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PAINT: Pareto front interpolation for nonlinear multiobjective optimization


  • Markus Hartikainen


  • Kaisa Miettinen


  • Margaret Wiecek



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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    Cited by:

    1. Thibaut Mastrolia, 2017. "Moral hazard in welfare economics: on the advantage of Planner's advices to manage employees' actions," Working Papers hal-01504473, HAL.
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    5. Nomeda Dobrovolskienė & Rima Tamošiūnienė, 2016. "Sustainability-Oriented Financial Resource Allocation in a Project Portfolio through Multi-Criteria Decision-Making," Sustainability, MDPI, Open Access Journal, vol. 8(5), pages 1-18, May.
    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. Vesa Ojalehto & Kaisa Miettinen & Timo Laukkanen, 2014. "Implementation aspects of interactive multiobjective optimization for modeling environments: the case of GAMS-NIMBUS," Computational Optimization and Applications, Springer, vol. 58(3), pages 757-779, July.
    8. Thibaut Mastrolia, 2017. "Moral hazard in welfare economics: on the advantage of Planner's advices to manage employees' actions," Papers 1706.01254,


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