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Reference Point Method with Importance Weighted Partial Achievements

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Języki publikacji
EN
Abstrakty
EN
The reference point method (RPM) is based on the so-called augmented max-min aggregation where the worst individual achievement maximization process is additionally regularized with the average achievement. In order to avoid inconsistencies caused by the regularization, we replace it with the ordered weighted average (OWA) which combines all the individual achievements allocating the largest weight to the worst achievement, the second largest weight to the second worst achievement, and so on. Further following the concept of the weighted OWA (WOWA) we incorporate the importance weighting of several achievements into the RPM. Such a WOWA RPM approach uses importance weights to affect achievement importance by rescaling accordingly its measure within the distribution of achievements rather than by straightforward rescaling of achievement values. The recent progress in optimization methods for ordered averages allows us to implement the WOWA RPM quite effectively as extension of the original constraints and criteria with simple linear inequalities.
Rocznik
Tom
Strony
17--25
Opis fizyczny
Bibliogr. 21 poz., rys., tab.
Twórcy
autor
  • Institute of Control and Computation Engineering, Warsaw University of Technology, Nowowiejska st 15/19, 00-665 Warsaw, Poland, wogrycza@ia.pw.edu.pl
Bibliografia
  • [1] A. P. Wierzbicki, “A mathematical basis for satisficing decision making”, Math. Model., vol. 3, pp. 391–405, 1982.
  • [2] J. Granat and M. Makowski, “ISAAP – interactive specification and analysis of aspiration-based preferences”, Eur. J. Opnl. Res., vol. 122, pp. 469–485, 2000.
  • [3] A. Lewandowski and A. P. Wierzbicki, Aspiration Based Decision Support Systems – Theory, Software and Applications. Berlin: Springer, 1989.
  • [4] W. Ogryczak and S. Lahoda, “Aspiration/reservation decision support – a step beyond goal programming”, J. MCDA, vol. 1, pp. 101–117, 1992.
  • [5] A. P. Wierzbicki, M. Makowski, and J. Wessels, Model Based Decision Support Methodology with Environmental Applications. Dordrecht: Kluwer, 2000.
  • [6] W. Ogryczak and T. Śliwiński, “On solving linear programs with the ordered weighted averaging objective”, Eur. J. Opnl. Res., vol. 148, pp. 80–91, 2003.
  • [7] V. Torra, “The weighted OWA operator”, Int. J. Intell. Syst., vol. 12, pp. 153–166, 1997.
  • [8] F. Ruiz, M. Luque, and J. M. Cabello, “A classification of the weighting schemes in reference point procedures formultiobjective programming”, J. Opnl. Res. Soc., 2008 (forthcoming), doi: 10.1057/palgrave.jors.2602577.
  • [9] A. P. Wierzbicki, “On completeness and constructiveness of parametric characterizations to vector optimization problems”, OR Spectrum, vol. 8, pp. 73–87, 1986.
  • [10] K. Miettinen and M. M. M¨akel¨a, “On scalarizing functions in multiobjective optimization”, OR Spectrum, vol. 24, pp. 193–213, 2002.
  • [11] W. Ogryczak, “Preemptive reference point method”, in Multicriteria Analysis — Proceedings of the XIth International Conference on MCDM, J. Climaco, Ed. Berlin: Springer, 1997, pp. 156–167.
  • [12] W. Ogryczak, K. Studziński, and K. Zorychta, “DINAS: a computer-assisted analysis system for multiobjective transshipment problems with facility location”, Comp. Opns. Res., vol. 19, pp. 637–647, 1992.
  • [13] R. R. Yager, “On ordered weighted averaging aggregation operators in multicriteria decision making”, IEEE Trans. Syst., Man Cyber., vol. 18, pp. 183–190, 1988.
  • [14] R. R. Yager, “On the analytic representation of the Leximin ordering and its application to flexible constraint propagation”, Eur. J. Opnl. Res., vol. 102, pp. 176–192, 1997.
  • [15] W. Ogryczak, “On goal programming formulations of the reference point method”, J. Opnl. Res. Soc., vol. 52, pp. 691–698, 2001.
  • [16] W. Ogryczak and A. Tamir, “Minimizing the sum of the k largest functions in linear time”, Inform. Proc. Let., vol. 85, pp. 117–122, 2003.
  • [17] X. Liu, “Some properties of the weighted OWA operator”, IEEE Trans. Syst. Man Cyber. B, vol. 368, pp. 118–127, 2006.
  • [18] W. Ogryczak and T. Śliwiński, “On optimization of the importance weighted OWA aggregation of multiple criteria”, in International Conference Computational Science and Its Applications ICCSA 2007, LNCS, vol. 4705. Heidelberg: Springer, 2007, pp. 804–817.
  • [19] W. Ogryczak and T. Śliwiński, “On decision support under risk by the WOWA optimization”, in Ninth European Conference on Symbolic and Quanlitative Approaches to Reasoning with Uncertainty ECSQARU 2007, LNAI, vol. 4724. Heidelberg: Springer, 2007, pp. 779–790.
  • [20] W. Ogryczak and A. Ruszczyński, “Dual stochastic dominance and related mean-risk models”, SIAM J. Opt., vol. 13, pp. 60–78, 2002.
  • [21] M. M. Kostreva, W. Ogryczak, and A. Wierzbicki, “Equitable aggregations and multiple criteria analysis”, Eur. J. Opnl. Res., vol. 158, pp. 362–367, 2004.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BATA-0004-0038
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