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Integrating Approximation and Interactive Decision Making in Multicriteria Optimization

Author

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  • Kathrin Klamroth

    (Institute of Applied Mathematics, University of Erlangen-Nuremberg, D-91058 Erlangen, Germany)

  • Kaisa Miettinen

    (Department of Mathematical Information Technology, FI-40014 University of Jyvaskyla, Finland, and Helsinki School of Economics, FI-00101 Helsinki, Finland)

Abstract

We present a new interactive hybrid approach for solving multicriteria optimization problems where features of approximation methods and interactive approaches are incorporated. We produce rough approximations of the nondominated set and let the decision maker indicate with the help of reference points where to refine the approximation. In this way, (s)he iteratively directs the search toward the best nondominated solution. After the decision maker has identified the most interesting region of the nondominated set, the final solution can be fine-tuned with existing interactive methods. We suggest different ways of updating the reference point as well as discuss visualizations that can be used in comparing different nondominated solutions. The new method is computationally relatively inexpensive and easy to use for the decision maker.

Suggested Citation

  • Kathrin Klamroth & Kaisa Miettinen, 2008. "Integrating Approximation and Interactive Decision Making in Multicriteria Optimization," Operations Research, INFORMS, vol. 56(1), pages 222-234, February.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:1:p:222-234
    DOI: 10.1287/opre.1070.0425
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    References listed on IDEAS

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    1. 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.
    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. K Miettinen & M M Mäkelä, 1999. "Comparative evaluation of some interactive reference point-based methods for multi-objective optimisation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(9), pages 949-959, September.
    4. Korhonen, Pekka J. & Laakso, Jukka, 1986. "A visual interactive method for solving the multiple criteria problem," European Journal of Operational Research, Elsevier, vol. 24(2), pages 277-287, February.
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    Citations

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    Cited by:

    1. Miettinen, Kaisa & Molina, Julián & González, Mercedes & Hernández-Díaz, Alfredo & Caballero, Rafael, 2009. "Using box indices in supporting comparison in multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 197(1), pages 17-24, August.
    2. Gijs Rennen & Edwin R. van Dam & Dick den Hertog, 2011. "Enhancement of Sandwich Algorithms for Approximating Higher-Dimensional Convex Pareto Sets," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 493-517, November.
    3. 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.
    4. Xiaoning Shen & Yu Guo & Qingwei Chen & Weili Hu, 2010. "A multi-objective optimization evolutionary algorithm incorporating preference information based on fuzzy logic," Computational Optimization and Applications, Springer, vol. 46(1), pages 159-188, May.
    5. Kaliszewski, Ignacy & Miroforidis, Janusz & Podkopaev, Dmitry, 2012. "Interactive Multiple Criteria Decision Making based on preference driven Evolutionary Multiobjective Optimization with controllable accuracy," European Journal of Operational Research, Elsevier, vol. 216(1), pages 188-199.
    6. 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.
    7. 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.
    8. Lou, Youcheng & Wang, Shouyang, 2016. "Approximate representation of the Pareto frontier in multiparty negotiations: Decentralized methods and privacy preservation," European Journal of Operational Research, Elsevier, vol. 254(3), pages 968-976.

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