Interactive Multiobjective Optimization Methods for Continuous Problems

Lecturer

Readings

• Kaisa Miettinen: Nonlinear Multiobjective Optimization, Kluwer Academic Publishers, 1999

Contents

Nonlinear Continuous Multiobjective Optimization. Basics of several interactive methods for nonlinear continuous multiobjective optimization with some applications.

Exercises

1. Use WWW-NIMBUS and solve the nutrition problem (saved in the system for guest users). Use different scalar solvers.
2. Input some multiobjective optimization problem in WWW-NIMBUS and use different scalarizing functions, the solution database and visualizations. Which type of visualization do you prefer?
3. Use both the symbolic and graphical classification in WWW-NIMBUS. Which one do you prefer? Why?

Further material on the Internet

• Practical Multiobjective Optimisation, by C. Lucas
• Evolutionary Multiobjective Optimization by C.A. Coello Coello

Further printed material

• Chankong V., Y. Y. Haimes: Multiobjective Decision Making Theory and Methodology, Elsevier Science Publishing Co., New York, 1983 (multiobjective optimization)
• Deb K.: Multi-Objective Optimization using Evolutionary Algorithms, John Wiley & Sons, 2001 (covering collection of methods for generating a representation of the Pareto optimal set using evolutionary algorithms)
• Hwang C. L., A. S. M. Masud: Multiple Objective Decision Making - Methods and Applications: A State-of-the-Art Survey, Springer-Verlag, Berlin, Heidelberg, 1979 (nice collection of different methods for multiobjective optimization with examples)
• Miettinen K., M. M. Mäkelä, P. Neittaanmäki, J. Periaux (Eds.) Evolutionary Algorithms in Engineering and Computer Science, John Wiley & Sons, 1999 (evolutionary algorithms and different applications)
• Steuer R. E.: Multiple Criteria Optimization: Theory, Computation, and Applications , John Wiley & Sons, Inc., 1986 (multiobjective optimization methods, mostly linear)

