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; NAG; PAINT; MOEA/D; SMS-EMOA; NBI; GAMS-NIMBUS; Ipopt; NSOLIB; Qhull; Octave; PATH Solver; MacMPEC; AlphaECP; Nonconvex Pareto Navigator; QSM; LDGB; MPBNGC; PBNCGC Cited in: 64 Documents all top 5 Cited by 84 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 Cuate, Oliver 1 Deb, Kalyanmoy 1 del Mar Muñoz, María 1 Dellnitz, Michael 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 Li, Jie 1 Männikkö, Timo 1 Manninen, Jussi 1 Martín, Adanay 1 Miguel, Francisca 1 Mustajoki, Jyri 1 Nikulin, Yury N. 1 Ojalehto, Vesa 1 Peitz, Sebastian 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 Schütze, Oliver 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 all top 5 Cited in 29 Serials 8 OR Spectrum 7 European Journal of Operational Research 4 Computational Optimization and Applications 3 Computers & Operations Research 3 Journal of Multi-Criteria Decision Analysis 2 Journal of Optimization Theory and Applications 2 Journal of Global Optimization 2 Optimization Methods & Software 2 Mathematical Methods of Operations Research 2 CEJOR. Central European Journal of Operations Research 1 Applied Mathematics and Computation 1 Computing 1 Control and Cybernetics 1 Fuzzy Sets and Systems 1 Journal of Computational and Applied Mathematics 1 Journal of the Operational Research Society 1 Management Science 1 Operations Research 1 Optimization 1 Statistical Science 1 Annals of Operations Research 1 Applied Mathematical Modelling 1 INFORMS Journal on Computing 1 Journal of Discrete Algorithms 1 Engineering Optimization 1 Bericht. Universität Jyväskylä. Mathematisches Institut 1 International Series in Operations Research & Management Science 1 Advances in Design and Control 1 Optimization Letters all top 5 Cited in 12 Fields 58 Operations research, mathematical programming (90-XX) 6 Computer science (68-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Numerical analysis (65-XX) 3 Information and communication theory, circuits (94-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Citations by Year