A classification of the weighting schemes in reference point procedures for multiobjective programming

The reference point-based methods form one of the most widely used class of interactive procedures for multiobjective programming problems. The achievement scalarizing functions used to determine the solutions at each iteration usually include weights. In this paper, we have analysed nine weighting schemes from the preferential point of view, that is, examining their performance in terms of which reference values are given more importance and why. As a result, we have carried out a systematic classification of the schemes attending to their preferential meaning. This way, we distinguish pure normalizing schemes from others where the weights have a preferential interpretation. This preferential behaviour can be either designed (thus, predetermined) by the method, or decided by the decision maker. Besides, several figures have been used to illustrate the way each scheme works. This paper enables the potential users to choose the most appropriate scheme for each case.