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Decision Making on Pareto Front Approximations with Inherent Nondominance

In: New State of MCDM in the 21st Century

Author

Listed:
  • Markus Hartikainen

    (University of Jyväskylä)

  • Kaisa Miettinen

    (University of Jyväskylä)

  • Margaret M. Wiecek

    (University of Jyväskylä)

Abstract

Approximating the Pareto fronts of nonlinear multiobjective optimization problems is considered and a property called inherent nondominance is proposed for such approximations. It is shown that an approximation having the above property can be explored by interactively solving a multiobjective optimization problem related to it. This exploration can be performed with available interactive multiobjective optimization methods. The ideas presented are especially useful in solving computationally expensive multiobjective optimization problems with costly function value evaluations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:lnechp:978-3-642-19695-9_3
    DOI: 10.1007/978-3-642-19695-9_3
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    Citations

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    Cited by:

    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 & 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.
    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. I. Kaliszewski & J. Miroforidis, 2018. "On upper approximations of Pareto fronts," Journal of Global Optimization, Springer, vol. 72(3), pages 475-490, November.

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