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PAINT: Pareto front interpolation for nonlinear multiobjective optimization

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  • Markus Hartikainen
  • Kaisa Miettinen
  • Margaret Wiecek

Abstract

A method called PAINT is introduced for computationally expensive multiobjective optimization problems. The method interpolates between a given set of Pareto optimal outcomes. The interpolation provided by the PAINT method implies a mixed integer linear surrogate problem for the original problem which can be optimized with any interactive method to make decisions concerning the original problem. When the scalarizations of the interactive method used do not introduce nonlinearity to the problem (which is true e.g., for the synchronous NIMBUS method), the scalarizations of the surrogate problem can be optimized with available mixed integer linear solvers. Thus, the use of the interactive method is fast with the surrogate problem even though the problem is computationally expensive. Numerical examples of applying the PAINT method for interpolation are included. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:52:y:2012:i:3:p:845-867
    DOI: 10.1007/s10589-011-9441-z
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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. 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.
    3. 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.
    4. 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.
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