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Constructing a Pareto front approximation for decision making

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  • Markus Hartikainen
  • Kaisa Miettinen
  • Margaret Wiecek

Abstract

An approach to constructing a Pareto front approximation to computationally expensive multiobjective optimization problems is developed. The approximation is constructed as a sub-complex of a Delaunay triangulation of a finite set of Pareto optimal outcomes to the problem. The approach is based on the concept of inherent nondominance. Rules for checking the inherent nondominance of complexes are developed and applying the rules is demonstrated with examples. The quality of the approximation is quantified with error estimates. Due to its properties, the Pareto front approximation works as a surrogate to the original problem for decision making with interactive methods. Copyright Springer-Verlag 2011

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:73:y:2011:i:2:p:209-234
    DOI: 10.1007/s00186-010-0343-0
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    References listed on IDEAS

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    1. 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.
    2. Keeney,Ralph L. & Raiffa,Howard, 1993. "Decisions with Multiple Objectives," Cambridge Books, Cambridge University Press, number 9780521438834, October.
    3. 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.
    4. 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.
    5. Roman Efremov & Georgy Kamenev, 2009. "Properties of a method for polyhedral approximation of the feasible criterion set in convex multiobjective problems," Annals of Operations Research, Springer, vol. 166(1), pages 271-279, February.
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    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. Daniel Vanderpooten & Lakmali Weerasena & Margaret M. Wiecek, 2017. "Covers and approximations in multiobjective optimization," Journal of Global Optimization, Springer, vol. 67(3), pages 601-619, March.
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    4. Benjamin Martin & Alexandre Goldsztejn & Laurent Granvilliers & Christophe Jermann, 2016. "On continuation methods for non-linear bi-objective optimization: towards a certified interval-based approach," Journal of Global Optimization, Springer, vol. 64(1), pages 3-16, January.
    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. Kalyan Shankar Bhattacharjee & Hemant Kumar Singh & Tapabrata Ray, 2017. "An approach to generate comprehensive piecewise linear interpolation of pareto outcomes to aid decision making," Journal of Global Optimization, Springer, vol. 68(1), pages 71-93, May.
    7. 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.

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