Abstract
The Reference Point Method (RPM) is an interactive technique formalizing the so-called quasi-satisficing approach to multiple criteria optimization. The DM’s preferences are there specified in terms of reference (target) levels for several criteria. The reference levels are further used to build the scalarizing achievement function which generates an efficient solution when optimized. Typical RPM scalarizing functions are based on the augmented min-max aggregation where the worst individual achievement minimization process is additionally regularized with the average achievement. The regularization by the average achievement is easily implementable but it may disturb the basic min-max model. We show that the OWA regularization allows one to overcome this flaw since taking into account differences among all ordered achievement values. Further, allowing to define importance weights we introduce the WOWA enhanced RPM. Both the theoretical and implementation issues of the WOWA enhanced method are analyzed. Linear Programming implementation model is developed and proven.
The research was partially supported by the Polish Ministry of Science and Higher Education under the research grant N N516 4307 33.
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References
Granat, J., Makowski, M.: ISAAP – Interactive Specification and Analysis of Aspiration-Based Preferences. Eur. J. Opnl. Res. 122, 469–485 (2000)
Lewandowski, A., Wierzbicki, A.P.: Aspiration Based Decision Support Systems – Theory, Software and Applications. Springer, Berlin (1989)
Liu, X.: Some properties of the weighted OWA operator. IEEE Trans. Systems, Man Cyber. B 368, 118–127 (2006)
Ogryczak, W.: Preemptive reference point method. In: Climaco, J. (ed.) Multicriteria Analysis — Proceedings of the XIth International Conference on MCDM, pp. 156–167. Springer, Berlin (1997)
Ogryczak, W.: On Goal Programming Formulations of the Reference Point Method. J. Opnl. Res. Soc. 52, 691–698 (2001)
Ogryczak, W., Lahoda, S.: Aspiration/Reservation Decision Support – A Step Beyond Goal Programming. J. MCDA 1, 101–117 (1992)
Ogryczak, W., Studziński, K., Zorychta, K.: DINAS: A Computer-Assisted Analysis System for Multiobjective Transshipment problems with Facility Location. Comp. Opns. Res. 19, 637–647 (1992)
Ogryczak, W., Śliwiński, T.: On solving linear programs with the ordered weighted averaging objective. Eur. J. Opnl. Res. 148, 80–91 (2003)
Ogryczak, W., Śliwiński, T.: On Optimization of the Importance Weighted OWA Aggregation of Multiple Criteria. In: Gervasi, O., Gavrilova, M.L. (eds.) ICCSA 2007, Part I. LNCS, vol. 4705, pp. 804–817. Springer, Heidelberg (2007)
Ogryczak, W., Śliwiński, T.: On decision Support Under Risk by the WOWA Optimization. In: Mellouli, K. (ed.) ECSQARU 2007. LNCS (LNAI), vol. 4724, pp. 779–790. Springer, Heidelberg (2007)
Ogryczak, W., Tamir, A.: Minimizing the sum of the k largest functions in linear time. Inform. Proc. Let. 85, 117–122 (2003)
Ruiz, F., Luque, M., Cabello, J.M.: A classification of the weighting schemes in reference point procedures formultiobjective programming. J. Opnl. Res. Soc. (forthcoming)
Torra, V.: The weighted OWA operator. Int. J. Intell. Syst. 12, 153–166 (1997)
Torra, V., Narukawa, Y.: Modeling Decisions Information Fusion and Aggregation Operators. Springer, Berlin (2007)
Wierzbicki, A.P.: A Mathematical Basis for Satisficing Decision Making. Math. Modelling 3, 391–405 (1982)
Wierzbicki, A.P., Makowski, M., Wessels, J.: Model Based Decision Support Methodology with Environmental Applications. Kluwer, Dordrecht (2000)
Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. Systems, Man and Cyber. 18, 183–190 (1988)
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Ogryczak, W. (2008). WOWA Enhancement of the Preference Modeling in the Reference Point Method. In: Torra, V., Narukawa, Y. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2008. Lecture Notes in Computer Science(), vol 5285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88269-5_5
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DOI: https://doi.org/10.1007/978-3-540-88269-5_5
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