NIMBUS - Info

NIMBUS is a Nondifferentiable Interactive Multiobjective BUndle-based optimization System

NIMBUS has been developed at the University of Jyväskylä, Department of Mathematical Information Technology. This is a fourth version of the WWW interface.

NIMBUS is suitable for both differentiable and nondifferentiable multiobjective and single objective optimization problems subject to nonlinear and linear constraints with bounds for the variables. The problems to be solved are of the form

where k is the number of the objective functions, m is the number of the nonlinear constraints, decision variable vector x and its lower and upper bounds are n-dimensional vectors, b is an l-dimensional vector and A is an l x n-dimensional matrix of linear constraint coefficients. Integer variables can also be handled.

When the objective functions are to be minimized, the user is assumed to prefer less to more in the objective function values.

Pareto optimality and weak Pareto optimality are used as optimality concepts.

In the NIMBUS method, the idea is that the user examines the values of the objective functions calculated at a current solution and divides the objective functions into up to five classes. The classes are functions whose values

should be improved,
should be improved till some aspiration level,
are satisfactory at the moment,
are allowed to impair till some bound, and
are allowed to change freely.

A new subproblem is formed according to the classification and the connected information. This problem is solved alternatively by a multiobjective proximal bundle (MPB) method or genetic algorithms.

The flowchart of the NIMBUS algorithm is the following.

Note: Every WWW-NIMBUS -page includes a help page.

For further information, contact nimbus@mit.jyu.fi

References

Miettinen K. (1994) On the Methodology of Multiobjective Optimization with Applications, Doctoral Thesis, University of Jyväskylä, Department of Mathematics, Report 60.
Miettinen K., Mäkelä M.M. Interactive Bundle-based Method for Nondifferentiable Multiobjective Optimization: NIMBUS, Optimization, Vol. 34, pp. 231-246, 1995.
Miettinen K., Mäkelä M.M., Mäkinen R.A.E. Interactive Multiobjective Optimization System NIMBUS Applied to Nonsmooth Structural Design Problems, in "System Modelling and Optimization", Proceedings of the 17th IFIP Conference on System Modelling and Optimization, Edited by J. Dolezal, J. Fidler, Chapman & Hall, London, 379-385, 1996.
Miettinen K., Mäkelä M.M., Männikkö T. Nondifferentiable Multiobjective Optimizer NIMBUS Applied to an Optimal Control Problem of Continuous Casting, Report 22/1996, University of Jyväskylä, Department of Mathematics, Laboratory of Scientific Computing, 1996.
Miettinen K., Mäkelä M.M. Comparing Two Versions of NIMBUS Optimization System, Report 23/1996, University of Jyväskylä, Department of Mathematics, Laboratory of Scientific Computing, 1996.
Miettinen K., Mäkelä M.M. Interactive Method NIMBUS for Nondifferentiable Multiobjective Optimization Problems , in "Multicriteria Analysis", Proceedings of the XIth International Conference on MCDM, Edited by J. Climaco, Springer-Verlag, Berlin, Heidelberg, pp. 310--319, 1997.
Miettinen K., Mäkelä M.M., Männikkö T. Optimal Control of Continuous Casting by Nondifferentiable Multiobjective Optimization, Computational Optimization and Applications, Vol. 11, pp. 177-194, 1998.
Miettinen K., Mäkelä M.M. Interactive MCDM Support System in the Internet in "Trends in Multicriteria Decision Making", Proceedings of the 13th International Conference on Multiple Criteria Decision Making, Edited by T.J. Stewart, R.C. van den Honert, Springer-Verlag, pp. 424-433, 1998.
Miettinen K., Mäkelä M.M. Theoretical and Computational Comparison of Multiobjective Optimization Methods NIMBUS and RD, Report 5/1998, University of Jyväskylä, Department of Mathematics, Laboratory of Scientific Computing, Jyväskylä, 1998.
Miettinen K., Mäkelä M.M. Optimization System WWW-NIMBUS, Report 9/1998, University of Jyväskylä, Department of Mathematics, Laboratory of Scientific Computing, Jyväskylä, 1998
Miettinen, K. (1999) Nonlinear Multiobjective Optimization, Kluwer Academic Publishers, Boston.
Miettinen K., Mäkelä M.M. Comparative Evaluation of Some Interactive Reference Point-based Methods for Multi-Objective Optimisation, Journal of the Operational Research Society, Vol. 50, pp. 949-959, 1999.
Miettinen K., Mäkelä M.M. Interactive Multiobjective Optimization System WWW-NIMBUS on the Internet, Computers & Operations Research, Vol. 27, pp. 709-723, 2000. doi:10.1016/S0305-0548(99)00115-X
Miettinen K., Mäkelä M.M. Synchronous Scalarizing Functions within the Interactive NIMBUS Method for Multiobjective Optimization, Reports of the Department of Mathematical Information Technology, Series B, Scientific Computing, No. B 9/2002, University of Jyväskylä, 2002.
Miettinen K., Mäkelä M.M. On Scalarizing Functions in Multiobjective Optimization, OR Spectrum, 24, 193-213, 2002.
Miettinen K., Mäkelä M.M., Toivanen J. Numerical Comparison of Some Penalty-Based Constraint Handling Techniques in Genetic Algorithms, Journal of Global Optimization, Vol 27(4), pp. 427-446, 2003.
Hakanen J., Miettinen K. and Mäkelä M.M. An Application of Multiobjective Optimization to Process Simulation, in "CD-rom Proceedings of ECCOMAS 2004, 4th European Congress on Computational Methods in Applied Sciences and Engineering", (Eds. P. Neittaanmäki, T. Rossi, S. Korotov, E. Onate, J. Periaux and D. Knörzer), Jyväskylä, Finland, July 24-28, 2004.
Miettinen K., Mäkelä M.M. Synchronous Approach in Interactive Multiobjective Optimization, European Journal of Operational Research, Vol. 170/3, pp. 909-922, 2006. doi:10.1016/j.ejor.2004.07.052

Current NIMBUS usage statistics

Old NIMBUS usage statistics