A mathematical basis for satisficing decision making

Wierzbicki, Andrzej P.

doi:10.1016/0270-0255(82)90038-0

Cited by 430 publications

(141 citation statements)

References 18 publications

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“…Problem (2) uses an achievement (scalarizing) function employed in the reference point method (Wierzbicki 1980(Wierzbicki , 1982(Wierzbicki , 1986 where w i , i = 1, . .…”

Section: Navigation Phasementioning

confidence: 99%

“…If the DM has specified preferences in the form of reference points or classifications, it may be natural and intuitive to continue with interactive reference point (Jaszkiewicz and Slowiński 1999;Wierzbicki 1982) or classification based methods (Miettinen and Mäkelä 1995, 2000, 2006Nakayama and Sawaragi 1984), respectively. Alternatively, the DM can continue the learning phase and, for example, ask for a more accurate approximation of the Pareto optimal set to be generated in the neighborhood of the selected solution (see, e.g., Klamroth and Miettinen 2008).…”

Section: Navigation Phasementioning

confidence: 99%

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Pareto navigator for interactive nonlinear multiobjective optimization

Eskelinen¹,

Miettinen

Klamroth

et al. 2008

OR Spectrum

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We describe a new interactive learning-oriented method called Pareto navigator for nonlinear multiobjective optimization. In the method, first a polyhedral approximation of the Pareto optimal set is formed in the objective function space using a relatively small set of Pareto optimal solutions representing the Pareto optimal set. Then the decision maker can navigate around the polyhedral approximation and direct the search for promising regions where the most preferred solution could be located. In this way, the decision maker can learn about the interdependencies between the conflicting objectives and possibly adjust one's preferences. Once an interesting region has been identified, the polyhedral approximation can be made more accurate in that region or the decision maker can ask for the closest counterpart in the actual Pareto optimal set. If desired, (s)he can continue with another interactive method from the solution obtained. Pareto navigator can be seen as a nonlinear extension of the linear Pareto race method. After the representative set of Pareto optimal solutions has been generated, Pareto navigator is computationally efficient because the computations are performed in the polyhedral approximation and for that reason function evaluations of the actual objective functions are not needed. Thus, the method is well suited especially for problems with computationally costly functions. Furthermore, thanks to the visualization technique used, the method is applicable also for problems with three or more objective functions, and in fact it is best suited for such problems. After introducing the method in more detail, we illustrate it and the underlying ideas with an example.

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“…Problem (2) uses an achievement (scalarizing) function employed in the reference point method (Wierzbicki 1980(Wierzbicki , 1982(Wierzbicki , 1986 where w i , i = 1, . .…”

Section: Navigation Phasementioning

confidence: 99%

Section: Navigation Phasementioning

confidence: 99%

Pareto navigator for interactive nonlinear multiobjective optimization

Eskelinen¹,

Miettinen

Klamroth

et al. 2008

OR Spectrum

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show abstract

“…The second paper, by Ogryczak, focuses on the reference point method (RPM) (Wierzbicki 1982) and develops an extension incorporating the importance weighting of several achievements following the concept of the WOWA operator (Torra 1997). This paper is followed by another one by Cabrerizo, Moreno, Pérez, and Herrera-Viedma in which the authors analyze different consensus approaches in fuzzy decision making.…”

Section: Structure Of the Special Issuementioning

confidence: 99%

Soft Computing in decision modeling

Torra

Narukawa

2009

Soft Comput

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“…for all k ∈ K and any strict inequality would contradict efficiency of x o within the restricted problem (19). Thus,…”

Section: Fair Allocations and Partial Throughputsmentioning

confidence: 97%

“…On the other hand, quantity r represents the number of various possible outcomes (flow sizes). In order to reduce the problem size one may attempt the restrict the number of distinguished outcome values (criteria in the problem (18) (19), then it is an efficient (Pareto-optimal) solution of the multiple criteria problem (7) and it can be fairly dominated only by another efficient solution x of (19) with exactly the same values of criteria: …”

Section: Fair Allocations and Partial Throughputsmentioning

confidence: 99%

On fair and efficient bandwidth allocation by the multiple target approach

Ogryczak

Milewski

Wierzbicki

2006 2nd Conference on Next Generation Internet Design and Engineering, 2006. NGI '06.

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Abstract-Expanding demand on the Internet services leads to an increased role of the network dimensioning problem for elastic traffic where one needs to allocate bandwidth to maximize service flows and simultaneously to reach a fair treatment of all the elastic services. Thus, both the overall efficiency (throughput) and the fairness (equity) among various services are important. The Max-Min Fairness (MMF) approach, widely used to this problem, guarantees fairness but may lead to significant losses in the overall throughput of the network. In this paper we show how the concepts of multiple criteria equitable optimization can be effectively used to generate various fair resource allocation schemes. We introduce a multiple target model equivalent to equitable optimization and we develop a corresponding procedure to generate fair efficient bandwidth allocations. The procedure is tested on a sample network dimensioning problem and its abilities to model various preferences are demonstrated.

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A mathematical basis for satisficing decision making

Cited by 430 publications

References 18 publications

Pareto navigator for interactive nonlinear multiobjective optimization

Pareto navigator for interactive nonlinear multiobjective optimization

Soft Computing in decision modeling

On fair and efficient bandwidth allocation by the multiple target approach

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