Computational Approach to Essential and Nonessential Objective Functions in Linear Multicriteria Optimization

The question of obtaining well-defined criteria for multiple-criteria decision making problems is well known. One of the approaches dealing with this question is the concept of nonessential objective functions. A certain objective function is called nonessential if the set of efficient solutions is the same with or without that objective function. We present two methods for determining nonessential objective functions. A computational implementation is done using a computer algebra system. Portions of this paper were presented at the 23rd IFIP TC 7 International Conference on System Modelling and Optimization, Cracow, Poland, July 23–27, 2007. This work was supported by KBN under Bialystok Technical University Grant S/WI/1/08 and by the R&D unit CEOC of the University of Aveiro through FCT and FEDER/POCI 2010.