NIMBUS, an interactive method for nondifferentiable multiobjective optimization problems, is described. The algorithm is based on the classification of objective functions. At each iteration, a decision maker is asked to classify the objective functions into up to five different classes: those to be improved, those to be improved till some aspiration level, those to be accepted as they are, those to be impaired till some bound, and those allowed to change freely. According to the classification, a new (multiobjective) optimization problem is formed, which is solved by an MPB (Multiobjective Proximal Bundle) method. The MPB method is a generalization of Kiwiel’s proximal bundle approach for nondifferentiable single objective optimization into the multiobjective case. The multiple objective functions are treated individually without employing any scalarization. The method is capable of handling several nonconvex locally Lipschitz continuous objective functions subject to nonlinear (possibly nondifferentiable) constraints. Finally, numerical experiments with two academic test problems are reported. The aim is to briefly demonstrate how the method works.

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  1. Karmitsa, Napsu: Diagonal bundle method for nonsmooth sparse optimization (2015)
  2. Luque, Mariano: Modified interactive Chebyshev algorithm (MICA) for non-convex multiobjective programming (2015)
  3. Luque, M.; Marcenaro-Gutiérrez, O.D.; López-Agudo, L.A.: On the potential balance among compulsory education outcomes through econometric and multiobjective programming analysis (2015)
  4. Miettinen, Kaisa: Survey of methods to visualize alternatives in multiple criteria decision making problems (2014)
  5. Miettinen, Kaisa; Mustajoki, Jyri; Stewart, Theodor J.: Interactive multiobjective optimization with NIMBUS for decision making under uncertainty (2014)
  6. Ojalehto, Vesa; Miettinen, Kaisa; Laukkanen, Timo: Implementation aspects of interactive multiobjective optimization for modeling environments: the case of GAMS-NIMBUS (2014)
  7. Eskelinen, Petri; Miettinen, Kaisa: Trade-off analysis approach for interactive nonlinear multiobjective optimization (2012)
  8. Hartikainen, Markus; Miettinen, Kaisa; Wiecek, Margaret M.: PAINT: Pareto front interpolation for nonlinear multiobjective optimization (2012)
  9. Luque, Mariano; Miettinen, Kaisa; Ruiz, Ana B.; Ruiz, Francisco: A two-slope achievement scalarizing function for interactive multiobjective optimization (2012)
  10. Luque, Mariano; Ruiz, Francisco; Cabello, J.M.: A synchronous reference point-based interactive method for stochastic multiobjective programming (2012)
  11. Nikulin, Yury; Miettinen, Kaisa; Mäkelä, Marko M.: A new achievement scalarizing function based on parameterization in multiobjective optimization (2012)
  12. Ruiz, Francisco; Luque, Mariano; Miettinen, Kaisa: Improving the computational efficiency in a global formulation (GLIDE) for interactive multiobjective optimization (2012)
  13. Hartikainen, Markus; Miettinen, Kaisa; Wiecek, Margaret M.: Constructing a Pareto front approximation for decision making (2011)
  14. Luque, Mariano; Ruiz, Francisco; Miettinen, Kaisa: Global formulation for interactive multiobjective optimization (2011)
  15. Eskelinen, Petri; Miettinen, Kaisa; Klamroth, Kathrin; Hakanen, Jussi: Pareto navigator for interactive nonlinear multiobjective optimization (2010)
  16. Larbani, Moussa: Multiobjective problems with fuzzy parameters and games against nature (2010)
  17. Hakanen, Jussi; Kawajiri, Yoshiaki; Biegler, Lorenz T.; Miettinen, Kaisa: Interactive multiobjective optimization of superstructure SMB processes (2009)
  18. Leyffer, Sven: A complementarity constraint formulation of convex multiobjective optimization problems (2009)
  19. Miettinen, Kaisa; Molina, Julián; González, Mercedes; Hernández-Díaz, Alfredo; Caballero, Rafael: Using box indices in supporting comparison in multiobjective optimization (2009)
  20. Molina, Julián; Santana, Luis V.; Hernández-Díaz, Alfredo G.; Coello Coello, Carlos A.; Caballero, Rafael: g-dominance: Reference point based dominance for multiobjective metaheuristics (2009)

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