Stability achievement scalarization function for multiobjective nonlinear programming problems

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• 作者：Mohamed Abd El-Hady Kassem
• 关键词：Multiobjective nonlinear programming ; Achievement scalarization function ; nondominated solutions ; Stability
• 刊名：Applied Mathematical Modelling
• 出版年：2008
• 出版时间：June 2008
• 年：2008
• 卷：32
• 期：6
• 页码：1044-1055
• 全文大小：198 K

文摘

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.