Consequences of dropping nonessential objectives for the application of MCDM methods

In this article we consider the problem of nonessential objectives for multiobjective optimization problems (MOP) with linear objective functions. In 1977 an approach based on the reduction of size of the matrix of objective functions has been worked out by one of the present authors (Gal, T., Leberling, H., 1977. European Journal of Operations Research 1, 176–184). Although this method for dropping nonessential objectives leads to a mathematically equivalent MOP, problems concerning the application of MOP methods may arise. For instance, dropping some (or all) of the nonessential objectives the question is, how to ensure obtaining the same solution as with all objectives involved. We consider the problem of adapting the parameters of multiobjective optimization methods. For the case of weighting methods a simple procedure for adapting the weights is analyzed. For other methods, e.g. reference point approaches, such a simple possibility for adapting the parameters is not given.