Abstract
A hierarchical algorithm for generating Pareto-optimal alternatives for convex multicriteria problems is derived. At the upper level, values for Lagrange multipliers of the coupling constraints are first given. Then at the subsystems, Pareto-optimal values are determined for the subsystem objectives, whereby an additional term or an additional objective is included due to the Lagrange multipliers. In the subsystem optimizations, the coupling equations between the subsystems are not satisfied; therefore, the method is called nonfeasible. Finally, the upper level checks which of the subsystem solutions satisfy the coupling constraints; these solutions are Pareto-optimal solutions for the overall system.
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References
Haimes, Y. Y., Tarvainen, K., Shima, T., andThadathil, J.,Hierarchical Multiobjective Analysis of Large-Scale Systems, Hemisphere, Washington, DC, 1990.
Li, D., andHaimes, Y. Y.,The Envelope Approach for Multiobjective Optimization Problems, IEEE Transactions on Systems, Man, and Cybernetics, Vol. 17, No. 6, pp. 1026–1038, 1987.
Li, D. andHaimes, Y. Y.,Hierarchical Generating Method for Large-Scale Multiobjective Systems, Journal of Optimization Theory and Applications, Vol. 54, No. 2, pp. 303–333, 1987.
Chankong, V., andHaimes, Y. Y. Multiobjective Decision Making: Theory and Methodology, North-Holland, Amsterdam, Holland, 1983.
Bazaraa, M. S., andShetty, C. M.,Nonlinear Programming, Theory and Algorithms, Wiley, New York, New York, 1979.
Lasdon, L. S.,Optimization Theory for Large Systems, Macmillan, New York, New York, 1970.
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Communicated by G. Leimann
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Tarvainen, K. Generating pareto-optimal alternatives by a nonfeasible hierarchical method. J Optim Theory Appl 80, 181–185 (1994). https://doi.org/10.1007/BF02196601
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DOI: https://doi.org/10.1007/BF02196601