Title: Decisions, References and Achievements
Abstract. The concepts of references and measures are inherent to decision-making processes. This is so, first of all, because decision makers need to measure the impact of their decisions on the objectives to be taken into account. Secondly, because establishing reference or aspiration levels is a natural and intuitive way of providing preferential information. Furthermore, these two concepts are strongly linked to each other. Indeed, human beings do not understand measurement if it is not as a comparison with a certain reference unit. On the other hand, once the goals to be achieved have been established, the decision is made based on measuring the proximity of the possible solutions to these goals. For these reasons, achievement scalarizing functions play a vital role in a large part of the methods for solving multi-objective optimization problems. In this talk, a tour of the various existing achievement scalarizing functions is carried out and some of the author's contributions in this field are related.
In the field of Goal Programming, traditional achievement functions are reviewed, and the concept of Meta-Goal Programming is presented. Regarding the reference point methods, an additive achievement function is introduced, the effect of the different weight schemes (including the possibility of providing preferential weights) on the solutions obtained is studied, and the different effect that these weights may have, depending on whether the reference point is achievable or unachievable, is presented. Finally, achievement functions for problems with multiple reference points are introduced.
Keywords. Multiobjective Optimization; Goal Programming; Reference Points; Achievement Scalarizing Functions.
