Stability achievement scalarization function for multiobjective nonlinear programming problems

Abstract

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.

A modified approach for solving a fuzzy multi-objective programming problem

“…The problem (10) can be reformulated to take the following equivalent form (Kassem 2008). subject to…”

Compromise programming with Tchebycheff norm for discrete stochastic orders

“…The extension of the compromise programming model into the compromise hypersphere in the case of multi-criteria linear programming is presented by Gass and Roy (2003). Kassem (2008) studies the stability of solutions to multi-objective nonlinear programming problems, using a modified weighted achievement metric based on weighted Tchebycheff metric.…”