PAINT: Pareto front interpolation for nonlinear multiobjective optimization. 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.

References in zbMATH (referenced in 12 articles )

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  1. Kaliszewski, I.; Miroforidis, J.: Cooperative multiobjective optimization with bounds on objective functions (2021)
  2. Lovison, Alberto; Miettinen, Kaisa: On the extension of the \textscdirectalgorithm to multiple objectives (2021)
  3. Hartikainen, Markus; Miettinen, Kaisa; Klamroth, Kathrin: Interactive \textscNonconvexPareto Navigator for multiobjective optimization (2019)
  4. Kaliszewski, I.; Miroforidis, J.: On upper approximations of Pareto fronts (2018)
  5. Bhattacharjee, Kalyan Shankar; Singh, Hemant Kumar; Ray, Tapabrata: An approach to generate comprehensive piecewise linear interpolation of Pareto outcomes to aid decision making (2017)
  6. Vanderpooten, Daniel; Weerasena, Lakmali; Wiecek, Margaret M.: Covers and approximations in multiobjective optimization (2017)
  7. Martin, Benjamin; Goldsztejn, Alexandre; Granvilliers, Laurent; Jermann, Christophe: On continuation methods for non-linear bi-objective optimization: towards a certified interval-based approach (2016)
  8. Fettaka, Salim; Thibault, Jules; Gupta, Yash: A new algorithm using front prediction and NSGA-II for solving two and three-objective optimization problems (2015)
  9. Hartikainen, Markus E.; Lovison, Alberto: \textttPAINT-SICon: constructing consistent parametric representations of Pareto sets in nonconvex multiobjective optimization (2015)
  10. Ruiz, Ana B.; Sindhya, Karthik; Miettinen, Kaisa; Ruiz, Francisco; Luque, Mariano: E-NAUTILUS: a decision support system for complex multiobjective optimization problems based on the NAUTILUS method (2015)
  11. Ojalehto, Vesa; Miettinen, Kaisa; Laukkanen, Timo: Implementation aspects of interactive multiobjective optimization for modeling environments: the case of GAMS-NIMBUS (2014)
  12. Hartikainen, Markus; Miettinen, Kaisa; Wiecek, Margaret M.: PAINT: Pareto front interpolation for nonlinear multiobjective optimization (2012)