Seyyed Amir Babak Rasmi & Ali Fattahi & Metin Türkay, 2021. "SASS: slicing with adaptive steps search method for finding the non-dominated points of tri-objective mixed-integer linear programming problems," Annals of Operations Research, Springer, vol. 296(1), pages 841-876, January.
    7. 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.
    8. Finke, Jonas & Bertsch, Valentin, 2023. "Implementing a highly adaptable method for the multi-objective optimisation of energy systems," Applied Energy, Elsevier, vol. 332(C).
    9. Barbati, Maria & Greco, Salvatore & Kadziński, Miłosz & Słowiński, Roman, 2018. "Optimization of multiple satisfaction levels in portfolio decision analysis," Omega, Elsevier, vol. 78(C), pages 192-204.
    10. Lu Chen & Kaisa Miettinen & Bin Xin & Vesa Ojalehto, 2023. "Comparing reference point based interactive multiobjective optimization methods without a human decision maker," Journal of Global Optimization, Springer, vol. 85(3), pages 757-788, March.
    11. 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.
    12. Yahya Hanine & Youssef Lamrani Alaoui & Mohamed Tkiouat & Younes Lahrichi, 2021. "Socially Responsible Portfolio Selection: An Interactive Intuitionistic Fuzzy Approach," Mathematics, MDPI, vol. 9(23), pages 1-13, November.

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