A classification of the weighting schemes in reference point procedures for multiobjective programming

Ruiz, Francisco; Luque, Mariano; Cabello, José Manuel Jiménez

doi:10.1057/palgrave.jors.2602577

Cited by 44 publications

(27 citation statements)

References 14 publications

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“…Further, following the concept of Weighted OWA (Torra 1997), the importance weighting of several achievements may be incorporated into the RPM. Such a WOWA enhancement of the RPM uses importance weights to affect achievement importance by rescaling accordingly its measure within the distribution of achievements rather than straightforward rescaling of achievement values (Ruiz et al 2009). The ordered regularizations are more complicated in implementation due to the requirement of pointwise ordering of component achievements.…”

Section: Discussionmentioning

confidence: 99%

“…Typical RPM model allows weighting of several achievements only by straightforward rescaling of the achievement values (Ruiz et al 2009). The OWA RPM model enables one to introduce importance weights to affect achievement importance by rescaling accordingly its measure within the distribution of achievements as defined in the so-called weighted OWA (WOWA) aggregation (Torra 1997;Liu 2006).…”

Section: Wowa Enhancementmentioning

confidence: 99%

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

Ogryczak

2009

Soft Comput

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Wowa Enhancementmentioning

confidence: 99%

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

Ogryczak

2009

Soft Comput

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“…In most of the interactive methods using achievement functions, weights are kept unaltered during the whole process and their purpose is mainly to normalize different ranges of objectives. However, these weights can have different roles (from the original idea of purely normalizing to fully preferential) as described in Ruiz et al (2008) and they can be varied to get different Pareto optimal solutions (see, for example, Luque et al (2009)). …”

Section: Basic Concepts and Notationsmentioning

confidence: 99%

NAUTILUS framework: towards trade-off-free interaction in multiobjective optimization

Miettinen

Ruiz

2016

J Bus Econ

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In this paper, we present a framework of different interactive NAU-TILUS methods for multiobjective optimization. In interactive methods, the decision maker iteratively sees solution alternatives and provides one's preferences in order to find the most preferred solution. We question the widely used setting that the solutions shown to the decision maker should all be Pareto optimal which implies that improvement in any objective function necessitates allowing impairment in some others. Instead, in NAUTILUS we enable the decision maker to make a free search without having to trade-off by starting from an inferior solution and iteratively approaching the Pareto optimal set by allowing all objective functions to improve. The framework presented consists of different modules for preference elicitation and optimization. Four main NAUTILUS method variants are introduced as well as ideas of utilizing the framework in a flexible way to derive further variants.

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“…For further investigation, it is concluded that the reference point could be projected to different Pareto optimal solutions between A and B by altering weighting vectors 26 . And recently, many researchers focus on the influences of different weights on the DM preferences 17,27,28 . There are also other achievement scalarizing functions that are frequently used in literatures, for example,…”

Section: Co-published By Atlantis Press and Taylor And Francismentioning

confidence: 99%

Hybrid Multiobjective Differential Evolution Incorporating Preference Based Local Search

Dong¹,

Wang²

2014

IJCIS

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The performance of Differential Evolution (DE) for multiobjective optimization problems (MOPs) can be greatly enhanced by hybridizing with other techniques. In this paper, a new hybrid DE incorporating preference based local search is proposed. In every generation, a set of nondominated solutions is generated by DE operation. Usually these solutions distribute unevenly along the obtained nondominated set. To get solutions in the sparse region of the nondominated set, a mini population and preference based local search algorithm is specifically designed, and is used to exploit the sparse region by optimizing an achievement scalarizing function (ASF) with the dynamically adjusted reference point. As a result, multiple solutions in the sparse region can be obtained. Moreover, to retain uniformly spread nondominated solutions, an improved ε-dominance strategy, which would not delete the extreme points found during the evolution, is proposed to update the external archive set. Finally, numerical results and comparisons demonstrate the efficiency of the proposed algorithm.

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A classification of the weighting schemes in reference point procedures for multiobjective programming

Cited by 44 publications

References 14 publications

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

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

NAUTILUS framework: towards trade-off-free interaction in multiobjective optimization

Hybrid Multiobjective Differential Evolution Incorporating Preference Based Local Search

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