A modified weighted tchebycheff metric for multiple objective programming

Kaliszewski, Ignacy

doi:10.1016/0305-0548(87)90069-4

Cited by 59 publications

(26 citation statements)

References 6 publications

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“…And we show that this modified weighted achievement metric (in cases when sets of all criterion vectors are finite or polyhedral) coincides with the metric introduced by both Kaliszewski [10,13] and Choo and Atkins [2]. Also, we study the stability of solutions to multiobjective nonlinear programming problems, using a modified weighted achievement metric and introduce an example to explain compute this stability of solutions.…”

Section: Introductionmentioning

confidence: 85%

Stability achievement scalarization function for multiobjective nonlinear programming problems

Kassem

2008

Applied Mathematical Modelling

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In this paper, we present a method to determine the stability of nondominated criterion vectors using a modified weighted achievement scalarization metric. This method is based on the application of a particular objective function which scalarizes and parameterizes the original multiobjective nonlinear programming problem. Also, we show that this modified weighted achievement metric coincides with the metric introduced by Choo and Atkins [E.-U. Choo, D.R. Atkins, Proper efficiency in nonconvex multicriteria programming, Math. Oper. Res. 8 (1983) 467-470] and Kaliszewski [I. Kaliszewski, A modified weighted Tchebycheff metric for multiple objective programming, Comput. Oper. Res. 14 (1987) 315-323] in cases when sets of all criterion vectors are finite or polyhedral.

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Section: Introductionmentioning

confidence: 85%

Stability achievement scalarization function for multiobjective nonlinear programming problems

Kassem

2008

Applied Mathematical Modelling

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“…Algorithms based on this finding have been proposed later by Eswaran, Ravindran, and Moskowitz (1989) and Kaliszewski (1987) among others. However, applying the theoretical findings computationally has remained a challenge.…”

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confidence: 87%

Algorithm robust for the bicriteria discrete optimization problem

Kouvelis

Sayın

2006

Ann Oper Res

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We apply Algorithm Robust to various problems in multiple objective discrete optimization. Algorithm Robust is a general procedure that is designed to solve bicriteria optimization problems. The algorithm performs a weight space search in which the weights are utilized in min-max type subproblems. In this paper, we experiment with Algorithm Robust on the bicriteria knapsack problem, the bicriteria assignment problem, and the bicriteria minimum cost network flow problem. We look at a heuristic variation that is based on controlling the weight space search and has an indirect control on the sample of efficient solutions generated. We then study another heuristic variation which generates samples of the efficient set with quality guarantees. We report results of computational experiments.

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“…These modifications were seen in the work of Steuer and Choo, (1983); Kaliszewski (1985); Romero et al (1998) using the augmented weighted Tchebycheff method and that of Kaliszewski, (1987) as shown in equation (12) and (13) respectively:…”

Section: Review Of Multi-criteria Optimization Methods -Theory and Apmentioning

confidence: 99%

Review of Multi-criteria Optimization Methods – Theory and Applications

Odu¹,

Charles-Owaba²

2013

IOSRJEN

112

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-A review of multi-criteria optimization concepts and methods is presented. The techniques provide solutions to the problems involving conflicting and multiple objectives. Several methods based on weighted averages, priority setting, outranking and their combinations are employed. The application and procedure in respect to material selection is presented. It is observed from the literature that no single approach is superior, rather, the selection of a specific method depends on the type of information that is provided in the problem, the designer"s preferences, the solution requirements and the availability of software adopted.

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A modified weighted tchebycheff metric for multiple objective programming

Cited by 59 publications

References 6 publications

Stability achievement scalarization function for multiobjective nonlinear programming problems

Stability achievement scalarization function for multiobjective nonlinear programming problems

Algorithm robust for the bicriteria discrete optimization problem

Review of Multi-criteria Optimization Methods – Theory and Applications

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