Reference point method with importance weighted ordered partial achievements

Ogryczak, W. & Kozlowski, B. (2011). Reference point method with importance weighted ordered partial achievements. TOP 19 (2) 380-401. 10.1007/s11750-009-0121-4.

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The Reference Point Method (RPM) is a very convenient technique for interactive analysis of the multiple criteria optimization problems. The interactive analysis is navigated with the commonly accepted control parameters expressing reference levels for the individual objective functions. The partial achievement functions quantify the DM satisfaction from the individual outcomes with respect to the given reference levels, while the final scalarizing achievement function is built as the augmented max-min aggregation of the partial achievements. In order to avoid inconsistencies caused by the regularization, the max-min solution may be regularized by the Ordered Weighted Averages (OWA) with monotonic weights which combines all the partial 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), the importance weighting of several achievements may be incorporated 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 one to implement the WOWA RPM quite effectively as extension of the original constraints and criteria with simple linear inequalities. There is shown that the OWA and WOWA RPM models meet the crucial requirements with respect to the efficiency of generated solutions as well as the controllability of interactive analysis by the reference levels.

Item Type: Article
Uncontrolled Keywords: Multicriteria decision making; Interactive methods; Efficiency; Reference point method; OWA; WOWA
Research Programs: Ecosystems Services and Management (ESM)
Bibliographic Reference: TOP; 19(2):380-401 (December 2011) (Published online 02 November 2009)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 08:45
Last Modified: 27 Aug 2021 17:39

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