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NIMBUS

swMATH ID: 4339
Software Authors: Miettinen K.; Mäkelä M.M.
Description: 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.
Homepage: http://nimbus.mit.jyu.fi/
Related Software: IND-NIMBUS; Pareto navigator; PAINT; NAG; NBI; GAMS-NIMBUS; Ipopt; NSOLIB; MacMPEC; PATH Solver; AlphaECP; MOEA/D; Nonconvex Pareto Navigator; MPBNGC; LDGB; QSM; PBNCGC; NSO; GradSamp; L-BFGS
Referenced in: 63 Publications
all top 5

Referenced by 78 Authors

37 Miettinen, Kaisa M.
15 Mäkelä, Marko Mikael
7 Luque, Mariano
4 Hakanen, Jussi
4 Klamroth, Kathrin
3 Hartikainen, Markus E.
2 Berezkin, Vadim E.
2 Biegler, Lorenz T.
2 Borgulya, István
2 Caballero, Rafael E.
2 Eskelinen, Petri
2 Hernández-Díaz, Alfredo G.
2 Kaario, Katja
2 Kamenev, Georgy K.
2 Kawajiri, Yoshiaki
2 Lotov, Alexander V.
2 Mäkinen, Raino A. E.
2 Molina, Julián
2 Svaiter, Benar Fux
2 Toivanen, Jari
2 Wiecek, Margaret M.
1 Borisov, Nikita
1 Borovička, Adam
1 Boyer, Frédéric
1 Cabello, Javier M.
1 Chew, Monica
1 Coello Coello, Carlos A.
1 Cressie, Noel A. C.
1 Deb, Kalyanmoy
1 del Mar Muñoz, María
1 do Lago, Alair Pereira
1 Dyer, James S.
1 Fiala, Petr
1 Fishburn, Peter Clingerman
1 Fliege, Jörg
1 Fu, Zhao
1 Furman, Vladimir
1 Gonzalez, Mercedes V.
1 Graña Drummond, L. M.
1 Hämäläinen, Jari P.
1 Haslinger, Jaroslav
1 Jacobson, Sheldon H.
1 Johnson, Rob
1 Kaliszewski, Ignacy
1 Kao, Gio K.
1 Karmitsa, Napsu
1 Kassem, Mohamed Abd El-Hady
1 Kirilov, Leoneed
1 Kornak, John
1 Larbani, Moussa
1 Laukkanen, Timo
1 Leyffer, Sven
1 Männikkö, Timo
1 Manninen, Jussi
1 Miguel, Francisca
1 Mustajoki, Jyri
1 Nikulin, Yury N.
1 Ojalehto, Vesa
1 Peterlongo, Pierre
1 Pisanti, Nadia
1 Ruiz, Ana Belén
1 Sagot, Marie-France
1 Salcher, Ewald
1 Salminen, Pekka
1 Santana, Luis V.
1 Steuer, Ralph E.
1 Stewart, Theodor J.
1 Tarvainen, Pasi
1 Tind, Jørgen
1 Wagner, David A.
1 Wallenius, Jyrki
1 Wang, Guoyin
1 Wong, Brandon Y. H.
1 Xie, Yongfang
1 Yang, Jian-Bo
1 Yu, Hong
1 Zionts, Stanley
1 Zust, Sibylle

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