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PAINT: Pareto front interpolation for nonlinear multiobjective optimization

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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.

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Acknowledgements

We thank Mr. Karthik Sindhya for providing the Pareto optimal outcomes for the Viennet’s test problem. We also thank Dr. Jussi Hakanen for his help with the wastewater treatment planning problem.

This research was partly supported by the Academy of Finland (grant number 128495) and Jenny and Antti Wihuri Foundation.

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Authors and Affiliations

  1. Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 25 (Agora), 40014, Jyväskylä, Finland

    Markus Hartikainen & Kaisa Miettinen

  2. Department of Mathematical Sciences, Clemson University, Clemson, USA

    Margaret M. Wiecek

Authors
  1. Markus Hartikainen
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  2. Kaisa Miettinen
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  3. Margaret M. Wiecek
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Correspondence to Markus Hartikainen.

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Hartikainen, M., Miettinen, K. & Wiecek, M.M. PAINT: Pareto front interpolation for nonlinear multiobjective optimization. Comput Optim Appl 52, 845–867 (2012). https://doi.org/10.1007/s10589-011-9441-z

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  • DOI: https://doi.org/10.1007/s10589-011-9441-z

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