Abstract
We consider the situation where a decision-maker in a multicriteria optimization problem must follow additional constraints in the criteria space defined by availability of resources. The set defined by such constraints - called demanded set - is assumed to be uncertain as a result of a priori experts estimations. The analysis of numerous real-life situations showed that a method of looking for a non-dominated solution on the so-called skeleton allows to find a solution maximally safe with respect to the random perturbations of the demanded set. We formulate a maximal safety principle as a requirement that the expected value of distance from the solution chosen to the boundary of the demanded set were maximal. Then we prove that the search executed on the skeleton curve satisfies this principle for a class of demanded sets defined by aspiration levels.
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References
Gorecki, H., (1981). Problem of choice of an optimal solution in a multicriteria space. Proceedings of the 8th IFAC World Congress. Kyoto 1981; Pergamon Press, London, Vol. 10, pp 106–110.
Gorecki, H., A.M. Skulimowski (1986a). A joint consideration of multiple reference points in multicriteria decision-making. Found. Contr. Engrg. 11; No. 2.
Gorecki, H., A.M. Skulimowski (1986b). Group decision-making maximally safe with respectto the change of aspiration levels. (to appear).
Gorecki, H., G. Dobrowolski, J. Kopytowski, M. Zebrowski (1982). The quest for a concordance between technologies and resources as a multiobjective decision process. M. Grauer, A. Lewandowski, and A.P. Wierzbicki Eds. Multiobjective and Stochastic Optimization, IIASA Collaborative Paper CP-82-S12, Laxenburg, Austria, pp 463–476.
Gorecki, H., G. Dobrowolski, T. Rys, M. Wiecek, M. Zebrowski (1985). Decision support system based on the skeleton method - the HG package. Interactive Decision Making, Proc. Sopron 1984, pp 269–280.
Skulimowski, A.M. (1985a). Solving vector optimization problems via multilevel analysis of foreseen consequences. Found. of Control Engrg. 10; No. 1.
Skulimowski, A.M. (1985b). Generalized distance scalarization in Banach spaces Rev. Belge de Stat.Inf. Rech. Operationelle, 25, No.1, pp 3–14.
Skulimowski, A.M. (1986). A sufficient condition for 0-optimality of distance scalarizing procedures. Proc. of the Int. Conference on Vector Optimization J.Jahn, W.Krabs (Eds.), Darmstadt, 5–8 August 1986.
Wierzbicki, A.P. (1980). On the use of reference objectives in multicriteria optimization. G.Fandel, T.Gal (Eds.) Multiple Criteria Decision Making - Theory and Application.
Wiecek, M. (1984). The skeleton method in multicriteria problems. Found. Contr. Engrg., 9? No.4,pp 193–200.
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© 1989 Springer-Verlag Berlin Heidelberg
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Gorecki, H., Skulimowski, A.M.J. (1989). Safety Principle in Multiobjective Decision Support in the Decision Space Defined by Availability of Resources. In: Lewandowski, A., Wierzbicki, A.P. (eds) Aspiration Based Decision Support Systems. Lecture Notes in Economics and Mathematical Systems, vol 331. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21637-8_8
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DOI: https://doi.org/10.1007/978-3-662-21637-8_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51213-4
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