• Hämäläinen, J.P., Miettinen, K., Tarvainen, P., Toivanen, J., Multiobjective Paper Machine Headbox Shape Optimization, in "Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems", Ed. by Giannakoglou, K.C., Tsahalis, D.T., Periaux, J., Papailiou, K.D. and Fogarty, T., Proceedings of the EUROGEN2001 Conference, Athens, Greece, September 19-21, 2001, International Center for Numerical Methods in Engineering (CIMNE), 343-348, 2002 (application of evolutionary multiobjective optimization to paper machine headbox design)
• Hämäläinen, J., Miettinen, K., Tarvainen, P., Toivanen, J., Interactive Solution Approach to a Multiobjective Optimization Problem in Paper Machine Headbox Design, Journal of Optimization Theory and Applications 116(2), 265-281, 2003 (application of NIMBUS to paper machine headbox design with three objectives)
• Miettinen, K., Some Methods for Nonlinear Multi-Objective Optimization, in "Evolutionary Multi-Criterion Optimization", Ed. by Zitzler E., Deb K., Thiele L., Coello Coello C. A., Corne D., First International Conference, EMO 2001, Zurich, Switzerland, March 2001, Proceedings, Springer-Verlag, Berlin, Heidelberg, 1-20, 2001
• Miettinen, K. Interactive Nonlinear Multiobjective Procedures, in "Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys", Ed. by Ehrgott, M. and Gandibleux, X., Kluwer Academic Publishers, 227-276, 2002
• Miettinen, K., Supporting Comparison of Alternatives in Multiple Criteria Decision Making with the Help of Visualizations, Reports of the Department of Mathematical Information Technology, Series B, Scientific Computing, No. B 1/2003, University of Jyväskylä, Jyväskylä, 2003 (visualizations of alternatives)
• Miettinen, K., Lotov, A.V., Kamenev, G.K., Berezkin, V.E., Integration of Two Multiobjective Optimization Methods for Nonlinear Problems, Optimization Methods and Software 18(1), 63-80, 2003 (hybrids of NIMBUS and feasible goasl method)
• Miettinen, K. and Mäkelä, M.M., Interactive Bundle-Based Method for Nondifferentiable Multiobjective Optimization: NIMBUS, Optimization 34, 231-246, 1995 (introduction of the interactive NIMBUS method)
• Miettinen, K., Mäkelä, M.M., Comparative Evaluation of Some Interactive Reference Point-based Methods for Multi-Objective Optimisation, Journal of the Operational Research Society 50, 949-959, 1999
• Miettinen, K., Mäkelä, M.M., Interactive Multiobjective Optimization System WWW-NIMBUS on the Internet, Computers & Operations Research 27, 709-723, 2000 (description of WWW-NIMBUS)
• Miettinen, K., Mäkelä, M.M., On Cone Characterizations of Weak, Proper and Pareto Optimality in Multiobjective Optimization, Mathematical Methods of Operations Research, 53, 233-245, 2001. Full text in PDF format
• Miettinen, K., Mäkelä, M.M., On Generalized Trade-Off Directions in Nonconvex Multiobjective Optimization, Mathematical Programming 92, 141-151, 2002. Published online February 14, 2002. Full text in PDF format
• Miettinen, K., Mäkelä, M.M., On Scalarizing Functions in Multiobjective Optimization, OR Spectrum, 24, 193-213, 2002 (comparison of different classification and reference point based scalarizing functions)
• 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, Jyväskylä, 2002 (synchronous variant of the NIMBUS method)
• Miettinen, K., Mäkelä, M.M., Characterizing Generalized Trade-Off Directions, Mathematical Method of Operations Research 57(1), 89-100, 2003
• Miettinen, K., Mäkelä, M.M. and 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", Ed. by Dolezal, J., Fidler, J., 17th IFIP Conference on System Modelling and Optimization, Prague, Czech Republic, Chapman & Hall, London, 379-385, 1996
• Miettinen, K., Mäkelä, M.M and Männikkö, T., Optimal Control of Continuous Casting by Nondifferentiable Multiobjective Optimization, Computational Optimization and Applications 11, 177-194, 1998 (application of NIMBUS to continuous casting of steel)
• Miettinen, K., Mäkelä, M.M., Toivanen, J., Numerical Comparison of Some Penalty-Based Constraint Handling Techniques in Genetic Algorithms, Journal of Global Optimization, 27(4), 427-446, 2003 (comparison of methods based on adaptive penalties, superiority of feasible solutions and parameter free penalties)
• Toivanen, J., Hämäläinen, J. Miettinen, K., Tarvainen, P., Designing Paper Machine Headbox Using GA, Materials and Manufacturing Processes, 18(3), 533-541, 2003 (application of evolutionary multiobjective optimization)
• Miettinen, K., Mäkelä, M.M., Synchronous Approach in Interactive Multiobjective Optimization, European Journal of Operational Research, to appear. (description of the synchronous version of the NIMBUS method)
• Hakanen, J., Miettinen, K., Mäkelä, M.M., An Application of Multiobjective Optimization to Process Simulation, in "4th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS2004", CD-Proceedings Ed. by Neittaanmäki, P., Rossi, T., Korotov, S., Onate, E., Periaux, J., Knörzer, D., Volume II, 2004
• Kaario, K., Miettinen, K., Mäkelä, M.M., Saariluoma, P., Symbolic and Graphic Classification in Interactive Multiobjective Optimization System WWW-NIMBUS, in "4th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS2004", CD-Proceedings Ed. by Neittaanmäki, P., Rossi, T., Korotov, S., Onate, E., Periaux, J., Knörzer, D., Volume II, 2004
• Hämäläinen. J., Miettinen, K., Madetoja, E., Mäkelä, M.M., Tarvainen, P., Multiobjective Decision Making for Papermaking, in "MCDM2004, the 17th International Conference on Multiple Criteria Decision Making", CD-Proceedings, Ed. by Wedley, W.C., 2004.
• Hakanen, J., Mäkelä, M.M., Miettinen, K., Manninen, J., On Interactive Multiobjective Optimization with NIMBUS in Chemical Process Design, in "MCDM2004, the 17th International Conference on Multiple Criteria Decision Making", CD-Proceedings, Ed. by Wedley, W.C., 2004.

Software operating on the Internet - free for academic purposes

Further links

• List collected by Kaisa Miettinen
• International Society on Multiple Criteria Decision Making

Keywords for search engines

• Multiobjective/multi-objective/multiple objectives/multicriteria/multiple criteria/vector optimization