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Autor
Kadziński Miłosz (Institute of Computing Science, Poznań University of Technology), Słowiński Roman (Institute of Computing Science, Poznań University of Technology)
Tytuł
Preference-Driven Multiobjective Optimization Using Robust Ordinal Regression for Cone Contraction
Źródło
Multiple Criteria Decision Making / University of Economics in Katowice, 2013, vol. 8, s. 67-83, rys., tab., bibliogr. 15 poz.
Słowa kluczowe
Optymalizacja wielokryterialna, Podejmowanie decyzji, Odporne metody statystyczne
Multiple criteria optimization, Decision making, Robust statistical methods
Uwagi
summ.
Abstrakt
We present a new interactive procedure for multiobjective optimization problems (MOO), which involves robust ordinal regression in contraction of the preference cone in the objective space. The most preferred solution is achieved by means of a systematic dialogue with the decision maker (DM) during which (s)he species pairwise comparisons of some non-dominated solutions from a current sample. The origin of the cone is located at a reference point chosen by the DM. It is formed by all directions of isoquants of the achievement scalarizing functions compatible with the pairwise comparisons of non-dominated solutions provided by the DM. The compatibility is assured by robust ordinal regression, i.e. the DM's statements concerning strict or weak preference relations for pairs of compared solutions are represented by all compatible sets of weights of the achievement scalarizing function. In successive iterations, when new pairwise comparisons of solutions are provided, the cone is contracted and gradually focused on a subregion of the Pareto optimal set of greatest interest. The DM is allowed to change the reference point and the set of pairwise comparisons at any stage of the method. Such preference information does not need much cognitive e ort on the part of the DM. The phases of preference elicitation and cone contraction alternate until the DM nds at least one satisfactory solution, or there is no such solution for the current problem setting. (original abstract)
Dostępne w
Biblioteka Główna Uniwersytetu Ekonomicznego w Krakowie
Biblioteka Szkoły Głównej Handlowej
Biblioteka Główna Uniwersytetu Ekonomicznego w Katowicach
Biblioteka Główna Uniwersytetu Ekonomicznego w Poznaniu
Biblioteka Główna Uniwersytetu Ekonomicznego we Wrocławiu
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Bibliografia
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  1. Branke J., Deb K., Miettinen K., Słowiński R. (eds.) (2008), Multiobjective Optimization: Interactive and Evolutionary Approaches, Series: Lecture Notes in Computer Science, Vol. 5252, Springer, Berlin.
  2. Granat J., Guerriero F. (2003), The Interactive Analysis of the Multicriteria Shortest Path Problem by the Reference Point Method, European Journal of Operational Research. 151(1). p. 103 - 118.
  3. Greco S., Kadziński M., Mousseau V., Słowiński R. (2011). ELECTREGKMS: Robust Ordinal Regression for Outranking Methods. European Journal of Operational Research. 214(1). p. 118-135. DOI: 10.1016/j.ejor.2011.03.045.
  4. Greco S., Mousseau V., Słowiński R. (2008). Ordinal Regression Revisited: Multiple Criteria Ranking Using a Set of Additive Value Functions, European Journal of Operational Research. 191(2). p. 415-435.
  5. Jaszkiewicz A., Słowiński R. (1992), Cone Contraction Method with Visual Interaction for Multiple Objective Non Linear Programmes, Journal of Multi-Criteria Decision Analysis. 1(1). p. 29-46.
  6. Kadziński M., Słowiński R. (2012). Interactive Robust Cone Contraction Method for Multiple Objective Optimization Problems. Int. Journal of Information Technology and Decision Making, 11(2), p. 327-357.
  7. Kaliszewski I. (1994), Quantitative Pareto Analysis by Cone Separation Technique. Kluwer Academic Publishers, Dordrecht.
  8. Ogryczak W. (2001), On Goal Programming Formulations of the Reference Point Method, The Journal of the Operational Research Society, 52. p. 691-698.
  9. Steuer R.,. Choo E. (1983), An Interactive Weighted Tchebycheff Procedure for Multiple Objective Programming, Mathematical Programming, 26(1). p. 326-344.
  10. Steuer R.E. (1978), Vector-Maximum Gradient Cone Contraction Techniques, in: Lecture Notes in Economics and Mathematical Systems, Vol. 155, Springer, Berlin, p. 462-481.
  11. Vanderpooten D., Vincke P. (1997), Description and Analysis of Some Representative Interactive Multicriteria Procedures, Appl. Math. Comp.. 83(2-3). p. 261-280.
  12. Wierzbicki A. (1982), A Mathematical Basis for Satisficing Decision Making. Mathematical Modelling, 3, p. 391-405.
  13. Wierzbicki A. (1986), On the Completeness and Constructiveness of Para-metric Characterizations to Vector Optimization Problems, OR Spektrum, 8, p. 73-87.
  14. Wierzbicki A. (1999), Reference Point Approaches, in: Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory, and Applications, eds. T. Gal, T. Stewart. T. Hanne, Kluwer Academic Publishers, Boston, p. 9.1-9.39.
  15. Zitzler E., Deb K., Thiele L. (2000), Comparison of Multiobjective Evolutionary Algorithms: Empirical Results, Evolutionary Computation, 8(2), p. 173-195.
Cytowane przez
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ISSN
2084-1531
Język
eng
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