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reference point method with importance weighted ordered partial achievements

TOP 2011年第2期19卷 380-401页

作者： Ogryczak, Wlodzimierz Kozlowski, Bartosz Warsaw Univ Technol Inst Control & Computat Engn PL-00665 Warsaw Poland Int Inst Appl Syst Anal A-2361 Laxenburg Austria

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.

关键词： Multicriteria decision making Interactive methods Efficiency reference point method OWA WOWA

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reference point method with importance weighted ordered achievements

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8th International Conference on Fuzzy Logic and Intelligent Technologies in Nuclear Science

作者： Ogryczak, W. Kozlowski, B. Warsaw Univ Technol Inst Control & Comp Engg PL-00665 Warsaw Poland

ISBN: (纸本)9789812799463

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 final scalarizing achievement function is built as the augmented max-min aggregation of partial achievements with respect to the given reference levels. 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.

关键词： multicriteria decision making interactive methods efficiency reference point method OWA WOWA

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The interactive analysis of the multicriteria shortest path problem by the reference point method

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2003年第1期151卷 103-118页

作者： Granat, J Guerriero, F Univ Calabria Dipartimento Elettr Informat & Sistemist I-87030 Arcavacata Di Rende CS Italy Warsaw Univ Technol Inst Control & Computat Engn Warsaw Poland Inst Natl Telecommun Warsaw Poland

The multicriteria shortest path problem is considered. The paper presents the interactive method of analyzing this problem by the reference point approach. The reference point guided labeling algorithm was developed. This algorithm finds the Pareto-optimal shortest path which is best attuned to the specified preferences. (C) 2002 Elsevier B.V. All rights reserved.

关键词： multiple criteria analysis pareto-optimal paths reference point method

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A decision support model based on a reference point method for end-of-life electronic product management

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2007年第11-12期31卷 1251-1259页

作者： Jin, Kai Zhang, Hong C. Texas A&M Univ Dept Mech & Ind Engn Kingsville TX 78363 USA Texas Tech Univ Dept Ind Engn Lubbock TX 79404 USA

Although a decision support system is an efficient tool that has been widely used in management areas, it still encounters some problems when it is implemented in an environmentally conscious decision- making problem. Those problems include lack of sufficient and reliable data on environmental impact of end-of- life product treatment, material composition analysis, proper expression of the users' aspiration levels, system architecture, and the proper optimization method. This paper proposes a systematic decision- making tool for end-of-life (EOL) electronic product recycling scenario analysis and selection. This model can help original equipment manufacturers (OEMs) specify the most satisfactory recyclers based on the buyers' prices and environmental impacts;it can also assist recyclers decide the recycling scenarios for a batch of end-of-life electronic products based on the EOL value, environmental impacts, and processing time. The decision- making process includes the following steps: selection and definition of attributes, quantifying impacts, scaling of attributes, aggregation, and an interactive optimization process. A reference point method is used in the optimization process.

关键词： multiple criteria analysis decision support systems electronic product recovery reference point method

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Synthetic indicators of mutual funds' environmental responsibility: An application of the reference point method

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2014年第1期236卷 313-325页

作者： Cabello, J. M. Ruiz, F. Perez-Gladish, B. Mendez-Rodriguez, P. Univ Malaga Dpt Appl Econ Math E-29071 Malaga Spain Univ Oviedo Sch Business & Econ Dpt Quantitat Econ E-33006 Oviedo Asturias Spain

Socially Responsible Investing (SRI) is broadly defined as an investment process that integrates not only financial but also social, environmental, and ethical (SEE) considerations into investment decision making. SRI has grown rapidly around the world in the last decades. In the last years, given the causes of the 2008 financial crisis, ethical, social, environmental and governance concerns have become even more relevant investment decision criteria. However, while a diverse set of models have been developed to support investment decision-making based on financial criteria, models including also social responsibility criteria are rather scarce. The aim of this paper, in which we focus on the environmental dimension, is to assist individual investors in their investment decisions providing them with a synthetic indicator of mutual funds' environmental responsibility, which is by nature a multicriteria concept and therefore multicriteria techniques are to be used to measure it. The proposed approach is based on the double (reservation-aspiration) reference point method. This scheme is applied to each fund of a randomly selected set of U.S. equity mutual funds, in order to determine, on the basis of a given set of indicators, a pair of synthetic indicators that measure the weak and the strong environmental responsibility degree of each mutual fund, relying on the particular preferences of the investor. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Socially Responsible Investment Environment Equity mutual funds evaluation Multicriteria decision analysis reference point method Synthetic indicators

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Incorporating preferential weights as a benchmark into a Sequential reference point method

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第2期291卷 575-585页

作者： Jimenez, Mariano Bilbao-Terol, Amelia Arenas-Parra, Mar Univ Basque Country Dept Appl Econ 1 UPV EHU Leioa Spain Univ Oviedo Dept Quantitat Econ Avda CristoS-N E-33006 Oviedo Spain

In multi-objective optimization models, it is common that the decision maker expresses the relative importance of objectives through a weighting scheme. However, many solving techniques do not assure that the corresponding solution fits the preferential weights. It could be the case that an objective with a very low weight achieves a good value, whereas another with a high weight yields a very poor achievement. In order to overcome the aforementioned drawback, this paper proposes a new resolution method based on the well-known reference point method. The methodology consists in generating a sequence of reference point method models which share the same reference point fixed at the vector of preferential weights. In the iterative process, the projection direction on the Pareto frontier changes in each iteration according to the deviations between the preferential weights and the current normalised objective values. In this way, a sequence of Pareto-efficient solutions is generated which converges towards a solution that best fits the decision maker's preferential weights. The proposed method is illustrated by means of a numerical example. In order to show its feasibility and usefulness, the methodology is applied to a portfolio selection problem where the corporate sustainability performance of each firm is taken into account. (c) 2020 Elsevier B.V. All rights reserved.

关键词： Multi-objective optimisation Pareto optimality Preferential weights reference point method

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Goal programming, compromise programming and reference point method formulations: linkages and utility interpretations

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 1998年第9期49卷 986-991页

作者： Romero, C Tamiz, M Jones, DF Univ Portsmouth Sch Math Studies Portsmouth PO1 2EG Hants England Tech Univ Madrid Madrid Spain

This paper looks at connections between the multi-criteria techniques of goal programming, compromise programming, and the reference point method. The utility function structure of each method is examined and interpretation of the techniques in terms of pareto efficiency and the equilibrated nature of the solution is given. Means of ensuring pareto efficiency whilst maintaining as much as possible the equilibrated character are given for a certain class of model. methods for ensuring conceptual correctness and computational accuracy by reducing reference point models to equivalent goal programmes are given. The findings are illustrated by means of an example.

关键词： MCDM compromise programming goal programming reference point method utility theory

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Ordered weighted enhancement of preference modeling in the reference point method for multiple criteria optimization

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SOFT COMPUTING 2010年第5期14卷 435-450页

作者： Ogryczak, Wlodzimierz Warsaw Univ Technol Inst Control & Computat Engn PL-00665 Warsaw Poland

The reference point method is an interactive technique for multiple criteria optimization problems. It is based on the optimization of the scalarizing achievement function built as the augmented max-min aggregation of individual outcomes with respect to the given reference levels. Actually, the worst individual achievement is optimized, but regularized with the term representing the average achievement. In order to avoid inconsistencies caused by the regularization, we apply the ordered weighted averages (OWA) with monotonic weights to combine all the individual achievements. Further, following the concept of the weighted OWA (WOWA), we incorporate the importance weighting of several achievements into the RPM. We show that the resulting WOWA RPM can be quite effectively implemented as an extension of the original constraints and criteria with simple linear inequalities.

关键词： Multicriteria decision making Aggregation methods reference point method OWA WOWA

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On goal programming formulations of the reference point method

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2001年第6期52卷 691-698页

作者： Ogryczak, W Warsaw Univ Technol Inst Control & Computat Engn PL-00665 Warsaw Poland

This paper discusses connections between the multi-criteria techniques of goal programming (GP) and the reference point method (RPM). Both approaches use a certain target point in the criterion (outcome) space as a key element to model decision maker preferences. Therefore, RPM can be expressed similarly to GP, in the modelling framework of deviational variables. The paper gives a systematic survey and analysis of the lexicographic GP models of RPM. The corresponding preference models are formalised and analysed with respect to target values interpretations as M;ell as the Pareto efficiency of their solutions. The properties of equity among the individual achievements of solutions are also analysed with respect to the Rawlsian principle of justice.

关键词： multi-objective goal programming reference point method efficiency equity

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POD-Based Bicriterial Optimal Control by the reference point method

POD-Based Bicriterial Optimal Control by the Reference Point...

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2nd IFAC Workshop on the Control of Systems Modeled by Partial Differential Equations (CPDE)

作者： Banholzer, Stefan Beermann, Dennis Volkwein, Stefan Univ Konstanz Dept Math & Stat D-78457 Constance Germany

In the present paper a bicriterial optimal control problem governed by a parabolic partial differential equation (PDE) and bilateral control constraints is considered. For the numerical optimization the reference point method is utilized. The PDE is discretized by a Galerkin approximation utilizing the method of proper orthogonal decomposition (POD). POD is a powerful approach to derive reduced-order approximations for evolution problems. Numerical examples illustrate the efficiency of the proposed strategy. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Optimal control multiobjective optimization reference point method proper orthogonal decomposition a-posteriori error analysis

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